Week8/STA410_W24_Week8_Lecture_IRLS.ipynb

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    "<a name=\"cell-TOC-opt\"></a>\n",
    "\n",
    "### 8. [Optimizers: pragmatic implementations of Newton's Method](#cell-opt-fx-)\n",
    "\n",
    "1. [Gradient and Newton-Like Methods](#cell-opt-fx-newtonlike)\n",
    "2. [Quasi-Newton Methods](#cell-opt-fx-quasi-newton) \n",
    "3. [Modern Optimizers](#cell-opt-fx-modern-optimizers)\n",
    "4. [Newton's Method Review and Re-Examination: The Sandwich Estimator](#cell-opt-fx-sandwich)\n",
    "5. [Iteratively Reweighted Least Squares (IRLS): The Logistic Regression Example](#cell-opt-fx-irls) \n",
    "   (`STA410_W24_Week8_Homework_LogisticRegressionIRLS.ipynb`)\n",
    "5. [M Estimation (maximum likelihood type)](#cell-opt-fx-m-est)\n",
    "    1. [Robust Regression with Huber Loss](#cell-opt-fx-huber) \n",
    "       (`STA410_W24_Week8_Extra_HuberLossIRLS.ipynb`)\n",
    "4. [Quasi-Likelihoods](#cell-opt-fx-quasi)\n",
    "      \n",
    "\n",
    "<!--\n",
    "    1. ~Combinatorial (Discrete) Optimzation~\n",
    "      - ~Simulated Annealing~\n",
    "    2. ~Constrained optimization~\n",
    "      - ~Expectation-Maximization~\n",
    "      - ~Interior and Exterior Point Algorithms~\n",
    "-->"
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    "<a name=\"cell-opt-fx-1\"></a>\n",
    "\n",
    "## 8. Optimizers: pragmatic implementations of Newton's Method ([Return to TOC](#cell-TOC-opt)) \n",
    "---\n",
    "\n",
    "1. ***Newton's method*** is extremely effective when \n",
    "    1. it isn't overly computationally prohibitive and \n",
    "    2. the objective functions of interest are reasonably ***convex*** \n",
    "\n",
    "2. But many contexts, can benefit from approximation or simplification of ***Newton's method*** which either \n",
    "\n",
    "    1. reduce the computational cost or \n",
    "    2. extend the usefulness of Newton's method into the context of ***non-convex*** functions\n",
    "\n",
    "> Essentially all derivative-based optimization methods<br>can be viewed as some sort of practical and pragmatic variation on ***Newton's method***\n",
    "\n",
    "***Gradient*** and ***Newton-like methods*** substitute computationally simpler alternatives $M^{(t)}$ in place of the Hessian $H_{g(x^{(t)})}$ and use\n",
    "\n",
    "$$x^{(t+1)} = x^{(t)} - \\alpha[M^{(t)}]^{-1}\\nabla_x g(x^{(t)}) \\quad \\text{ instead of } \\quad x^{(t+1)} = x^{(t)} - \\alpha\\left[H_{(x^{(t)})}\\right]^{-1}\\nabla_x g(x^{(t)})$$\n",
    "\n",
    "- ALWAYS avoid inversion $[M^{(t)}]^{-1}$ and just solve for $d$ in $M^{(t)}_{p\\times p}d = \\nabla_x f(x)$, and for high dimensions with large $p$... \n",
    "- \"direction search\" computational cost can be reduced with ***truncated (\"doubly iterative\") methods*** that instead approximate $d = [M^{(t)})^{-1}]\\nabla_x f(x)$ with a few steps $s$ of $O(sn^2)$ ***iterative methods*** like ***Gauss-Seidel*** (or ***conjugate gradient descent***)"
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    "\n",
    "<table>\n",
    "<tr><td>\n",
    "\n",
    "Newton's Method Converging \"Quadratically\" Quickly\n",
    "<img src=\"https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/images/gradient_descent/gradientfigures.png\" style='width:615px'>\n",
    "<img src=\"https://www.cs.cornell.edu/courses/cs4780/2021fa/lectures/images_new/GD/Compare.jpg\" style='width:615px'>\n",
    "<img src=\"https://www.researchgate.net/publication/341040067/figure/fig1/AS:885861650546689@1588217284910/Behaviour-of-gradient-descent-and-Newtons-method-for-a-quadratic-function-Image.ppm\" style='width:615px'>\n",
    "    \n",
    "</td><td>\n",
    "    \n",
    "Gradient Descent Step Size Tuning with Momentum Speedups\n",
    "<img src=\"https://i.stack.imgur.com/VxQgz.png\" style='width:725px'>\n",
    "<img src=\"https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRDVEvK1_keJCST6km5ZM03WduqVVIwx6ifXmWAP1if8w-uQ1wdxoQ_OrSxWEHojZ9R68Q&usqp=CAU\" style='width:725px'>\n",
    "<img src=\"https://miro.medium.com/v2/resize:fit:618/1*FUAKhbj7lvKxq73EPl4rzg.png\" style='width:725px'>\n",
    "    \n",
    "</td><td>\n",
    "\n",
    "Quadratic Optimization Considerations\n",
    "<img src=\"https://qph.cf2.quoracdn.net/main-qimg-591ce5575f71110585d9246bf8c2ca0b-pjlq\" style='width:450px'>\n",
    "<img src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-1-4842-4470-8_16/MediaObjects/463852_1_En_16_Fig3_HTML.jpg\" style='width:450px'>\n",
    "<img src=\"https://doc.cfd.direct/notes/cfd-general-principles/img/index2353x.png\" style='width:450px'>\n",
    "<img src=\"https://i.stack.imgur.com/ac9O7.png\" style='width:450px'>\n",
    "\n",
    "</td></tr></table>"
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    "<a name=\"cell-opt-fx-newtonlike\"></a>\n",
    "\n",
    "## 8.1 Gradient and Newton-Like Methods ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "> The ***step size*** $\\alpha$ parameter somewhat partially addresses the ***line search problem*** and ***monotonic ascent/descent***, but see `STA410_W24_Week8_Extra_Details.ipynb` for further notes\n",
    "\n",
    "While the approximation $M^{(t)} \\approx H_{g(x)}(x^{(t)})$ may attempt to be accurate, often the motivation is simply computational feasibility \n",
    "\n",
    "- $\\alpha H_{g(x^{(t)})}^{-1} \\approx \\alpha I \\quad\\quad\\;\\,: \\quad\\theta^{(t)} - \\alpha \\sum_{i=1}^n \\nabla_\\theta f_{x_i}(\\theta^{(t)}) \\quad\\quad\\quad\\quad \\nabla_\\theta f_{\\mathbf x}(\\theta^{(t)}) = \\sum_{i=1}^n \\nabla_\\theta f_{x_i}(\\theta^{(t)})$\n",
    "\n",
    "- $\\alpha H_{l(\\theta^{(t)})}^{-1} \\approx \\alpha {\\mathcal I(\\theta^{(t)})}{}^{-1}: \\quad \\theta^{(t)} + \\alpha {\\mathcal I(\\theta^{(t)})}{}^{-1} \\sum_{i=1}^n \\nabla_\\theta l_i(\\theta)|_{\\theta^{(t)}}\\quad\\, \\nabla_\\theta l(\\theta)|_{\\theta^{(t)}} = \\sum_{i=1}^n \\nabla_\\theta l_i(\\theta)|_{\\theta^{(t)}}$\n",
    "$\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\, \\color{gray}{\\theta^{(t)} + \\alpha \\left(\\sum_{i=1}^n\\nabla_\\theta l_i(\\theta)|_{\\theta^{(t)}}(\\nabla_\\theta l_i(\\theta)|_{\\theta^{(t)}})^T\\right)^{-1} \\sum_{i=1}^n \\nabla_\\theta l_i(\\theta)|_{\\theta^{(t)}}}$\n",
    "\n",
    "- $\\alpha H_{l(\\theta^{(t)})}^{-1} \\approx \\cdots \\quad\\quad\\;\\;\\; : \\quad \\theta^{(t)} + \\alpha \\left((J g_x(\\theta^{(t)})^TJ g_x(\\theta^{(t)}\\right) ^{-1} \\sum_{i=1}^n \\nabla_\\theta f_{x_i}(\\theta^{(t)}) ({y^{(t)}_i - f_{x_i}(\\theta^{(t)})})$\n",
    "\n",
    "- $\\alpha H_{l(\\theta^{(t)})}^{-1} \\approx \\alpha[M^{(t)}]^{-1}: \\quad x^{(t)} - \\alpha[M^{(t)}]^{-1}\\nabla_x g(x^{(t)}) \\quad \\text{is called a }\\textbf{quasi-Newton's method }\\text{when}$\n",
    "\n",
    "$M^{(t)}$ satisfies the so-called ***secant condition*** (a discrete approximation of second order derivatives <u>which is not quite the ***Hessian***...</u>)\n",
    "$$ \\overbrace{\\nabla_{x}g(x^{(t)}) - \\nabla_{x}g(x^{(t-1)})}^{\\Delta^{(t)}_{\\nabla_{x}g}} = M^{(t)}\\overbrace{(x^{(t)} - x^{(t-1)})}^{\\Delta_x^{(t)}}$$\n",
    "\n",
    "The ***secant method*** is a discrete approximation of ***univariate Newton's method*** which has slower convergence but faster computation that sometimes improves overall performance: <u>***Quasi-Newton's method's*** is the multivariate generalization</u>\n"
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    "<a name=\"cell-opt-fx-quasi-newton\"></a>\n",
    "\n",
    "## 8.2 Quasi-Newton Methods ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "$M^{(t)} \\approx H_{g(x^{(t)})}$ need not necessarily be a good esimtate of the ***(negative) observed Fisher information***; and, the ***secant condition*** alone does not provide an efficient \n",
    "calculation of $M^{(t)}$ but the (computationally inexpensive) ***rank-one update*** (derived [here](https://personal.math.ubc.ca/~loew/m604/web-ho/sr1.pdf))\n",
    "\n",
    "$$M^{(t)} = M^{(t-1)} + \\underbrace{\\frac{v^{(t)}[v^{(t)}]^T}{[v^{(t)}]^T\\Delta_x^{(t)}c}}_{\\text{rank-one update}} \\quad \\text{ where } \\quad v^{(t)} = \\left(\\Delta^{(t)}_{\\nabla_{x}g} - M^{(t-1)}\\Delta_x^{(t)}\\right)$$\n",
    "\n",
    "results in $M^{(t)}$ which satisfies the ***secant condition***, subject to some caveats\n",
    "\n",
    "A ***rank-two version*** of the above which both satisfies the ***secant condition*** and confers ***hereditary definiteness*** is the so-called ***BFGS*** update (named after its authors). The (*rank-two*) ***BFGS*** update is just the (*rank-two*) ***Broyden class update*** \n",
    "\n",
    "$$\\begin{align*} M^{(t)} = {} & M^{(t-1)} - \\frac{M^{(t-1)}\\Delta_x^{(t)} [M^{(t-1)}\\Delta_x^{(t)}]^T}{[\\Delta_x^{(t)}]^TM^{(t-1)}\\Delta_x^{(t)}} + \\frac{\\Delta^{(t)}_{\\nabla_{x}g}[\\Delta^{(t)}_{\\nabla_{x}g}]^T}{[\\Delta_x^{(t)}]^T\\Delta^{(t)}_{\\nabla_{x}g}} + \\delta^{(t)}\\left([\\Delta_x^{(t)}]^TM^{(t-1)}\\Delta_x^{(t)} \\right)[d^{(t)}]^Td^{(t)}\\\\\n",
    "{} & \\text{where } d^{(t)} = \\frac{\\Delta^{(t)}_{\\nabla_{x}g}}{[\\Delta_x^{(t)}]^T\\Delta^{(t)}_{\\nabla_{x}g}} - \\frac{M^{(t-1)}\\Delta_x^{(t)}}{[\\Delta_x^{(t)}]^TM^{(t-1)}\\Delta_x^{(t)}}\n",
    "\\end{align*}$$\n",
    "\n",
    "with $\\delta^{(t)}=0$, and again subject to some caveats\n",
    "\n",
    "> See `STA410_W24_Week8_Extra_Details.ipynb` for further notes\n"
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    "<a name=\"cell-opt-fx-modern-optimizers\"></a>\n",
    "\n",
    "## 8.3 Modern Optimizers ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "***High-dimensional non-convex*** optimization is increasingly predominant (e.g., in ***deep learning***)\n",
    "- in which case ***curvature*** information ***Hessians*** only speeds convergence towards ***local optima***\n",
    "- (while requireing $O(p^2)$ computation <u>[for a single data point]</u> and subsequent $O(p^3)$ or $O(sp^2)$ \"direction solving\")\n",
    "\n",
    "The main challenge is to make sufficient progress to avoid initial ***local optima*** \"traps\" early in the optimization process; whereas, \"optimal performance\" is typically equivalently reached before ***gradient norms*** vanish across different \"sufficient\" ***local optima*** \n",
    "\n",
    "- ***Stochastic gradient descent (SGD)*** uses small ***batches*** (often $n\\neq m=32$) and multiple passes (***epochs***) through a data set $$E_x\\left[ \\nabla_\\theta g_x(\\theta_{t-1}) \\right] \\approx \\frac{1}{m} \\sum_{i=1}^m \\nabla_\\theta g_{x_i}(\\theta_{t-1}) \\color{gray}{= \\nabla_\\theta \\frac{1}{m} \\sum_{i=1}^m g_{x_i}(\\theta_{t-1})} \\quad \\longrightarrow \\quad \\theta_{t} = \\theta_{t-1} + \\alpha \\nabla_\\theta g_{x_{m=32}}(\\theta_{t-1})$$\n",
    "\n",
    "    - For $m<<n$ there is huge computational savings... and \"steps $\\times$ samples $\\times$ parameters in ***SGD*** is $O(smp)$<br><u>which will likely actually even even outperform ***Newton's Method*** on a per computational cost basis...</u>\n",
    "    - ***SGD*** also tends to empirically outpeform full sample ***GD*** because the stochastic gradients travel \"more loosely\" and cannot overfit as much as in the end since their final update is never an \"optimum\" due to its stochasticity\n",
    "        "
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    "<a name=\"cell-opt-fx-modern-optimizers-1\"></a>\n",
    "\n",
    "## 8.3 Modern Optimizers \n",
    "\n",
    "---\n",
    "\n",
    "- <font style='color:gray'>***Neterov***</font> ***Momentum*** uses a \"gradient running average\" $\\displaystyle v_t = \\epsilon_t v_{t-1} + \\alpha_t \\nabla_\\theta \\frac{1}{m} \\sum_{i=1}^m g_{x_i}(\\theta_{t-1} \\color{gray}{+ \\epsilon_{t} v_{t-1}})$ \n",
    "\n",
    "    - with ***learning rate*** $\\alpha_t$ and ***historic decay*** weighting schedules $\\epsilon_t$ finally specifying $\\theta_t = \\theta_{t-1} - v_t$  \n",
    "    - which, instead of using the ***Hessian*** to understand function shape,<br>\"predicts\" function shape under the assumption that previous ***gradients*** are good estimates of future ***gradients***  \n",
    "\n",
    "- ***Adagrad*** adds coordinate-specific learning inverse to accumulated progress along each axis so far \n",
    "  $$\\begin{align*}\n",
    "  g_t = {} & \\nabla_\\theta \\frac{1}{m} \\sum_{i=1}^m g_{x_i}(\\theta_{t-1}) \\;\\;\\quad\\quad r_t = r_{t-1} + g_t \\odot g_t \\quad \\text{  element-wise product}\\\\\n",
    "  \\theta_t = {} & \\theta_{t-1} - \\frac{\\alpha_t}{\\delta_t+\\sqrt{r_t}} \\odot g_t \\quad \\text{  element-wise square root, division, and product}\n",
    "  \\end{align*}$$\n",
    "  \n",
    "    - ideally making step sizes smaller along fast-moving axes and larger along slow-moving axes\n",
    "\n",
    "- ***RMSprop*** improves the accumulation in ***Adagrad*** with a decaying running average and incorporates ***momentum*** \n",
    "  $$\\begin{align*}\n",
    "  r_t = \\rho r_{t-1} + (1-\\rho) g_t \\odot g_t \\quad\\quad v_t = {} & \\epsilon_t v_{t-1} + \\frac{\\alpha_t}{\\delta_t+\\sqrt{r_t}} \\odot g_t \\quad\\quad \n",
    "  \\theta_t = \\theta_{t-1} - v_t\n",
    "  \\end{align*}$$\n",
    "\n",
    "    - allowing for locally variying coordinate-specific learning rates while maintaining fast-moving axes\n"
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    "<a name=\"cell-opt-fx-modern-optimizers-2\"></a>\n",
    "\n",
    "## 8.3 Modern Optimizers \n",
    "\n",
    "---\n",
    "\n",
    "- ***Adam*** is a slight (typically equivalently performing) variant of ***RMSprop*** that alternatively implements ***momentum*** as a decaying running average\n",
    "\n",
    "  $$\\begin{align*}\n",
    "  v_t = {} & \\rho_v v_{t-1} + (1-\\rho_v) g_t \\quad\\quad\\quad \\times \\frac{1}{1-\\rho_v^t} \\text{ to correct if } v_0 = 0  \\\\\n",
    "  r_t = {} & \\rho_s r_{t-1} + (1-\\rho_s) g_t \\odot g_t \\quad \\;\\, \\times  \\frac{1}{1-\\rho_s^t} \\text{ to correct if } r_0=0 \\\\\n",
    "  g_t = {} & \\nabla_\\theta \\frac{1}{m} \\sum_{i=1}^m g_{x_i}(\\theta_{t-1}) \\quad \\quad \\quad \\;\\;\\;   \n",
    "  \\theta_t = \\theta_{t-1} - \\frac{\\alpha_t}{\\delta_t+\\sqrt{r_t}} \\odot v_t\n",
    "  \\end{align*}$$\n",
    "  \n",
    "The methods beyond ***SGD*** rescale the ***gradient*** in the same manner as a ***diagonal approximation*** $H_{g(\\theta)}^{-1} \\approx I \\circ H_{g(\\theta)}^{-1} = D_\\gamma^{-1}$ which ignores the off-diagonal elements of the ***Hessian***, and could be directly approximated using the second order partial derivatives as\n",
    "\n",
    "  $$[D_{\\gamma}]_{ii} = \\frac{\\partial^2 g (\\theta)}{\\partial\\theta_i\\partial\\theta_i} \\approx \\gamma_i \\quad \\text{ and } \\quad [D_{\\gamma}]_{ij} = \\frac{\\partial^2 g( \\theta)}{\\partial\\theta_i\\partial\\theta_j} \\approx 0$$ \n",
    "\n",
    "  and subsequently approximate ***Newton's method*** as $\\theta^{(t+1)} = \\theta^{(t)} - \\alpha D_\\gamma^{-1} \\nabla_\\theta g(\\theta^{(t)})$ perhaps incorporating ***momentum*** forms\n",
    "\n",
    "> Emtiyaz Khan characterizes these common algorithms as varying degrees of approximation to \"Bayesian Learning Rules\" in this [presentation](https://slideslive.com/38923183/deep-learning-with-bayesian-principles), starting around slide 60.\n",
    "\n",
    "\n"
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    "<a name=\"cell-opt-fx-modern-optimizers-3\"></a>\n",
    "\n",
    "## 8.3 Modern Optimizers \n",
    "\n",
    "---\n",
    "\n",
    "| ![](https://miro.medium.com/v2/resize:fit:1400/1*m7-otgfbxiAvSipInHliXw.gif) |\n",
    "|-|\n",
    "| |"
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    "<a name=\"cell-opt-fx-sandwich\"></a>\n",
    "## 8.4 Newton's Method Review and Re-Examination:<br>The Sandwich Estimator ([Return to TOC](#cell-TOC-opt)) \n",
    "---\n",
    "\n",
    "***Log likelihood***  $g(\\theta) = \\log f(x|\\theta) = \\sum_{i=1}^n \\log f(x_i|\\theta) = \\sum_{i=1}^n g_i(\\theta)\\;$ maximization by ***Newton's Method*** is\n",
    "\n",
    "\\begin{align*}\n",
    "\\theta^{(t+1)} & = {} \\theta^{(t)} - \\frac{g'(\\theta^{(t)})}{g''(\\theta^{(t)})} = \\theta^{(t)} -  \\frac{ \\sum_{i=1}^n  g_i'(\\theta^{(t)})}{ \\sum_{i=1}^n  g_i''(\\theta^{(t)})} \\\\ \n",
    "& = {} \\sum_{i=1}^n \\frac{g_i''(\\theta^{(t)})}{\\sum_{j=1}^n g_j''(\\theta^{(t)})} \\left( \\theta^{(t)} - \\frac{g_i'(\\theta^{(t)})}{g_i''(\\theta^{(t)})} \\right) = \\sum_{i=1}^n w_j\\left( \\theta^{(t)} - \\frac{g_i'(\\theta^{(t)})}{g_i''(\\theta^{(t)})} \\right) \n",
    "\\end{align*}\n",
    "\n",
    "which is a weighted average; so, at convergence the variance of the ***pseudo sample*** $\\left\\{\\theta^{*} - \\frac{g_i'(\\theta^{*})}{g_i''(\\theta^{*})}: i=1,\\cdots,n \\right\\}$$\\require{cancel}$ is \n",
    "\n",
    "\\begin{align*}\n",
    "\\hat \\sigma^2 & = {} \\sum_{i=1}^n \\frac{g_i''(\\theta^{*})^2}{\\left(\\sum_{j=1}^n g_j''(\\theta^{*})\\right)^2 } \\left(\\theta^{*} - \\frac{g_i'(\\theta^{*})}{g_i''(\\theta^{*})}  - \\cancel{\\text{E}\\left[\\theta^{*} - \\frac{g_i'(\\theta^{*})}{g_i''(\\theta^{*})}\\right]}^{\\theta^{*}}\\right)^2\\\\\n",
    "& = {}  \\sum_{i=1}^n \\frac{g_i''(\\theta^{*})^2}{\\left(\\sum_{j=1}^n g_j''(\\theta^{*})\\right)^2 } \\left(\\frac{g_i'(\\theta^{*})}{g_i''(\\theta^{*})}\\right)^2 = \\frac{ \\sum_{i=1}^n g_i'(\\theta^{*})^2}{\\left(\\sum_{j=1}^n g_j''(\\theta^*)\\right)^2 }\n",
    "\\end{align*}\n",
    "\n",
    "which is the so-called ***sandwich estimate*** of the variance of the estimate $\\theta^*$\n",
    "\n",
    "<!-- *Uncertainty estimation can be facilitated by ***Newton's method***.* -->\n",
    "\n"
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    "<a name=\"cell-opt-fx-irls\"></a>\n",
    "## 8.5 Iteratively Reweighted Least Squares (IRLS):<br>The Logistic Regression Example ([Return to TOC](#cell-TOC-opt)) \n",
    "---\n",
    "\n",
    "In ***exponential family*** form the ***log likelihood*** of the ***logistic regression*** (***generalized linear model***) is\n",
    "<br><br>\n",
    "\n",
    "$$\\large l(\\beta) = \\overbrace{y \\underbrace{Z\\beta}_{\\theta} - \\mathbf{1}^T \\underbrace{\\log \\left(1 + \\exp(Z\\beta) \\right)}_{g(\\theta=Z\\beta)}}^{\\log f(y|\\theta) \\;= \\;[y^T\\theta - b(\\theta)]/a(\\phi)+c(y,\\phi)}$$\n",
    "\n",
    "where $\\Pr(y_i=1) = \\underset{\\text{a property of the exponential family}}{E[y_i] = \\frac{d}{d\\theta_i} \\overbrace{\\log \\left(1 + \\exp(\\theta_i) \\right)}^{g(\\theta_i)\\;=\\;g(z_i^T\\beta)}} = \\frac{\\exp(\\theta_i)}{1 + \\exp(\\theta_i)} = \\frac{1}{1 + \\exp(-\\theta_i)}$\n",
    "\n",
    "so the ***natural parameter*** $\\theta_i =  z_i^T\\beta = \\log\\left(\\frac{\\Pr(y_i=1)}{1-\\Pr(y_i=1)} \\right) = \\log \\left( \\frac{\\frac{\\exp(\\theta_i)}{1 + \\exp(\\theta_i)}}{\\frac{1}{1 + \\exp(\\theta_i)}} \\right) = \\log(\\exp(\\theta_i)) = \\theta_i$ is the ***log odds*** \n"
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    "## 8.5 Iteratively Reweighted Least Squares (IRLS):<br>The Logistic Regression Example\n",
    "\n",
    "The ***gradient*** and ***Information*** and ***Hessian*** of the ***log likelihood*** of ***logistic regression*** are  \n",
    "\n",
    "$$\n",
    "  \\begin{align*}\n",
    "  \\nabla_\\beta l(\\beta)  & = {}Z^Ty - Z^T\\frac{\\exp(Z\\beta)}{1+\\exp(Z\\beta)} = Z^Ty - Z^T\\frac{1}{1+\\exp(-Z\\beta)} = Z^T(y-E[y]) \\\\\n",
    "  & = {} Z^Ty - Z^T(1+\\exp(-Z\\beta))^{-1} \\\\\n",
    "  I(\\beta) & = {} E\\left[ Z^T (Y-E[Y])(Y-E[Y])^T Z\\right] \n",
    "   = Z^T Cov\\left(Y\\right)Z{} = Z^T\\overbrace{\\text{diag}(E[Y_i](1-E[Y_i]))}^{\\text{diag}(p_i(1-p_i)) \\text{ for i.i.d. Bernoulli}}Z \\\\\n",
    "  & = - E[H_{l(\\beta)}] = -H_{l(\\beta)}  \\\\\\\\\n",
    "  H_{l(\\beta)} & = {} \\nabla_\\beta(\\nabla_\\beta l(\\beta))^T = \\nabla_\\beta (-[E[Y_1],E[Y_2],\\cdots, E[Y_n]])Z = -[z_1W_{11},z_2W_{22}, \\cdots, z_nW_{nn}] Z\\\\\n",
    "  & = {} -Z^TWZ \\quad \\text{ where } \\quad W_{ij}=0 \\text{ for } i\\not=j \\\\\n",
    "  & \\quad\\quad\\quad\\quad\\quad\\quad\\quad\\, \\text{ and } \\quad W_{ii} = \\frac{\\exp(-z_i^T\\beta)}{\\left(1+\\exp(-z_i^T\\beta)\\right)^2} = \\frac{1}{1+\\exp(-z_i^T\\beta)}\\frac{\\exp(-z_i^T\\beta)}{1+\\exp(-z_i^T\\beta)} \\\\\n",
    "  &  \\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\, = E[Y_i](1-E[Y_i])\n",
    "  \\end{align*}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 8.5 Iteratively Reweighted Least Squares (IRLS):<br>The Logistic Regression Example\n",
    "\n",
    "\n",
    "$$\\text{Thus, }\\textbf{Newton's method }\\text{is }\\quad \\beta^{(t+1)} = \\beta^{(t)} - \\underbrace{\\overbrace{( -Z^T \\overset{(t)}{W}Z )^{-1}}^{H_{l(\\beta^{(t)})}^{-1}} \\overbrace{Z^T(y-\\overset{(t)}{E[y]})}^{\\nabla_\\beta l(\\beta^{(t)})}}_{\\text{$E[y]$ (and hence $W$) depends on $\\beta^{(t)}$}}\\quad\\quad\\;\\;\\,$$\n",
    "$$\\text{which is identical to }\\textbf{Fisher scoring }\\quad \\beta^{(t+1)} = \\beta^{(t)} + \\underbrace{\\!{\\mathcal I(\\beta^{(t)})\\!}}_{-H_{l(\\beta^{(t)})}}{}^{-1} Z^T(y-\\overset{(t)}{E[y]}) \\quad \\text{ and rearranges as} $$\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\beta^{(t+1)} = {} & \\beta^{(t)} + \\mathcal I(\\beta)^{-1} Z^T(y-\\overset{(t)}{E[y]})\\quad  \\quad\\quad\\quad\\quad\\quad\\quad\\quad\\quad\\;\\; \\dagger \\longrightarrow \\tilde y^{(t)} = Z\\beta^{(t)}+ \\overset{(t)}{W}{}^{-1}(y- \\overset{(t)}{E[y]}) \\\\\n",
    " = {} & \\mathcal I(\\beta)^{-1} \\left(\\mathcal I(\\beta) \\beta^{(t)} + Z^T\\underbrace{\\overset{(t)}{W}\\overset{(t)}{W}{}^{-1}}(y-\\overset{(t)}{E[y]})\\right) = I(\\beta)^{-1} \\left( \\underbrace{Z^T \\overset{(t)}{W}Z}_{\\mathcal I(\\beta)} \\beta^{(t)} + Z^T\\overset{(t)}{W} \\underbrace{(\\tilde y^{(t)}-Z\\beta^{(t)})}_{\\dagger}\\right)\\\\\n",
    " = {} & \\underbrace{\\left(Z^T \\overset{(t)}{W}Z\\right)^{-1} \\!\\! Z^T\\overset{(t)}{W} \\tilde y^{(t)}}_{\\text{which is weighted least squares}}\n",
    "\\end{align*}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 8.5 Iteratively Reweighted Least Squares (IRLS):<br>The Logistic Regression Example\n",
    "\n",
    "The previous updates specify a ***weighted least squares*** problem; so,<br> re-expressed ***Newton's method*** fits ***logistic regression*** through an ***iteratively reweighted least squares*** process\n",
    "\n",
    "| | |\n",
    "|-|-|\n",
    "|0. initializing $\\beta^{(0)}$ which implies $W^{(0)}$ and $E[y]^{(0)}$|and then repeatedly iteratively updating between|\n",
    "|1. updating $y^{(t)}$ with $\\dagger$ based on $W^{(t)}$ and $E[y]^{(t)}$|2. $\\beta^{(t+1)}$ with the solution to a ***weighted least squares*** problem|\n",
    "\n",
    "You will implement ***Logistic Regression IRLS*** in `STA410_W24_Week8_Homework_LogisticRegressionIRLS.ipynb`\n",
    "\n",
    "<u>This is also equivalent to a ***Gauss-Newton*** formulation</u> <font style='color:gray'>linear approximation of ***nonlinear*** (in $\\beta$) $\\frac{1}{1+\\exp(-Z_i\\beta)}$</font>\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    " {}& \\max_\\beta || y - E_{\\beta^{(t)}}[y] - \\nabla_\\beta E_{\\beta^{(t)}}[y] (\\beta - \\beta^{(t)}) ||_2^2\n",
    " & \\nabla_\\beta E_{\\beta^{(t)}}[y_i] (\\beta - \\beta^{(t)}) ={}& z_i\\frac{1}{1+\\exp(-z_i^T\\beta)} \\frac{\\exp(-z_i^T\\beta)}{1+\\exp(-z_i^T\\beta)} (\\beta - \\beta^{(t)})  \\\\\n",
    "= {} & \\max_\\beta || y - E_{\\beta^{(t)}}[y] - \\overset{(t)}{W} Z(\\beta - \\beta^{(t)}) ||_2^2 & \\nabla_\\beta E_{\\beta^{(t)}}[y](\\beta - \\beta^{(t)})  = {}& \\overset{(t)}{W} Z(\\beta - \\beta^{(t)}) \\quad \\color{gray}{\\text{$W_{ii}$ diagonal of $W$ above}} \n",
    "\\end{align*}$$\n",
    "$$\n",
    "\\begin{align*}\n",
    "= {}& \\max_\\beta (y - E_{\\beta^{(t)}}[y]+  \\overset{(t)}{W} Z \\beta^{(t)} - \\overset{(t)}{W} Z\\beta )^T\\overset{(t)}{W^{-1}}(y - E_{\\beta^{(t)}}[y]+  \\overset{(t)}{W} Z \\beta^{(t)} - \\overset{(t)}{W} Z\\beta)) \\; \\color{gray}{\\min_x||b-Ax||_2^2 = \\min_x||b-Ax||_2^A}\\\\\n",
    "\\Rightarrow {}& \\nabla_\\beta \\Bigg[{\\tilde y^{(t)}}^T{\\tilde y^{(t)}}  -2 \\Big(\\underset{\\tilde y^{(t)}}{\\underline{Z \\beta^{(t)} + \\overset{(t)}{W}{}^{-1}(y - E_{\\beta^{(t)}}[y])}} \\Big)^T \\overset{(t)}{W} Z \\beta  + \\beta ^TZ^T \\overset{(t)}{W} Z\\beta  \\Bigg] = 0 = - Z^T\\overset{(t)}{W}{\\tilde y^{(t)}} + Z^T \\overset{(t)}{W} Z \\beta \\quad\\quad\\quad\\quad\\quad\\;\\;\\; \\\\\n",
    "\\Rightarrow {}& \\beta^{(t+1)} = \n",
    "(Z^T \\overset{(t)}{W} Z)^{-1} Z^T\\overset{(t)}{W}{\\tilde y^{(t)}} \n",
    "\\end{align*}$$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<!-- https://stats.stackexchange.com/questions/344309/why-using-newtons-method-for-logistic-regression-optimization-is-called-iterati -->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZkVEy2kpQ_AH",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-m-est\"></a>\n",
    "## 8.6 M (maximum likelihood type) Estimation ([Return to TOC](#cell-TOC-opt)) \n",
    "---\n",
    "\n",
    "***M (maximum likelihood type) estimators*** optimize alternative non-$L_2$ loss functions beyond $||\\cdot||_2^2$ \n",
    "\n",
    "$$\\min_\\beta \\sum_{i=1}^n \\rho(y_i-x_i^T \\beta) \\quad \\text{ where $\\rho(0)=0$ and $\\rho(t)$ increases with $|t|$ and $\\psi = \\rho' \\neq 0$ and $\\psi' = \\rho'' \\neq 0$}$$\n",
    "\n",
    "$$\\text{So } \\quad \\nabla_\\beta \\sum_{i=1}^n \\rho(y_i-x_i^T \\beta) = \\sum_{i=1}^n -\\psi(y_i-x_i^T \\beta)x_i = -X^T\\psi(y-X\\beta) \\quad \\text{ and then subsequently}$$\n",
    "$$\\text{the Hessian is } \\quad \\sum_{i=1}^n \\psi'(y_i-x_i^T \\beta)x_ix_i^T = X^TWX \\quad \\text{ for diagonal matrix $W_{ii} = \\psi'(y-X\\beta)_i$}$$\n",
    "\n",
    "and once again ***Newton's method*** can be re-expressed as a sequence of ***iteratively reweighted least squares*** problems\n",
    "\n",
    "\\begin{align*}\n",
    "\\beta^{(t+1)} & = {} \\beta^{(t)} + (X^TWX)^{-1} X^T\\psi(y-X\\beta^{(t)})\\\\\n",
    "& = {} (X^TWX)^{-1} X^TW \\overset{\\text{weighted least squares outcome variable}}{\\overbrace{\\left[X\\beta^{(t)}  +  W^{-1}\\psi(y-X\\beta^{(t)}) \\right]}}\n",
    "\\end{align*}\n",
    "\n",
    "so $\\beta^{(t+1)}$ solves ***weighted least squares*** for outcome $\\left[X\\beta^{(t)} +  W^{-1}\\psi(y-X\\beta^{(t)})\\right]$ with weights $W_{ii}$ and design matrix $X$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bwdYFa3o5dG-",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-huber\"></a>\n",
    "\n",
    "## 8.6.A Robust Regression with Huber Loss ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "$$\\text{If }\\quad \\rho_c(t) = \\left\\{\\begin{array}{ll}t^2/2&|t|\\leq c\\\\ c|t| + c^2/2 & |t|>c\\end{array}\\right. \\quad \\text{ then } \\quad \\psi_c(t) = \\left\\{\\begin{array}{ll}c&t>c\\\\t & |t| \\leq c\\\\-c&t<-c\\end{array}\\right. \\quad \\text{ and } \\quad \\psi'_c(t) = \\left\\{\\begin{array}{ll}0&t>c\\\\1 & |t| \\leq c\\\\0&t<-c\\end{array}\\right.$$\n",
    "\n",
    "then $W_{ii} = \\psi'(y-X\\beta)_i = 0$ whenever $|y_i - x_i^T\\beta|>c$ and $W_{ii} = 1$ whenever $|y_i - x_i^T\\beta| \\leq c$ so\n",
    "\n",
    "\\begin{align*}\n",
    "\\beta^{(t+1)} & = {} (X^TWX)^{-1} X^TW \\left[X\\beta^{(t)} +  W^{-1}\\psi_c(y-X\\beta^{(t)}) \\right]\\\\\n",
    "& = {} ({X_c^TX_c})^{-1} X_c^T y_c\n",
    "\\end{align*}\n",
    "\n",
    "where $X_c$ and $y_c$ only includes data $x_i$ and $y_i$ satisfying $\\quad|y_i-x_i^t\\beta^{(t)}| \\leq c\\quad$ <!--or $\\quad\\psi_c'(y_i-x_i^t\\beta^{(t)})=1$-->\n",
    "\n",
    "- ***Linear Regression*** using ***Huber loss*** as opposed to ***least squares (squared loss)*** will be implemented in `STA410_W24_Week8_Extra_HuberLossIRLS.ipynb`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EaKlX9e_RyIX",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 8.6.A Robust Regression with Huber Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "nndM1Rkp6U3a",
    "outputId": "b8e16183-163f-4819-8673-4037f5b30119"
   },
   "outputs": [
    {
     "data": {
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zos2nKs0i2yJbJ9P+nTDnN+EVx8LdYVa35cFXHK+H9DpRppMkSZIkSTr5dq6CGQ/Bu09DWVGYNe0KQ8fAGV+F5JRo86lasMi2yFZFKNoL8yfBzEdgz6Ywy2wA/W+FAbdCrYaRxpMkSZIkSfrctiwJZ4gtfgESZWHWuj8MGwOdLoCkpGjzqVqxyLbIVkUqLYL3ng37aO9cGWaptcPq7MF3QL2WUaaTJEmSJEk6cWtnw7T74YPXDs1yzg0FdtshEItFl03VlkW2RbZOhXgZLP1r+Ca/eVGYJaVCr6tgyGholBNpPEmSJEmSpGNKJCDvTZh6P6yZfnAYg65fgaF3QcteUaZTDWCRbZGtUymRgBVvhkL7o2/6saSD3/THQIse0eaTJEmSJEk6XPnivAdg88IwS0qFnleGxXmNO0YaTzXHiXS5Fbqpzb333ku/fv2oW7cuTZs25dJLL2X58uWf+nF//vOfOf3008nIyKB79+68+uqrFRlT+nxiMeh0HtzwKtz4z7BfVCIOS16Ex4bBU5fDmhlRp5QkSZIkSTVdaTG88yQ80g/+ckMosVNrwcDb4bvvwVcescRWpVWhRfbkyZO5/fbbmTVrFq+//jolJSWcf/757Nu37xM/ZsaMGVx11VXcdNNNvPvuu1x66aVceumlLF68uCKjSidHm4Fw9XNw23To9rWwMnvFGzDxQvjtBfDBP8MKbkmSJEmSpFOlaC/MfBQe7Al/+w7szIOM+jD8h3DXEvjizyGrVdQppWM6pVuLbNu2jaZNmzJ58mTOOuuso97niiuuYN++fbz88svls4EDB9KrVy8mTJjwqV/DrUVUqexcCdMfggVPQ1lxmDXrFvaZ6nopJKdEGk+SJEmSJFVj+3fCnN/A7AlwYFeY1W0Bg+6APtdDep1I40kn0uWe0hYtPz8fgIYNG37ifWbOnMmYMWOOmF1wwQW89NJLR71/UVERRUVF5e8XFBR8/qDSydKwA1wyFkb8MLzyOe93sGUxPH8TvPUzGPJd6PlNSM2IOqkkSZIkSaouCjYe7CEmQsnBnREadjjYQ1wFKenR5pM+gwrdWuRw8Xic0aNHM2TIELp16/aJ99u8eTPNmjU7YtasWTM2b9581Pvfe++9ZGVllb9lZ2ef1NzSSVG3OZz/M7hrMZz9P5DZEHathpfvCpf1TH8IivZEnVKSJEmSJFVlO/Lgb3eGrmHmI6HEbtYdvvY7uGNeWIVtia0q6pQV2bfffjuLFy/m2WefPamf9+677yY/P7/8bd26dSf180snVWYDGP4fodD+4i+gXivYuxlevwce6AZv/S/s2xF1SkmSJEmSVJVsWgh/vgEe6Qvv/D5sb9pmMFz9F7htKnS7HJKSo04pfS6nZGuRO+64g5dffpkpU6bQunXrY963efPmbNmy5YjZli1baN68+VHvn56eTnq6rySpikmrDQNHQt+bYNFzMG0s7PgQpvwyvGJ65nUw+A7IOva/F0mSJEmSVIOtmQnT7ocP/3Vo1ul8GDoG2g6KLpdUASr0sMdEIsF3vvMdXnzxRXJzc+nUqdOnfswVV1zB/v37+fvf/14+Gzx4MD169PCwR1Vf8TJ4/2WYej9sWhBmSanQ4woYOhoaf/q/HUmSJEmSVAMkEvDh66HAXjszzGJJcMZXYehd0Lx7tPmkE3AiXW6FFtmjRo3imWee4a9//SudO3cun2dlZZGZmQnAtddeS6tWrbj33nsBmDFjBsOHD+cXv/gFF198Mc8++yw///nPeeedd465t/ZHLLJVpSUSsPLtUGivnnpwGIMul8CwMdCyd6TxJEmSJElSROJlsOTFcFX3lkVhlpwGvb4Jg++ERjmRxpM+i0pTZMdisaPOJ06cyPXXXw/AiBEjaNeuHZMmTSq//c9//jP/8z//w+rVq+nUqRO//OUvueiii47ra1pkq9pYNze8urr81UOznHPC5UHthsIn/PuSJEmSJEnVSGkRLHgGpj8Iu1aFWWpt6HsDDLoD6rWINp/0OVSaIjsKFtmqdrYsheljYdFfIFEWZq37hUL7tC9C0ik7s1WSJEmSJJ0qRXtg/iSY8Qjs3RxmmQ1hwG3Q/xao1TDSeNLJYJFtka3qaNdqmPEwvPMHKCsKsyZdwv5X3S6H5FNydqskSZIkSapI+3fC7Akw+zEo3B1mdVvC4O9An+sgrXak8aSTySLbIlvV2Z4tMGsczP0tFO8Js/ptwn5Yvb8FqZnR5pMkSZIkSScufwPMfCSswi7ZH2aNOsKQ0dDjCkhJizKdVCEssi2yVRMc2A1zn4BZ42H/9jCr3RQGjoR+N0FGVqTxJEmSJEnScdi+AqY/AO/9CeIlYda8BwwbA12+DEnJ0eaTKpBFtkW2apLi/fDuUzDjIchfF2bpWdD/ZhgwEuo0iTafJEmSJEn6uI0LYNr9sPRvwMF6ru1QGHYX5JwLsViU6aRTwiLbIls1UVlJOBBy2gOwfXmYpWTCmdeEfbTqt4k2nyRJkiRJNV0iAWumw9T7IO+tQ/PTLgwrsLP7R5dNioBFtkW2arJ4HJa/Gn4obnwnzJJSoPs3YOhoaNI50niSJEmSJNU48Th8+E+Yej+snxNmsWTodnl4rt7sjEjjSVGxyLbIlsKrvKsmhx+SqyYfHMbg9IvDq7yt+kQaT5IkSZKkaq+sFJa8EK6e3ro0zJLTofe3wtXTDdtHm0+KmEW2RbZ0pA3zQ6H9/suHZu2Hh0K7/XD33ZIkSZIk6WQqKYQFT8H0h2D3mjBLqwv9boSBt0PdZtHmkyoJi2yLbOnoti2HaWNh0XMQLw2zVn1g6F3Q+WJISoo0niRJkiRJVVphAcz7LcwcB/u2hlmtRjBwJPS7BTLrRxpPqmwssi2ypWPbvRZmPAzvPAmlhWHWuHPYl6v71yE5NdJ4kiRJkiRVKfu2w6zxMOdxKMoPs3qtYcid0PsaSKsVbT6pkrLItsiWjs/ebTB7PMx54tAP2qzssE+XP2glSZIkSTq23esOWyh2IMwanwZDRoeFYilpkcaTKjuLbIts6cQU5sO83/3bpU+NYeBtXvokSZIkSdK/O9rWnS17w9AxcPqX3LpTOk4W2RbZ0mdTcgAWPA3THwzbj8DBwyhugoGjPIxCkiRJklSzbZgPU++H918BDlZq7c8KBXaHERCLRZlOqnIssi2ypc+nrBQWPw/THoBty8IsOR16fyvs79WgXaTxJEmSJEk6ZRIJWDUFpt0PK3MPzU//UiiwW/eJLJpU1VlkW2RLJ0c8Dh+8Fn5Yr58bZrFk6HY5DL0LmnWNNp8kSZIkSRUlHoflr4bnxBvmh1ksGXp8I+yB3fT0SONJ1YFFtkW2dHIlErB6WvjhnffWoXnni8Krz9n9ossmSZIkSdLJVFYCi/4C08fCtvfDLCUDel8Dg78DDdpGGk+qTiyyLbKlirPx3bAf2LK/U74fWLthYYV2zjnuByZJkiRJqppKDsC7T8H0hyD/4LlR6fWg380wcCTUaRptPqkassi2yJYq3rYPwqGQC589dEJzi16h0O5yCSQlRxpPkiRJkqTjUpgPc5+AWeNh37Ywq90EBo6CfjdBRla0+aRqzCLbIls6dfLXw4xHYP4kKD0QZo06wdDR0P0bkJIWZTpJkiRJko5u71aYNQ7m/haKCsIsqw0MuRN6fwtSM6PNJ9UAFtkW2dKpt28HzJ4Acx4Lr2YD1GsV9g8781pIqx1tPkmSJEmSAHatgRkPw7t/gNLCMGtyerjCuNvlkJwabT6pBrHItsiWolNYAPMnwsxHYe+WMKvVCAbcBv1vgcwG0eaTJEmSJNVMW9+HaQ/Aoj9DoizMWvWFYWPgtAshKSnafFINZJFtkS1Fr6QQ3nsm7KO9a3WYpdWBvjfCoNuhbvNI40mSJEmSaoj182Dq/bD8lUOzDmeHArvdMIjFossm1XAW2RbZUuVRVgpLXwqvem9ZHGbJadDr6rDvWMMOkcaTJEmSJFVDiQSsfDsU2KunHhzGoMuXYOgYaHVmpPEkBRbZFtlS5ZNIwIf/Cg8i1s0Ks1gSnHFZ2Iesebdo80mSJEmSqr54HN7/e1hMtfHdMEtKgR5XwJDR0OS0SONJOpJFtkW2VLmtmQFT74MVbxyadbogXNbVZmB0uSRJkiRJVVNpMSx6DqaNhR0fhllKJvS5DgbdAfWzI40n6egssi2ypaph03vhVfIlLwEHvxW1GQzDvgcdz3WfMkmSJEnSsRXvh3eehBkPQ8H6MMvIgv7fhgG3Qe3G0eaTdEwW2RbZUtWyIw+mj4UFf4R4SZg17xG2HOn6FUhKjjSeJEmSJKmSObAL5jwBs8fD/h1hVqcZDLod+twAGXZCUlVgkW2RLVVNBRth5qMwbyKU7Auzhjkw5LvQ80pISY82nyRJkiQpWns2H3ze+Dso3htmDdodfN74TUjNiDSepBNjkW2RLVVt+3fCnN/A7AnhVXaAui0PvrJ+PaTXiTSeJEmSJOkU27kKZjwE7z4NZUVh1vSMcCXvGV+F5JRo80n6TCyyLbKl6qFoL7zz+7DX2Z5NYZbZAPrfCgNuhVoNo80nSZIkSapYW5aEs5UWPw+JeJhlD4ChY+C0CzxbSariLLItsqXqpbQI3ns27KO9c2WYpdaGvjeEVdr1WkYaT5IkSZJ0kq2dDdPuhw9eOzTreF4osNsOtsCWqgmLbItsqXqKl8HSv4YHM5sXhVlSKvS6CoaMhkY5kcaTJEmSJH0OiQTkvQlT74c10w8OY3DGpWELkRY9o0wnqQJYZFtkS9VbIgEr3gyF9kcPbmJJ0PUr4dX5Fj2izSdJkiRJOn7xMlj2t1Bgb14YZkmp0PPKsGipccdI40mqOBbZFtlSzbF2Vniw8+E/D806ngfDvhcuN5MkSZIkVU6lxbDwWZj+IOxYEWaptaDPwW0ks1pFm09ShbPItsiWap7Ni8MBIEteOOwAkIHh8jMPAJEkSZKkyqN4H8yfBDMegT0bwyyjPgy4FfrfCrUbRZlO0ilkkW2RLdVcO1fC9IdgwdNQVhxmTc+AYWOg66WQnBJpPEmSJEmqsfbvhDm/gdkT4MCuMKvbIqy+7nM9pNeNNJ6kU88i2yJb0p7NMPNRmPc7KN4bZg3awZDvQs9vQmpGpPEkSZIkqcYo2Hjw+dlEKNkXZg07HHx+dhWkpEebT1JkLLItsiV95MAumPM4zBoPB3aGWZ1m4RX/vjf6ir8kSZIkVZQdeWH/6/f+eOiK2WbdYdhd4YrZpORI40mKnkW2Rbakf1e8D955EmY8DAUbwiwjC/p/GwaMdA82SZIkSTpZNi+CqffD0pcOnWHUZnDY8rHjeZ5hJKnciXS5SRUZZMqUKVxyySW0bNmSWCzGSy+9dMz75+bmEovFPva2efPmiowpqSZIqw0DR8KdC+Arj0KjTlCYD1N+BWO7wT9+CPnro04pSZIkSVXXmhnw1NdgwlBY8kIosTudDze8Bjf+Azp9wRJb0mdWoaee7du3j549e3LjjTdy2WWXHffHLV++/IgGvmnTphURT1JNlJIGvb8V9mF7/+WwSmDTApg9HuY+AT2ugKGjoXGnqJNKkiRJUuWXSMCHr8O0+2HtzDCLJcEZX4Whd0Hz7tHmk1RtVGiRfeGFF3LhhRee8Mc1bdqU+vXrn/xAkvSRpGTo+hXo8mVY+XYotFdPhQVPwYKnocsl4bK3lr2jTipJkiRJlU+8DJa8CNPGwpZFYZacBr2+CYPvhEY5kcaTVP1UaJH9WfXq1YuioiK6devGj3/8Y4YMGfKJ9y0qKqKoqKj8/YKCglMRUVJ1EYtBzjnhbd3csIpg+auw7G/hLeccGDoG2g31EjhJkiRJKi2CBc+EQxx3rQqztDrQ9wYYeDvUaxFtPknVVqUqslu0aMGECRPo27cvRUVFPPHEE4wYMYLZs2dz5plnHvVj7r33Xn7yk5+c4qSSqqXsfnDVH2HLUpg+Fhb9BfLeCm+t+4VC+7QvQlKFHi8gSZIkSZVP0R6YPwlmPAJ7D55lltkwnEXU72ao1TDSeJKqv1gikUicki8Ui/Hiiy9y6aWXntDHDR8+nDZt2vCHP/zhqLcfbUV2dnb2cZ10KUnHtGs1zHgY3vkDlB38PtO0KwwZDd0uh+RK9VqgJEmSJJ18+3fC7Akw+zEo3B1m9VrBoDugz3WQVjvSeJKqtoKCArKyso6ry630LUz//v2ZNm3aJ96enp5Oenr6KUwkqcZo0A4uvg/O+gHMGgdzfwtbl8KL34a3/xeG3Am9vgWpGVEnlSRJkqSTK38DzHwkrMIu2R9mjTqGhT09roCUtCjTSaqBKn2RvWDBAlq0cH8lSRGq2wy+8JNw4vbcJ2DWeNi9Bl75HuT+HwwaBX1vggyvApEkSZJUxW1fAdMfgPf+BPGSMGveA4Z9D7pcAknJ0eaTVGNVaJG9d+9eVqxYUf7+qlWrWLBgAQ0bNqRNmzbcfffdbNiwgSeffBKAsWPH0r59e8444wwKCwt54okneOutt/jXv/5VkTEl6fhk1oezvg8DR8G7T8GMhyB/HbzxY5j6APS/GQaMhDpNok4qSZIkSSdm4wKYdj8s/RtwcBfatkNh2BjIOQdisSjTSVLFFtnz5s3j7LPPLn9/zJgxAFx33XVMmjSJTZs2sXbt2vLbi4uL+d73vseGDRuoVasWPXr04I033jjic0hS5NJqwYBvh1O5F/0Fpj0A25fD1Ptg5qNw5rUw+DtQv03USSVJkiTpkyUSsGZ6eC6T99ah+WkXhgI7u3902STp35yywx5PlRPZIFySTop4HJa/Gh78bXwnzJJSoPvXw/5xTU+PNJ4kSZIkHSEehw//CVPvh/VzwiyWHA61Hzoamp0RaTxJNceJdLkW2ZJ0siQSsGpyeDC4avKh+elfgqFjoHWf6LJJkiRJUlkpLHkhXFW6dWmYJadD72+Fq0obto82n6QaxyLbIltS1DbMD4X2+y8fmrU/KxTaHUa4v5wkSZKkU6ekEBY8BdMfCgfXA6TVhX43hTOA6jaLNp+kGssi2yJbUmWxbTlMGwuLnoN4aZi1PDPsN9f5YkhKijSeJEmSpGqssADm/S6c5bNva5jVagQDR0K/W8KB9pIUIYtsi2xJlc3utTDjEXjnSSg9EGaNO4f957p/HZJTI40nSZIkqRrZtx1mjYe5j0NhfphlZYftQ3pfEw6wl6RKwCLbIltSZbV3G8yeAHMeh6LDH1DeGfal8wGlJEmSpM9q9zqY8fC/LaA5DYbe5QIaSZWSRbZFtqTKrrAA5v0WZo477BK/xgcv8bvZS/wkSZIkHb9tH8D0sbDwT25pKKlKsci2yJZUVZQcgAVPw/QHw/YjAOn1oO+NHroiSZIk6dg2vAPT7odlLwMH6x0PmZdUhVhkW2RLqmrKSmHx8zDtAdi2LMyS08N2I0PuhAbtIo0nSZIkqZJIJGDVlFBgr8w9ND/9S2ELkdZ9I4smSSfKItsiW1JVFY/DB6+FB6Xr54ZZLBm6fy08KG3aJdp8kiRJkqIRj8PyV8NzhQ3zwyyWHPa+Hjra5wqSqiSLbItsSVVdIgGrp4UHqXlvHZp3vihcJpjdL7pskiRJkk6dshJY9JewB/a298MsJQN6XwODvwMN2kYaT5I+D4tsi2xJ1cnGd8OWI0v/Rvm+d+2GhRXaOee4750kSZJUHZUcgHefgukPQf5h5+n0uzkcEl+nabT5JOkksMi2yJZUHW3/EKaNhYXPHjqJvEWvUGh3uQSSkqNMJ0mSJOlkKMyHuU/ArPGwb1uY1W4SDoPvdxNkZEWbT5JOIotsi2xJ1Vn+epjxCLzzeyjZH2aNOoV98bp/A1LSIo0nSZIk6TPYuxVmjYO5v4WigjCr3wYG3xkOgU/NjDafJFUAi2yLbEk1wb4dMHsCzHksrNoAqNcq7JN35rWQVjvafJIkSZI+3a41MOOhsI1IaWGYNekSrrzsdhkkp0abT5IqkEW2RbakmqRoD8ybCDMfhb2bwyyzYdg3r/8tkNkg2nySJEmSPm7rsnAWzqK/QKIszFr1hWHfg9O+CElJ0eaTpFPAItsiW1JNVFII7/0Rpj8Iu1aFWVod6HsDDLoD6jaPNp8kSZIkWD8Ppt4Py185NOtwdiiw2w31MHdJNYpFtkW2pJqsrBSWvhRWd2xZHGbJadDrahhyJzTsEGk8SZIkqcZJJGDl26HAXj314DAWDm0fehe0OjPSeJIUFYtsi2xJCg+WP/xXeLC8blaYxZLgjMvCg+Xm3aLNJ0mSJFV38Ti8/zJMvQ82LQizpBTocSUM+S40OS3SeJIUNYtsi2xJOtKaGaHQXvH6oVmnC2DYGGgzMLpckiRJUnVUVgILn4PpY2H7B2GWkgl9rgvb/tXPjjSeJFUWFtkW2ZJ0dJsWhi1Hlr4EiXiYtRkcCu2O57kfnyRJkvR5FO+Hd56EGQ9Dwfowy8iC/t+GAbdB7cbR5pOkSsYi2yJbko5tR15YHbLgjxAvCbPm3cOWI10vhaTkKNNJkiRJVcuBXTDnCZg9HvbvCLM6zWDQ7dDnBsiwn5Cko7HItsiWpONTsBFmPgrzJkLJvjBrmBP26+t5JaSkR5tPkiRJqsz2bD70eLp4T5jVbxseT/e6GlIzos0nSZWcRbZFtiSdmP07Yc5vYPaEsJoEoG6LsH9fn+shvU6k8SRJkqRKZecqmPEQvPs0lBWFWdMzwhWOZ3wVklOizSdJVYRFtkW2JH02RXvhnd+HPf32bAqzzAbQ/1YYcCvUahhtPkmSJClKW5aEM2cWP3/ozJnsATB0DJx2gWfOSNIJssi2yJakz6e0CN57FqY/CDvzwiy1dlidPfgOqNcy0niSJEnSKbV2Nky7Hz547dCs43mhwG472AJbkj4ji2yLbEk6OeJlsPSv4UH75kVhlpQa9s8eehc0yok2nyRJklRREglY8WZ4LLxm+sFhDM64NDwWbtEzynSSVC1YZFtkS9LJdbQH8bEk6PqVsAqlRY9o80mSJEknS/lijgdg88Iw+2gxx5DR0LhjpPEkqTqxyLbIlqSK80mXVQ77XrisUpIkSaqKSoth4bMwbexh2+vVgj43wKDbIatVpPEkqTqyyLbIlqSKt3lxWKWy5IXDDroZCMPGQKfz3SdQkiRJVUP5geePwJ6NYZZRHwbc5oHnklTBLLItsiXp1Nm5EqY/BAuehrLiMGvWLewb2PVSSE6JNJ4kSZJ0VPt3wpzfwOwJcGBXmNVtAYPuCIecp9eJNJ4k1QQW2RbZknTq7dkMMx+Feb+D4r1h1qAdDPku9PwmpGZEGk+SJEkCoGDjwcetE6FkX5g17HDwcetVkJIebT5JqkEssi2yJSk6B3bBnMdh1ng4sDPM6jQP+wr2vQHS60abT5IkSTXTjjyY/iC898fDriTsDsMOXkmYlBxpPEmqiSyyLbIlKXrF++CdJ2HGw1CwIcwy6kP/b4f9Bms3ijSeJEmSaohNC8PZLktfOnS2S5vB4WyXjud5toskRcgi2yJbkiqP0mJY9Fw4/X3Hh2GWWgvOvA4G3wFZrSONJ0mSpGpqzQyYej+seP3QrNP5MHQMtB0UXS5JUjmLbItsSap84mWw7O8w7X7Y9F6YJaVCjytg6Gho3CnSeJIkSaoGEgn48F+hwF43K8xiSXDGV8Nh5M27R5tPknQEi2yLbEmqvBIJyHsrXN65eurBYQy6XBIu72zZO9J4kiRJqoLKSsPWIdMegC2Lwyw5DXp9EwbfCY1yIo0nSTo6i2yLbEmqGtbNDSu0l796aNbh7FBotxvmfoWSJEk6ttIiWPBMOMRx16owS60dDhkfdAfUaxFtPknSMVlkW2RLUtWyZWlYPbP4eUiUhVnrfuHyz9MuhKSkaPNJkiSpcinaA/MmwsxHYe/mMMtsGA4V738L1GoYbT5J0nGxyLbIlqSqaddqmP4QvPsUlBWFWZMuodDudjkkp0QaT5IkSRHbtwNmT4A5v4HC3WFWtyUM/g70uQ7SakcaT5J0Yk6ky63QJW5TpkzhkksuoWXLlsRiMV566aVP/Zjc3FzOPPNM0tPT6dixI5MmTarIiJKkyqRBO/jS/TB6EQwZDWl1YdsyePHb8HBvmPM4lByIOqUkSZJOtfwN8NrdMLYbTPllKLEb5sCXH4bvLoBBoyyxJamaq9Aie9++ffTs2ZNHH330uO6/atUqLr74Ys4++2wWLFjA6NGjufnmm/nnP/9ZkTElSZVN3WbwhZ/AXYvhnHugVmPYvRZe/T6M7RFOoS/MjzqlJEmSKtr2FfDX2+HBnjBrHJTsh+Y94OuT4I65cOa1kJIedUpJ0ilwyrYWicVivPjii1x66aWfeJ///M//5JVXXmHx4sXlsyuvvJLdu3fz2muvHdfXcWsRSaqGiveH7UZmPAT568IsPQv63wwDRkKdJtHmkyRJVcaufcUs3VRA9dpks/qpvXMx2Usm0Gjta8QIf1j5TQew7ozb2N3CQ8ElVT+xGAzp2DjqGKfciXS5lWqz0ZkzZ3LeeecdMbvgggsYPXr0J35MUVERRUVF5e8XFBRUVDxJUlTSasGAb4fT5xf9GaaNhe3LYep9MHMcnHlN2Bexfpuok0qSpEpqw+4DPD5lJc/OXUthSTzqODqqBANi7zMq5a/0Tl5YPn297EzGl36Zd9aeBmsB5kSWUJIqSkpSjBU/vyjqGJVapSqyN2/eTLNmzY6YNWvWjIKCAg4cOEBmZubHPubee+/lJz/5yamKKEmKUnIq9Pom9LgSlr8SthjZ+E447Gfe76D718PBkE06R51UkiRVEiu27mXC5DxeencDpfGwsje7YSa10yrV0+EaLZaI0790Ht8o/AtnlC0DoIwkJqcO47mMr7E6uR0Ap0eYUZIqWnKSV5p8mir/k/vuu+9mzJgx5e8XFBSQnZ0dYSJJUoVLSoIul8DpX4JVk0OhvWoyvPdHeO9ZOP1iGDYGWvWJOqkkSYrIwvW7Gfd2Hv9curl8G5HBOY0YNaIjQzo2IubWFNErK4UlL8C0ByB/aZglp0Pvq0kefCfnNGzPOdEmlCRVIpWqyG7evDlbtmw5YrZlyxbq1at31NXYAOnp6aSne7CDJNVIsRh0GBHe1s+HaffD+y8fems/PBTa7Ye7j6IkSTVAIpFgZt4OxuXmMW3F9vL5+V2bMXJEDr3bNIgwncqVFMKCp2D6Q7B7TZil1YV+N8LAUVC3ebT5JEmVUqUqsgcNGsSrr756xOz1119n0KBBESWSJFUZrfvAlU/D1vdh+lhY+FxYpb1qMrQ8MxTanS8Oq7klSVK1Eo8neGPZFh7NzeO9dbuBcIn2V3q25LYROZzWrG60ARUUFsC834YzTvZtDbNajWDgSOh3C2TWjzSeJKlyq9Aie+/evaxYsaL8/VWrVrFgwQIaNmxImzZtuPvuu9mwYQNPPvkkALfddhuPPPIIP/jBD7jxxht56623eO6553jllVcqMqYkqTppejp8dQKc/V8w42F458mwj/afvgWNO8PQ0WEv7eTUqJNKkqTPqaQszt/f28j43Dw+3LoXgPSUJK7ol80twzqQ3bBWxAkFwL7tMGs8zHkcivLDrF5rGHIn9L4mHOwtSdKniCUSH+0WdvLl5uZy9tlnf2x+3XXXMWnSJK6//npWr15Nbm7uER9z1113sXTpUlq3bs0999zD9ddff9xfs6CggKysLPLz86lXr95J+F1Ikqq0vdtg9kdPnArCLCsbBn/HJ06SJFVRhSVlPDdvHb+ZspL1uw4AUDc9hWsGteWGIe1pUtftJyuF3esOLSwoDX9OND4NhowOCwtS0iKNJ0mK3ol0uRVaZEfBIluSdFSF+TD3tzBrHOzbFma1GsPA27yUVZKkKqKgsIQ/zFzDxOmr2L63GIBGtdO4cWh7rhnUlnoZXnFVKWxbDtPGwqLnIF4aZi17w9Ax4bBut3qTJB1kkW2RLUn6JCUH4N2nYMZDsHttmKXVhX43HTxcqFm0+SRJ0sds21PE76av4qmZa9hTFIrRVvUzuXV4B77RN5uM1OSIEwqADfNh6v3w/ivAwaqh/VmhwO4wwsO3JUkfY5FtkS1J+jRlJbD4BZj2AGxbFmbJ6dD7W2G/xgbtIo0nSZJg3c79/GbKSp6bt46i0jgAnZrWYeSIHC7p2ZLUZFf2Ri6RgFVTYNr9sDL30LzzxeGw7dZ9I4smSar8LLItsiVJxysehw9eC0++1s8Ns1gydLscht4FzbpGm0+SpBrogy17mJCbx1/f20hZPDxl7ZVdn1EjcjivSzOSklzZG7l4HJa/Gh5DbZgfZrHksPf10NHQtEuk8SRJVYNFtkW2JOlEJRKwelp4Mpb31qF554vC5bDZ/aLLJklSDfHu2l2My83j9aVbymfDOjVm5IgcBnVoRMytKaJXVgKL/gLTx8K298MsJSMcoj34O9CgbaTxJElVi0W2RbYk6fPY+G7Y33HZ3ynf37HdsLBCO+cc93eUJOkkSiQSTFuxnXFv5zFz5Q4g/Kj94hnNGTkihx6t60cbUMFH54xMfwjyD54zkl4P+t0MA0dCnabR5pMkVUkW2RbZkqSTYdsHMP1BWPgsxMPBUrToFQrtLpdAkgdLSZL0WcXjCf61dDOPvp3Hog35AKQkxbi0dytuG55Dx6Z1Ik4oAArzYe4TMGs87NsWZrWbhEOy+90EGVnR5pMkVWkW2RbZkqSTKX89zHgE3vk9lOwPs0adwv6P3b8BKWmRxpMkqSopKYvz0rsbmDA5j7xt+wDISE3iyn5tuOWsDrSqnxlxQgGwdyvMGgdzfwtFBWGW1SYcit37W5Dqn5Mk6fOzyLbIliRVhH07YPYEmPNYWJ0EUK9V2A/yzGshrXa0+SRJqsQOFJfx7Ny1PD5lJRvzCwGol5HCdYPbcf3gdjSqkx5xQgGwaw3MeChsI1Ia/pxocnq4Iq3b5ZCcGm0+SVK1YpFtkS1JqkhFe2DeRJj5KOzdHGaZDcP+kP1vgcwG0eaTJKkSyT9Qwh9mruZ301ezc18xAE3qpnPz0PZ8c0Ab6mZYjFYKW5fBtLGw6M+QKAuzVn1h2Bg47UJISoo0niSperLItsiWJJ0KJYXw3jNhH+1dq8MsrQ70vQEG3QF1m0caT5KkKG3dU8hvp63i6Vlr2VsUzprIbpjJrWfl8LU+rclI9ayJSmH9vHDI9fJXDs06nB0K7HbDPORaklShLLItsiVJp1JZKSx9CaY9AFsWh1lyGvT6Jgz5LjTsEGk8SZJOpbU79vPYlDz+PH89xaVxADo3q8uos3O4uHsLUpJd2Ru5RAJWvh0K7NVTDw5j0OVLMHQMtDoz0niSpJrDItsiW5IUhUQCPvxXeFK4blaYxZLgjK+GJ4XNu0WbT5KkCvT+5gLG5+bx8sJNlMXD08wz29Rn1IiOnHN6U5KSXNkbuXgc3v97eKyyaUGYJaVAjytgyGhoclqU6SRJNZBFtkW2JClqa2bA1PtgxRuHZp0uCJfpthkYXS5Jkk6y+Wt2Mu7tPN58f2v57KzTmjBqRA4D2jck5tYU0SsthkXPhT2wd3wYZimZ0Oe6sB1a/exI40mSai6LbItsSVJlsem9sOXIkpeAgz9y2wwOhXbH89x3UpJUJSUSCaZ8uJ1H317BnFU7gfAj7aJuLRg5IodurbIiTigAivfDO0/CjIehYH2YpWeFw6kHjoTajaPNJ0mq8SyyLbIlSZXNjjyYPhYW/BHiJWHWvDsMvQu6XgpJHnglSar8yuIJXlu8mXG5K1iysQCA1OQYl/Vuza3DO9ChSZ2IEwqAA7tgzhMwezzs3xFmtZvCoNuh742Q4XNlSVLlYJFtkS1JqqwKNsLMR2HeRCjZF2YNc8KhkD2vhJT0aPNJknQUxaVxXnx3PY9NXsnK7eHnV2ZqMt8c0Iabh7WnRVZmxAkFwJ7Nhx5nFO8Js/ptw+OMXldDaka0+SRJ+jcW2RbZkqTKbv9OmP0YzJ4AhbvDrG7LsFKqz/WQ7oo2SVL09heX8szstTwxdRWbCwoByMpM5brB7bh+cDsa1k6LOKEA2LkKZjwE7z4NZUVh1vSMcOXXGV+F5JRo80mS9Akssi2yJUlVRdFemD8JZj4CezaFWWYD6H8rDLgVajWMNJ4kqWbavb+Y389Yw6QZq9i1P2yJ1bRuOrcM68BVA9pQJ91itFLYsiScxbH4eUjEwyx7AAwdA6dd4FkckqRKzyLbIluSVNWUFsF7z4Z9tHeuDLPU2tD3hrBKu17LSONJkmqGLQWFPDF1Jc/MXsu+4jIA2jWqxa3Dc7jszFakp3imQ6WwdjZMux8+eO3QLOdcGPY9aDvYAluSVGVYZFtkS5KqqngZLP1reHK6eVGYJaeF/bOHjIZGOZHGkyRVT6u37+OxKXk8P38DxWVhZW+XFvUYNSKHi7q3IDnJYjRyiQTkvQlT74c10w8OY9D1K2ELkZa9okwnSdJnYpFtkS1JquoSCVjxZii0P3qyGkuCrpeGJ6stekQaT5JUPSzdWMD4yXm8snAj8YPPDPu3a8jIs3MYcVoTYq7sjV68DJb9LRTYmxeGWVLqoRe5G3eMNJ4kSZ+HRbZFtiSpOlk7Kzx5/fCfh2YdvwDDxoTLhyVJOkFzV+9k3NsreHv5tvLZ2Z2bMOrsjvRr5/kMlUJpMSx8FqY/CDtWhFlqLehzcNuxrFbR5pMk6SSwyLbIliRVR5sXhwOdlrxw2IFOA0Oh3el898OUJB1TIpEgd/k2xuWuYO7qXQAkxeDiHi0ZOTyHri19/lQpFO8LB0HPeAT2bAyzjPrhEOj+t0LtRlGmkyTppLLItsiWJFVnO1fC9IdgwdNQVhxmzbqFLUe6XgrJKZHGkyRVLmXxBK8s2sT43DyWbSoAIC05icv7tObWszrQrnHtiBMKgP07Yc7jMHsCHNgZZnWaw+A7oM/1kF430niSJFUEi2yLbElSTVCwCWY9CvMmQvHeMGvQDoZ8F3p+E1IzIo0nSYpWUWkZz8/fwGNT8lizYz8AtdKSuXpAG24e1oFm9fw5USkUbIKZj4RV2OU/z9vD0NHQ8ypISY8ynSRJFcoi2yJbklSTHNgVVnDNGn/kCq5Bt0PfG1zBJUk1zN6iUv44ey2PT13J1j1FADSolcr1g9tz3eC21K+VFnFCAbAjL+x//d4fD7vCqnsosL3CSpJUQ1hkW2RLkmqi4n3wzpMw42Eo2BBmGfWh/7dhwG3uqSlJ1dyufcVMnLGa389YTf6BEgCa18vglrM6cFX/bGqlWYxWCpsXHTzz4sVDZ160GQRDx0CnL3jmhSSpRrHItsiWJNVkpcWw6LnwJHnHijBLrQVnXhf22cxqHW0+SdJJtSn/AI9PWcUf56zlQEkZAB0a1+a24Tlc2rsVaSlJEScUAGtmwrT74cN/HZp1Oj8U2G0HRZdLkqQIWWRbZEuSBPEyWPb38KR503thlpQKPa4Ily037hRpPEnS57Ny214mTM7jxXc3UFIWntZ1a1WPUSM6csEZzUlOcmVv5BIJ+PD18LN47cwwiyXBGV8NhzQ37x5tPkmSImaRbZEtSdIhiQSsfBum3g+rpx4cxqDLJTBsDLTsHWk8SdKJWbwhn3G5K/jH4s189GxuQPuG3H52R4Z1akzMrSmiFy8LW4dMGwtbFoVZchr0+iYMvhMa5UQaT5KkysIi2yJbkqSjWzc3rApb/uqhWc454bLmdkPdl1OSKqlEIsHsVTsZl5vHlA+2lc/P69KUkSM60qdtgwjTqVxpESx4JhziuGtVmKXWDocvD7oD6rWINp8kSZWMRbZFtiRJx7ZlKUwfC4v+Aomwnyqt+4VC+7QvQpL7qUpSZZBIJHhz2VbG5a7gnbW7AUhOinFJjxbcNiKH05v7nKdSKNoD8yfBjEdg7+Ywy2wYDlvufwvUahhpPEmSKiuLbItsSZKOz67VMONheOcPUFYUZk26hH07u10OySmRxpOkmqq0LM4rizYx7u08lm/ZA0BaShLf6Nuabw/LoU2jWhEnFAD7d8LsCTD7MSjcHWZ1W8Lg70Cf6yCtdqTxJEmq7CyyLbIlSToxe7bArHEw97dQHAoT6rcJ+3j2/hakZkabT5JqiMKSMv4yfz2/mbKStTv3A1AnPYWrB7bhpqHtaVo3I+KEAiB/A8x8JKzCLgl/TjTqCENGh0OVU9KiTCdJUpVhkW2RLUnSZ3NgN8x9AmaNh/3bw6x2Uxg0CvreBBn+bJWkirCnsISnZ6/lt9NWsW1PuEKmYe00bhzSjmsGtSMrMzXihAJg+wqY/gC89yeIl4RZ8x7h8OQuX4ak5GjzSZJUxVhkW2RLkvT5FO+Hd5+CGQ9B/rowS8+C/jfDgJFQp0m0+SSpmtixt4iJ01fz5MzVFBSWAtAyK4NbzurAlf3akJlmMVopbHoPpt4PS/8KHHwK3XYoDLsLcs71sGRJkj4ji2yLbEmSTo6yElj0Z5j2AGz/IMxSMuHMa8L+n/XbRJtPkqqoDbsP8PiUlTw7dy2FJXEAcprU5rbhOXylVyvSUjx0N3KJBKyZHgrsvDcPzU+7MKzAzu4fXTZJkqoJi2yLbEmSTq54HJa/AlPvg43vhllSCnT/BgwdDU06RxpPkqqKFVv3MmFyHi+9u4HSeHgq1qN1FqNG5HB+1+YkJbmyN3LxOHz4z1Bgr58TZrGkcAjy0Lug2RnR5pMkqRqxyLbIliSpYiQSsDI3rNBeNfngMAanXxxWp7XqE2U6Saq0Fq7fzbi38/jn0s189AxscE4jRo3oyJCOjYi5NUX0ykphyQvhZ9zWpWGWnA69rw6HHzdsH20+SZKqoUpXZD/66KP86le/YvPmzfTs2ZOHH36Y/v2PfhnWpEmTuOGGG46YpaenU1hYeFxfyyJbkqRTZP18mHY/vP/yoVn74aHQbj/c/UIl1XiJRIKZeTsYl5vHtBXby+fnd23GyBE59G7TIMJ0KldSCAuegukPwe41YZZWF/rdCANHQd3m0eaTJKkaO5EuN6Wiw/zpT39izJgxTJgwgQEDBjB27FguuOACli9fTtOmTY/6MfXq1WP58uXl77s6QZKkSqh1H7jyadj6PkwfCwufC6u0V02GlmeGQrvzxZDkPq+SapZ4PMHry7YwLjeP99btBiA5KcZXerVk5PAcOjWrG21ABYUFMO+3MHMc7NsaZrUawcCR0O9myPSFBkmSKpMKX5E9YMAA+vXrxyOPPAJAPB4nOzub73znO/zwhz/82P0nTZrE6NGj2b1792f6eq7IliQpIrvXwoyH4Z0nofTglVSNO4c9tLt/HZJTI40nSRWtpCzO3xZsZMLkPD7cuheA9JQkruyXzS1ndaB1g1oRJxQAe7fB7Akw53Eoyg+zeq3DIcZnXgtp/jlJknSqVJoV2cXFxcyfP5+77767fJaUlMR5553HzJkzP/Hj9u7dS9u2bYnH45x55pn8/Oc/54wzjn6gRlFREUVFReXvFxQUnLzfgCRJOn7128BFv4KzfgCzx4eCYPtyeGkkvPX/wuXZfa6DdFciSqpeCkvKeG7eOh6bvJINuw8AUDc9hWsGteWGIe1pUjc94oQCYEcezHwEFjxz2Auup8GQ0eEF15S0SONJkqRjq9Aie/v27ZSVldGsWbMj5s2aNeP9998/6sd07tyZ3/3ud/To0YP8/Hx+/etfM3jwYJYsWULr1q0/dv97772Xn/zkJxWSX5IkfQZ1msC5P4Ih34V5vwuXbBdsgH/9N0z+ZdhzdMBt7jkqqcorKCzhDzPXMHH6KrbvLQagcZ00bhzanm8NbEu9DK9EqRTWz4PpD8KyvwMHL0hu2RuGjoHTv+QWWJIkVREVurXIxo0badWqFTNmzGDQoEHl8x/84AdMnjyZ2bNnf+rnKCkpoUuXLlx11VX87Gc/+9jtR1uRnZ2d7dYikiRVFiWFsPBPYduRHR+GWXIa9LgCBt8JTU6LNp8knaBte4r43fRVPDVzDXuKSgFoVT+T24Z34Ot9s8lITY44oYjH4cN/wYyHYM30Q/NO54efPe2GeiixJEmVQKXZWqRx48YkJyezZcuWI+ZbtmyhefPjW4WVmppK7969WbFixVFvT09PJz3dS/UkSaq0UjPCliK9r4EP/gHTH4J1s+DdP4S3zheF1dttBkadVJKOad3O/Tw+dSV/mruOotI4AJ2a1mHkiBwu6dmS1GRX9kautBgW/TkU2NsOXgWclBq2Dhn8HWjWNdp8kiTpM6vQIjstLY0+ffrw5ptvcumllwLhsMc333yTO+6447g+R1lZGYsWLeKiiy6qwKSSJKnCJSXB6ReHt7WzQ8nw/iuw/NXw1ro/DLkTOl/sZd6SKpUPtuxhQm4ef31vI2XxcEFrr+z6jBqRw3ldmpGU5MreyBXmw/xJMGs87NkUZml1oe/1MGAkZLWKMp0kSToJKrTIBhgzZgzXXXcdffv2pX///owdO5Z9+/Zxww03AHDttdfSqlUr7r33XgB++tOfMnDgQDp27Mju3bv51a9+xZo1a7j55psrOqokSTpV2gyANk/D9g/DliPvPQvr58CfvgWNOsKgO8LWI2m1ok4qqQZ7d+0uxuXm8frSQ1eYDuvUmJEjchjUoRExt6aIXv56mP0YzJsIxXvCrG6LcBZD3xsgIyvafJIk6aSp8CL7iiuuYNu2bfzoRz9i8+bN9OrVi9dee638AMi1a9eSdNiqq127dnHLLbewefNmGjRoQJ8+fZgxYwZdu3oJmCRJ1U7jTvDlh+Ds/4Y5j8HcJ2DHCnh5NLz5EzjzOuh3M9TPjjqppBoikUgwbcV2xr2dx8yVO4CwlfIFXZszckQOPbPrRxtQkEjA2lkwe0I4wDFRFuZNTg/bh3T/OqS4/aQkSdVNhR72GIUT2SBckiRVMkV74Z0nQzmxe02YxZKhy5eg/63QdrCHc0mqEPF4gn8t3cy43DwWrs8HICUpxqW9W3Hb8Bw6Nq0TcUJRUgiLnw8/IzYvPDRvNywU2B2/4NZUkiRVMSfS5VpkS5KkyideBh/8M5QVqyYfmjfvHi4X7/a1cIikJH1OJWVxXnp3AxMm55G3bR8AGalJXNmvDbec1YFW9TMjTigKNsK834XtQ/ZvD7OUjLAF1YBbodkZ0eaTJEmfmUW2RbYkSdXHlqUw5zdhH+3SA2FWqxH0uR763uQBXpI+kwPFZTw7dy2PT1nJxvxCAOplpHDd4HZcP7gdjeq4NUWkEglYPze8oLn0rxAvDfN6raH/zWHrqVoNo80oSZI+N4tsi2xJkqqf/Tvh3T/AnMchf12YxZKh65fDKu3sAW47IulT5e8v4cmZq5k4YzU79xUD0KRuOjcPbc83B7ShbkZqxAlruNIiWPJiKLA3vnto3nZIWH3d+WJIrvCjniRJ0ilikW2RLUlS9VVWCh/8A2Y/BqunHpo37wF9b4TuX4P0utHlk1QpbS0o5LfTVvH07LXsLQqre7MbZnLrWTl8rU9rMlKTI05Yw+1aDfN/H16w3LctzJLTocfXwxkJLXpEGk+SJFUMi2yLbEmSaobNi2HOY7DwOSgNWwOQVieU2X1ugJa9Io0nKXprd+znsSl5/Hn+eopL4wCc3rwuI0fkcHH3FqQkezhgZMpKYPk/YP5EyHsbOPjUtG7Lg9uHXA+1G0WZUJIkVTCLbItsSZJqlv07YcEzMH8S7Pjw0Lxl71Bod7sc0utEFk/Sqff+5gLG5+bx9/c2Ej/4jKdP2waMGpHDOac3JeZWRNHZtQbeeRLefQr2bj40zzknnH/Q+SJIdosXSZJqAotsi2xJkmqmRALWTId5E2HZ36As7H9LWt1weXqfG7w8Xarm5q/Zybi383jz/a3ls7NOa8LtI3Lo376hBXZUykrhg9fC6usVb1K++rp2E+j9rXB4Y8P2kUaUJEmnnkW2RbYkSdq3/dAq7Z15h+at+oQVf90uh7TaUaWTdBIlEgmmfLidR99ewZxVO4Fw9utF3VowckQO3VplRZywBtu97uDq6z/Ank2H5h1GhBcXO18EKWmRxZMkSdGyyLbIliRJH0kkwqGQ8ybCsr9DvCTM0+uFvbR7XR3KbVdpSlVOWTzBa4s3My53BUs2FgCQmhzjst6tuXV4Bzo0cUuhSJQUhkN5FzwDH75O+errWo0Prr6+FhrlRBpRkiRVDhbZFtmSJOlo9m6D9z5apb3y0LxRJ+j1Teh5JdRrGVk8ScenuDTOi++u57HJK1m5fR8AmanJfHNAG24e1p4WWZkRJ6yBEgnY8A4seBoWPw+Fuw/d1n54uBLm9C+5+lqSJB3BItsiW5IkHUs8DqunhNWCS/8GpQcO3hCDnLOh5zfh9IshrVakMSUdaX9xKc/MXssTU1exuaAQgKzMVK4b3I7rB7ejYW1L0lOuYCMs/FP4frr9g0Pzeq3Ci4O9rnb1tSRJ+kQW2RbZkiTpeBUWwNK/wnt/DAdFfiS9HpxxaSi12wx06xEpQrv3FzNpxmomzVjN7v1he6Bm9dK5eWgHrhrQhjrpKREnrGFKDsD7r4TV1ytzIREP85RM6HJJuMKl/VmQlBxpTEmSVPlZZFtkS5Kkz2LnKnjv2VBq715zaN6wA/S8KqwurN8munxSDbM5v5Anpq7kmTlr2V9cBkC7RrW4dXgOl53ZivQUi9JTJpGAdbPDyuslL0JRwaHb2gyGXldB10shw+dgkiTp+FlkW2RLkqTPIx6HtTNgwR9DYVOy79BtbYdAt8tCYVO7cWQRpeps9fZ9PDYlj+fnb6C4LKz27dKiHqNG5HBR9xYkJ3mFxCmzZWnY83rx87Br1aF5/TaHXuBr2CG6fJIkqUqzyLbIliRJJ0vxPlj293AJ/aqpwMGHTrFk6DAcul0eDjDLrB9lSqlaWLIxn/G5eby6aBPxg//U+rdryMizcxhxWhNibvFzauzIg8UvhPJ627JD89TaB7dcuiq8qJeUFFlESZJUPVhkW2RLkqSKkL8+rNBe/DxsfPfQPDkNOn4hrNTufCGk1Y4uo1QFzVm1k3G5K8hdvq18dnbnJow6uyP92jWMMFkN8tH3t0V/gU0LDs0P//522hchvU5kESVJUvVjkW2RLUmSKtqOPFjyAiz69xWLtULZ0+1y6HgepGZEl1GqxBKJBLnLtzEudwVzV+8CICkGF/doycjhOXRt6WP5Crd3azjsdvHzsHbmoXksGTqMOHjFycVecSJJkiqMRbZFtiRJOpU+aQ/Z9Hph25GuX4YOZ1tqS0BZPMErizYxPjePZZvCgYFpyUlc3qc1t57VgXaNvaKhQu3dCu+/AktfglVTIBE/eEMM2g72DABJknRKWWRbZEuSpCgkEmHLkcXPh0v0CzYcui21NnQ6LxTbnc53haNqnKLSMp6fv4HHpuSxZsd+AGqlJXP1gDbcPKwDzer5Qk+F2bkSlr0cCux1synf6x+gVZ+w8rrrpZDVKqqEkiSphrLItsiWJElRi8dDYbTkhVAeHV5qJ6VA+7PCJfudL4Z6LaLLKVWwfUWlPDN7LU9MW8mWgiIAGtRK5frB7blucFvq10qLOGE1lEjA5oXhe8+yl2HrkiNvb9kbulwCZ1wGDdtHk1GSJAmLbItsSZJUuXy0Uvv9l0OptH35kbe37hdWap/+JWjcMZqM0km2a18xE2es5vczVpN/oASA5vUyuOWsDlzVP5taaSkRJ6xm4mVhn+v3Xwnfa3avPXRbLBnaDYHTL4HTL4Ks1tHllCRJOoxFtkW2JEmqzLZ/eKjU3jDvyNuanB5Wane6AFr3haTkaDJKn9Gm/AM8PmUVf5yzlgMlZQB0aFyb24bncGnvVqSlJEWcsBop2gMrJ8MH/4Dl/4D9Ow7dlpIJHc8NL5CddgHUahhdTkmSpE9gkW2RLUmSqoqCTbD84OX/q6dCvPTQbZkNIOecsKd2zrlQp0l0OaVPsXLbXiZMzuPFdzdQUhaeYpzRsh6jRnTki92ak5wUizhhNZBIwLb34cPX4cN/wdpZEC85dHtGfeh8YSivc86BtFqRRZUkSToeFtkW2ZIkqSo6sDuUU8tfhby3oDD/sBtj0LJXKLU7fgFanelqbVUKizfkMy53Bf9YvJmPnlkMaN+QUWd35KxOjYnFLLA/l6K9sGpK+N6w4g3IX3fk7Q07hO8Jp18MbQdDcmo0OSVJkj4Di2yLbEmSVNWVlYZtRz78V1h9uXnhkbdnNgzbBny0Wrt2o2hyqkZKJBLMXrWTR99ewdQPt5fPz+vSlJEjOtKnbYMI01VxiUTYfujDf8GK12HNDCgrPnR7cjq0HxbK605fgEY50WWVJEn6nCyyLbIlSVJ1s2dzWI354euQ9zYU/ftq7d7QYTi0Hw7ZA9xSQBUiHk/w1vtbGZe7gnfW7gYgOSnGJT1acNuIHE5v7uPvz2TPlrC10KrJsDL3yIMaARq0O3Q1Rruh/vuWJEnVhkW2RbYkSarOykph/ZyD++S+DlsWHXl7chq07g/tzwpvrfpASlo0WVUtlJbFeXnhJsbn5rF8yx4A0lKS+Ebf1nx7WA5tGlmsnpD9O2HN9LBlyKopYd/rwyWnQ7shB1ddnx9WXbtFiyRJqoYssi2yJUlSTVKwEVZOPliKTYaCDUfenloL2gw6VGy36On+2jouhSVl/Hn+en4zJY91Ow8AUCc9hW8NbMuNQ9vRtG5GxAmriKK9sHZm+Pe5agpsWggc/jQsBi16hH+f7c4KJXZa7ajSSpIknTIW2RbZkiSppkokYOfKQys9V02B/duPvE96VtieoN0QyB4YCjQPiNNh9hSW8PTstfx22iq27SkCoGHtNG4c0o5rBrUjK9O/L8d0YDesnxfK69VTYcN8iJceeZ8mpx96cantEKjVMJKokiRJUbLItsiWJEkKEgnYuuxQqb162r/trw2kZEKrM8Pe2m0GQut+lmo11I69RUycvponZ66moDAUr63qZ3LLsPZc0a8NmWmu5P+YRAJ2rYZ1s2HtrPDfrcs4csU1UL/tweJ6eDissW7zKNJKkiRVKhbZFtmSJElHFy+DTe+FLQ4+Kt0O7Pr4/ZqcDtn9w4rtNgOhYQf36K3GNuw+wONTVvLs3LUUlsQByGlSm5EjOvKVXi1JTU6KOGElUloMmxce/PczC9bNgb1bPn6/hh3Ci0Nth4TiukG7Ux5VkiSpsrPItsiWJEk6PvE47FgRCrm1s8N/d6z4+P1qNQ6lXOs+0LI3tOjlqu1qYMXWvUyYnMdL726gNB6eFvRsncXIER05v2szkpJq+IsXH6223rQANr4L6+bCxnegtPDI+yWlhn8X2f3DCz/ZA6BO0ygSS5IkVSkW2RbZkiRJn92+HWGl9kfl9sZ3oazo4/er3xZa9gqldsve4RBJy+0qYeH63Yx7O49/Lt3MR88GBuc0YtSIjgzp2IhYTVx9n0jA7jWwcUH4O79pQfh14e6P3zez4cHC+uBVCy17Q6oHX0qSJJ0oi2yLbEmSpJOntChsR7LuYKm98d1woOTRNGh3sNjudajczmxwCsPqkyQSCWbm7WBcbh7TVhw6APT8rs0YOSKH3m1q0J9TIgG71x4qqz8qro+2zU5yGjQ7I/y9btUnFNiNOrrVjiRJ0klgkW2RLUmSVLEO7A7l9kdbLmxcALtWHf2+WdnQtEvYd7tp14O/7gypmacwcM0Vjyd4Y9kWHs3N4711uwFITorxlZ4tuW1EDqc1qxttwIq2fydsXRoOYDz8v4X5H79vUmoorctfiOkV/s6mpJ3q1JIkSTWCRbZFtiRJ0ql3YFcotw9f4bpr9dHvG0uCBu1Dqf1Rud20KzTKgeTUUxi6+iopi/O3BRuZMDmPD7fuBSA9JYkr+mVzy7AOZDesFXHCk6xoD2xb/vHS+mgHMcLB0rrroa1xWvY6WFqnn8rUkiRJNZpFtkW2JElS5XBgN2x7/7BycRlsWQIHdh79/kmp0LhTKLQb5kDDDod+Xbe52zkch8KSMp6bt47HJq9kw+4DANRNT+GaQW25YUh7mtStwkVtWUnYEmRHHuzMO/jflbDjwzD/JPXbHvmCSdMu4e+ZpbUkSVKkTqTLTTlFmSRJklQTZdYPewq3GXholkjAvm1H2e5hGRTvPfj+0o9/rtTaodhu2P5Qud3oYNldp1mNL7kLCkv4w8w1TJy+iu17iwFoXCeNG4e251sD21Ivo4qsdC8rDYcu7lx5sKQ+rLTevRYSZZ/8sXWaf3yVf5POkF7n1OWXJElShbDIliRJ0qkVi0GdpuGtw4hD83gcCtbD1vdDcXl4ibl7LZTsgy2Lwtu/S60F9VpBVmvIagX1Wv/br1tBWu1T9ls8lbbtKeJ301fx1Mw17CkqBaBV/UxuG96Br/fNJiM1OeKEh0kkwhY0+esgfwMUbPi3X6+Hgo3HLqtTMg+u1O9w2IsZOaG4rtXw1P1eJEmSdEqdkiL70Ucf5Ve/+hWbN2+mZ8+ePPzww/Tv3/8T7//nP/+Ze+65h9WrV9OpUyf+7//+j4suuuhURJUkSVJUkpKgfpvw9u9Ki0OZXb6dxGFFd/46KNkftpfY8eEnf/7MBkcW3HVbQO0mh701Dv9Nq10lVnev27mf30xZyXPz1lFUGgegU9M6jByRwyU9W5KanHTqwsTjULg7rLQvf9sOe7eGYrpgfSip8zdA6YFP/3wpGQdX33c4tOr+o9K6bosq8ecjSZKkk6vCi+w//elPjBkzhgkTJjBgwADGjh3LBRdcwPLly2natOnH7j9jxgyuuuoq7r33Xr70pS/xzDPPcOmll/LOO+/QrVu3io4rSZKkyiglDRp3DG//rrToYEm6/tCq3iN+vQGK94SVwAd2HX1F9xFfK/PIYvvwX2fWh/R6kF4XMupBetbB/9YN5espKFg/2LKHCbl5/PW9jZTFw3E3vbLrM2pEDud1aUZS0ufIEI+Hle+FBVBUEA5QLCyAovzw3wM7Q0F9eFn90X+PtYr639VuctgK+tZH/jqrddgiJOkUFvGSJEmq9Cr8sMcBAwbQr18/HnnkEQDi8TjZ2dl85zvf4Yc//OHH7n/FFVewb98+Xn755fLZwIED6dWrFxMmTPjUr+dhj5IkSfqYwvxDpfZHq4P3bjmylN277fhWC3+SpNRDpXZ6PcjIOlRwp2SEMj45PRwwmJL+b79OO/I+RynEV27by6uLN/Peut3ls64t6/HFbs05vWktYmUlodQvLYSy4vDf0mIoKzo4Lzry1yX7D5bUe0Jp/VF5zed4epCR9fHyv27Lw7Z5OfiWmvHZv4YkSZKqjUpz2GNxcTHz58/n7rvvLp8lJSVx3nnnMXPmzKN+zMyZMxkzZswRswsuuICXXnrpqPcvKiqiqKio/P2CgoLPH1ySJEnVS0ZWeGt2xrHvV7zv31Ya/9s2GYX5/7ZS+eCvSUC8BPbvCG8VoANwB0DaYcPtQG4FfLGklI+vPE+vC7UaHWWl+sH3azUORbwkSZJUASq0yN6+fTtlZWU0a9bsiHmzZs14//33j/oxmzdvPur9N2/efNT733vvvfzkJz85OYElSZJUs6XVDm8N2h3/x8TjULz3sFXNH61wzg+/Li08uBq6+N9WTB++Srr4iHkC2L2/mM0FhewvDlt2xICGtdNoVi+DzH8/wDGWFErklIyDq7s/ZcV3SgakZh62gvyjLVIOvp+a6T7UkiRJqlROyWGPFenuu+8+YgV3QUEB2dnZESaSJElSjZKUFErgjHqQ9fk+VUlZnJfe3cCEyXnkbdsHQEZqElf2a8MtZ3WgVf3MkxBYkiRJqnoqtMhu3LgxycnJbNmy5Yj5li1baN68+VE/pnnz5id0//T0dNLT009OYEmSJCkCB4rLeHbuWh6fspKN+YUA1MtI4brB7bh+cDsa1fHxriRJkmq2Cj0KPC0tjT59+vDmm2+Wz+LxOG+++SaDBg066scMGjToiPsDvP766594f0mSJKmqyt9fwsNvfsiQ/3uLn/x9KRvzC2lSN527Lzyd6T88h++d39kSW5IkSeIUbC0yZswYrrvuOvr27Uv//v0ZO3Ys+/bt44YbbgDg2muvpVWrVtx7770AfPe732X48OHcd999XHzxxTz77LPMmzeP3/zmNxUdVZIkSTolthYU8ttpq3h69lr2FpUCkN0wk1vPyuFrfVqT8e97YEuSJEk1XIUX2VdccQXbtm3jRz/6EZs3b6ZXr1689tpr5Qc6rl27lqSkQwvDBw8ezDPPPMP//M//8F//9V906tSJl156iW7dulV0VEmSJKlCrd2xn8em5PHn+espLo0DcHrzuowckcPF3VuQklyhF0xKkiRJVVYskUgkog5xMhUUFJCVlUV+fj716tWLOo4kSZLE+5sLGJ+bx9/f20j84KPvPm0bMGpEDuec3pRYLBZtQEmSJCkCJ9LlVviKbEmSJKmmmr9mJ+PezuPN97eWz4af1oRRI3Lo376hBbYkSZJ0nCyyJUmSpJMokUgw+YNtjMvNY86qnQDEYnBR9xaMHJ5Dt1ZZESeUJEmSqh6LbEmSJOkkKIsn+MfiTYzPzWPJxgIAUpNjXNa7NbcO70CHJnUiTihJkiRVXRbZkiRJ0udQXBrnxXfXM2HySlZt3wdAZmoy3xzQhpuHtadFVmbECSVJkqSqzyJbkiRJ+gz2FZXyxzlreWLqKjYXFAKQlZnK9YPbcf3gdjSonRZxQkmSJKn6sMiWJEmSTsDu/cVMmrGaSTNWs3t/CQDN6qVzy7AOXNW/DbXTfYgtSZIknWw+ypYkSZKOw5aCQp6YupKnZ69lf3EZAG0b1eK24TlcdmYr0lOSI04oSZIkVV8W2ZIkSdIxrN6+j8em5PH8/A0Ul8UB6NKiHqNG5HBR9xYkJ8UiTihJkiRVfxbZkiRJ0lEs2ZjP+Nw8Xl20iXgizPq1a8CoER0Z0bkJsZgFtiRJknSqWGRLkiRJh5mzaifjcleQu3xb+ezszk0YdXZH+rVrGGEySZIkqeayyJYkSVKNl0gkeHv5Vsa9nce8NbsASIrBxT1aMnJ4Dl1b1os4oSRJklSzWWRLkiSpxioti/Pq4s2Me3sF72/eA0BachKX92nNrWd1oF3j2hEnlCRJkgQW2ZIkSaqBikrLeH7+Bh6bkseaHfsBqJ2WzNUD23LT0PY0q5cRcUJJkiRJh7PIliRJUo2xt6iUZ2av4Ympq9i6pwiABrVSuWFIe64d1Jb6tdIiTihJkiTpaCyyJUmSVO3t3FfMpOmr+P3MNeQfKAGgRVYGNw/rwFX9s6mV5sNiSZIkqTLzEbskSZKqrU35B3h8yir+OGctB0rKAOjQuDa3jcjh0l6tSEtJijihJEmSpONhkS1JkqRqZ+W2vUyYnMeL726gpCwBQLdW9Rg1oiMXnNGc5KRYxAklSZIknQiLbEmSJFUbizfkMy53Bf9YvJlE6K8Z0L4ht5/dkWGdGhOLWWBLkiRJVZFFtiRJkqq0RCLB7FU7GZebx5QPtpXPz+vSlJEjOtKnbYMI00mSJEk6GSyyJUmSVCXF4wneen8r43JX8M7a3QAkJ8W4pEcLbhuRw+nN60UbUJIkSdJJY5EtSZKkKqW0LM7LCzcxPjeP5Vv2AJCWksTX+7Tm1rNyaNOoVsQJJUmSJJ1sFtmSJEmqEgpLyvjz/PX8Zkoe63YeAKBOegpXD2zDTUPb07RuRsQJJUmSJFUUi2xJkiRVansKS3hq1lp+O20V2/cWAdCwdho3DmnHNYPakZWZGnFCSZIkSRXNIluSJEmV0o69RUycvprfz1zNnsJSAFpmZfDtszpwRb82ZKYlR5xQkiRJ0qlikS1JkqRKZf2u/TwxdRXPzl1LYUkcgJwmtRk5oiNf6dWS1OSkiBNKkiRJOtUssiVJklQprNi6h/G5K/nrgg2UxhMA9GydxcgRHTm/azOSkmIRJ5QkSZIUFYtsSZIkReq9dbsZl7uCfy3dQiL01wzOacSoER0Z0rERsZgFtiRJklTTWWRLkiTplEskEszM28G43DymrdhePj+/azNGjsihd5sGEaaTJEmSVNlYZEuSJOmUiccTvL5sC+Ny83hv3W4AkpNifKVXS0YOz6FTs7rRBpQkSZJUKVlkS5IkqcKVlMX524KNTJicx4db9wKQnpLEFf2yuWVYB7Ib1oo4oSRJkqTKzCJbkiRJFaawpIzn5q3jsckr2bD7AAB101O4ZlBbbhjSniZ10yNOKEmSJKkqsMiWJEnSSVdQWMIfZq5h4vRVbN9bDEDjOmncOLQ93xrYlnoZqREnlCRJklSVWGRLkiTppNm2p4jfTV/FUzPXsKeoFIBW9TO5bXgHvt43m4zU5IgTSpIkSaqKLLIlSZL0ua3buZ/fTFnJc/PWUVQaB6BT0zqMHJHDJT1bkpqcFHFCSZIkSVWZRbYkSZI+sw+27GFCbh5/fW8jZfEEAL2y6zNqRA7ndWlGUlIs4oSSJEmSqgOLbEmSJJ2wd9fuYlxuHq8v3VI+G9apMSNH5DCoQyNiMQtsSZIkSSePRbYkSZKOSyKRYNqK7Yx7O4+ZK3cAEIvBBV2bM+rsHHq0rh9tQEmSJEnVlkW2JEmSjikeT/DPJZsZPzmPhevzAUhJinFp71bcNjyHjk3rRJxQkiRJUnVnkS1JkqSjKi6N89KCDUyYnMfKbfsAyEhN4sp+bbjlrA60qp8ZcUJJkiRJNUWFHh+/c+dOrr76aurVq0f9+vW56aab2Lt37zE/ZsSIEcRisSPebrvttoqMKUmSpMMcKC5j4vRVjPjV2/zgLwtZuW0fdTNSuOPsjkz7z3P48ZfPsMSWJEmSdEpV6Irsq6++mk2bNvH6669TUlLCDTfcwLe//W2eeeaZY37cLbfcwk9/+tPy92vVqlWRMSVJkgTk7y/hyZmrmThjNTv3FQPQuE46Nw9rz9UD2lA3IzXihJIkSZJqqgorspctW8Zrr73G3Llz6du3LwAPP/wwF110Eb/+9a9p2bLlJ35srVq1aN68eUVFkyRJ0mG2FhTy22mreHr2WvYWlQKQ3TCTW8/K4Wt9WpORmhxxQkmSJEk1XYUV2TNnzqR+/frlJTbAeeedR1JSErNnz+arX/3qJ37s008/zVNPPUXz5s255JJLuOeeez5xVXZRURFFRUXl7xcUFJy834QkSVI1tnbHfh6bksef56+nuDQOQOdmdRl1dg4Xd29BSnKF7kInSZIkScetworszZs307Rp0yO/WEoKDRs2ZPPmzZ/4cd/85jdp27YtLVu2ZOHChfznf/4ny5cv54UXXjjq/e+9915+8pOfnNTskiRJ1dn7mwsYn5vH39/bSDwRZme2qc+oER055/SmJCXFog0oSZIkSf/mhIvsH/7wh/zf//3fMe+zbNmyzxzo29/+dvmvu3fvTosWLTj33HPJy8sjJyfnY/e/++67GTNmTPn7BQUFZGdnf+avL0mSVF3NX7OTcW/n8eb7W8tnZ53WhFEjchjQviGxmAW2JEmSpMrphIvs733ve1x//fXHvE+HDh1o3rw5W7duPWJeWlrKzp07T2j/6wEDBgCwYsWKoxbZ6enppKenH/fnkyRJqkkSiQSTP9jGuNw85qzaCUAsBhd1a8HIETl0a5UVcUJJkiRJ+nQnXGQ3adKEJk2afOr9Bg0axO7du5k/fz59+vQB4K233iIej5eX08djwYIFALRo0eJEo0qSJNVYZfEE/1i8ifG5eSzZGM4QSU2OcVnv1tw6vAMdmtSJOKEkSZIkHb9YIpFIVNQnv/DCC9myZQsTJkygpKSEG264gb59+/LMM88AsGHDBs4991yefPJJ+vfvT15eHs888wwXXXQRjRo1YuHChdx11120bt2ayZMnH9fXLCgoICsri/z8fOrVq1dRvzVJkqRKqbg0zovvrmfC5JWs2r4PgMzUZL45oA03D2tPi6zMiBNKkiRJUnAiXW6FHfYI8PTTT3PHHXdw7rnnkpSUxOWXX85DDz1UfntJSQnLly9n//79AKSlpfHGG28wduxY9u3bR3Z2Npdffjn/8z//U5ExJUmSqrx9RaX8cc5anpi6is0FhQBkZaZy3eB2XD+4HQ1rp0WcUJIkSZI+uwpdkR0FV2RLkqSaZPf+YibNWM2kGavZvb8EgKZ107llWAeuGtCGOukVum5BkiRJkj6zSrMiW5IkSRVjc34hT0xdyTNz1rK/uAyAto1qcdvwHC47sxXpKckRJ5QkSZKkk8ciW5IkqQpZvX0fj03J4/n5GyguiwPQpUU9Ro7I4aJuzUlJToo4oSRJkiSdfBbZkiRJVcCSjfmMz83j1UWbiB/cGK5fuwaMGtGREZ2bEIvFog0oSZIkSRXIIluSJKkSm7NqJ+NyV5C7fFv57OzOTRh1dkf6tWsYYTJJkiRJOnUssiVJkiqZRCJB7vJtjMtdwdzVuwBIisHFPVoycngOXVt6oLUkSZKkmsUiW5IkqZIoiyd4ZdEmxufmsWxTAQBpyUlc3qc1t57VgXaNa0ecUJIkSZKiYZEtSZIUsaLSMp6fv4HHpuSxZsd+AGqlJXP1gDbcPKwDzeplRJxQkqTKIR6PU1xcHHUMSdIJSEtLIynp8x9Kb5EtSZIUkb1FpTwzew1PTF3F1j1FADSolcr1g9tz3eC21K+VFnFCSZIqj+LiYlatWkU8Ho86iiTpBCQlJdG+fXvS0j7f8xuLbEmSpFNs575iJk1fxe9nriH/QAkAzetlcMtZHbiqfza10nyIJknS4RKJBJs2bSI5OZns7OyTsrJPklTx4vE4GzduZNOmTbRp04ZYLPaZP5fPkiRJkk6RjbsP8PjUlTw7Zx0HSsoA6NC4NrcNz+HS3q1IS/FJuSRJR1NaWsr+/ftp2bIltWrVijqOJOkENGnShI0bN1JaWkpqaupn/jwW2ZIkSRUsb9teJuTm8dKCDZSUJQA4o2U9Ro3oyBe7NSc56bOvSpAkqSYoKwsvAH/ey9IlSafeR9+7y8rKLLIlSZIqo8Ub8hmXu4J/LN5MIvTXDGjfkFFnd+SsTo0/12V1kiTVRP7slKSq52R977bIliRJOokSiQSzVu5kXO4Kpn64vXx+7ulNGXV2Dn3aNowwnSRJkiRVTW7EKEmSdBLE4wleX7qFy8bP4KrHZzH1w+0kxeArvVry2uhh/Pb6fpbYkiSJ3NxcYrEYu3fvjjrKMf34xz+mV69eUcc4phEjRjB69OhT8rWi/nObPn063bt3JzU1lUsvvTSSDB+5/vrrI8+gmskV2ZIkSZ9DaVmclxduYnxuHsu37AEgLSWJr/dpza1n5dCmkQdSSZKkyi0Wi/Hiiy+eknJyxIgR9OrVi7Fjxx4xnzRpEqNHj670BX9UxowZQ69evfjHP/5BnTp1TsnXXL16Ne3bt+fdd9894kWNBx98kMRH++ZJp5BFtiRJ0mdQWFLGn+ev5zdT8li38wAAddJTuHpgG24a0p6m9TIiTihJkiqb4uLiqCPoU5SVlRGLxUhKqlybGOTl5XHbbbfRunXrqKOQlZUVdQTVUJXrX6UkSVIlt6ewhAmT8xj2y7e556XFrNt5gIa10/j++acx/T/P4e4Lu1hiS5IkIKw+vuOOOxg9ejSNGzfmggsuKL9t/vz59O3bl1q1ajF48GCWL19+xMeOHz+enJwc0tLS6Ny5M3/4wx+O++vu3r2bW2+9lWbNmpGRkUG3bt14+eWXj3rfdu3aAfDVr36VWCxW/v5H/vCHP9CuXTuysrK48sor2bNnT/lt8Xice++9l/bt25OZmUnPnj35y1/+ctw5j+Vo21eMHj2aESNGHDErLS3ljjvuICsri8aNG3PPPfccsVq4qKiI73//+7Rq1YratWszYMAAcnNzy2+fNGkS9evX529/+xtdu3YlPT2dtWvXHlfG559/njPOOIP09HTatWvHfffdd8Tt48aNo1OnTmRkZNCsWTO+9rWvld/2l7/8he7du5OZmUmjRo0477zz2Ldv38e+xurVq4nFYuzYsYMbb7yRWCzGpEmTynMf7qWXXjriUL2Ptof5tD/DX/7yl3Ts2JH09HTatGnD//7v/wLQvn17AHr37k0sFiv/f//vfzZFRUXceeedNG3alIyMDIYOHcrcuXPLb/9oW5Y333zzmH/npU9jkS1JknQcduwt4tf/XM6QX7zFL/7xPtv2FNEyK4MfX9KV6f95Dnec04msWqlRx5QkqUZIJBLsLy6N5O1Et1T4/e9/T1paGtOnT2fChAnl8//+7//mvvvuY968eaSkpHDjjTeW3/biiy/y3e9+l+9973ssXryYW2+9lRtuuIG33377U79ePB7nwgsvZPr06Tz11FMsXbqUX/ziFyQnJx/1/h8VjhMnTmTTpk1HFJB5eXm89NJLvPzyy7z88stMnjyZX/ziF+W333vvvTz55JNMmDCBJUuWcNddd/Gtb32LyZMnn9D/o8/j97//PSkpKcyZM4cHH3yQ+++/nyeeeKL89jvuuIOZM2fy7LPPsnDhQr7+9a/zxS9+kQ8//LD8Pvv37+f//u//eOKJJ1iyZAlNmzb91K87f/58vvGNb3DllVeyaNEifvzjH3PPPfcwadIkAObNm8edd97JT3/6U5YvX85rr73GWWedBcCmTZu46qqruPHGG1m2bBm5ublcdtllR/27lZ2dzaZNm6hXrx5jx45l06ZNXHHFFcf9/+fT/gzvvvtufvGLX3DPPfewdOlSnnnmGZo1awbAnDlzAHjjjTfYtGkTL7zwwlG/xg9+8AOef/55fv/73/POO+/QsWNHLrjgAnbu3HnE/Y71d146Hm4tIkmSdAwbdh/g8SkreXbuWgpL4gDkNKnNbcNz+EqvVqSluC5AkqRT7UBJGV1/9M9IvvbSn15ArbTjr1M6derEL3/5y/L3N23aBMD//u//Mnz4cAB++MMfcvHFF1NYWEhGRga//vWvuf766xk1ahQQ9keeNWsWv/71rzn77LOP+fXeeOMN5syZw7JlyzjttNMA6NChwyfev0mTJgDUr1+f5s2bH3FbPB5n0qRJ1K1bF4BrrrmGN998k//93/+lqKiIn//857zxxhsMGjSo/OtMmzaNxx57rPz3djTjxo07omyGsLI6I+PEr2rLzs7mgQceIBaL0blzZxYtWsQDDzzALbfcwtq1a5k4cSJr166lZcuWAHz/+9/ntddeY+LEifz85z8HoKSkhHHjxtGzZ8/j/rr3338/5557Lvfccw8Ap512GkuXLuVXv/oV119/PWvXrqV27dp86Utfom7durRt25bevXsD4e9AaWkpl112GW3btgWge/fuR/06ycnJNG/enFgsRlZW1sf+jD7Nsf4M9+zZw4MPPsgjjzzCddddB0BOTg5Dhw4FDv3daNSo0Sd+3X379jF+/HgmTZrEhRdeCMDjjz/O66+/zm9/+1v+4z/+o/y+x/o7Lx0Pi2xJkqSjWLF1LxMm5/HSuxsojYfVMT1aZzFqRA7nd21OUlLsUz6DJEkS9OnT56jzHj16lP+6RYsWAGzdupU2bdqwbNkyvv3tbx9x/yFDhvDggw9+6tdbsGABrVu3Li+xP4927dqVF6Af5dy6dSsAK1asYP/+/XzhC1844mOKi4vLC9tPcvXVV/Pf//3fR8xeeOGF8mL5RAwcOPCI7TQGDRrEfffdR1lZGYsWLaKsrOxj/y+Kiopo1KhR+ftpaWlH/Hkcj2XLlvGVr3zliNmQIUMYO3YsZWVlfOELX6Bt27Z06NCBL37xi3zxi1/kq1/9KrVq1aJnz56ce+65dO/enQsuuIDzzz+fr33tazRo0OCEf/+f5lh/hsuWLaOoqIhzzz33M3/+vLw8SkpKGDJkSPksNTWV/v37s2zZsiPue6y/89LxsMiWJEk6zML1uxn3dh7/XLqZj67uHJzTiFEjOjKkY6MjnihJkqRoZKYms/SnF3z6HSvoa5+I2rVrH3WemnpoS7KPHl/E4/HPHuygzMzMz/05PnJ4Rgg5P8q4d+9eAF555RVatWp1xP3S09OP+XmzsrLo2LHjEbN/384jKSnpY1ttlJSUHH/4gxmTk5OZP3/+x7ZWqVOnTvmvMzMzT/pjvLp16/LOO++Qm5vLv/71L370ox/x4x//mLlz51K/fn1ef/11ZsyYwb/+9S8efvhh/vu//5vZs2eX70v9aY73/8+x/gxP5t+V41FRf+dVc1hkS5KkGi+RSDAzbwfjcvOYtmJ7+fz8rs0YOSKH3m1O/uoYSZL02cVisRPa3qOq6dKlC9OnTy/f7gFg+vTpdO3a9VM/tkePHqxfv54PPvjguFdlp6amUlZWdkIZDz8Y8VjbiHxWTZo0YfHixUfMFixY8LFidvbs2Ue8P2vWLDp16kRycjK9e/emrKyMrVu3MmzYsJOa76M/o8NNnz6d0047rbw0T0lJ4bzzzuO8887j//v//j/q16/PW2+9xWWXXUYsFmPIkCEMGTKEH/3oR7Rt25YXX3yRMWPGHNfXb9KkCXv27GHfvn3lL5YsWLDghH4PnTp1IjMzkzfffJObb775Y7enpaUBHPPvxkcHkk6fPr18m5SSkhLmzp3L6NGjTyiP9Gmq73d9SZKkTxGPJ3hj2RYezc3jvXW7AUhOivGVni25bUQOpzWre+xPIEmSVAH+4z/+g2984xv07t2b8847j7///e+88MILvPHGG5/6scOHD+ess87i8ssv5/7776djx468//77xGIxvvjFLx71Y9q1a8ebb77JkCFDSE9PP64tLurWrcv3v/997rrrLuLxOEOHDiU/P5/p06dTr169I0r4z+Kcc87hV7/6FU8++SSDBg3iqaeeYvHixR/btmTt2rWMGTOGW2+9lXfeeYeHH36Y++67Dwj7Vl999dVce+213HffffTu3Ztt27bx5ptv0qNHDy6++OLPnO973/se/fr142c/+xlXXHEFM2fO5JFHHmHcuHEAvPzyy6xcuZKzzjqLBg0a8OqrrxKPx+ncuTOzZ8/mzTff5Pzzz6dp06bMnj2bbdu20aVLl+P++gMGDKBWrVr813/9F3feeSezZ88uP2jyeGVkZPCf//mf/OAHPyAtLY0hQ4awbds2lixZwk033UTTpk3JzMzktddeo3Xr1mRkZJCVlXXE56hduzYjR47kP/7jP2jYsCFt2rThl7/8Jfv37+emm246oTzSp7HIliRJNU5JWZy/v7eR8bl5fLg1XBabnpLEFf2yuWVYB7Ib1oo4oSRJqskuvfRSHnzwQX7961/z3e9+l/bt2zNx4kRGjBhxXB///PPP8/3vf5+rrrqKffv20bFjR37xi1984v3vu+8+xowZw+OPP06rVq1YvXr1cX2dn/3sZzRp0oR7772XlStXUr9+fc4880z+67/+67g+/lguuOAC7rnnHn7wgx9QWFjIjTfeyLXXXsuiRYuOuN+1117LgQMH6N+/P8nJyXz3u989Yn/xiRMn8v/+3//je9/7Hhs2bKBx48YMHDiQL33pS58r35lnnslzzz3Hj370I372s5/RokULfvrTn3L99dcD4fDMF154gR//+McUFhbSqVMn/vjHP3LGGWewbNkypkyZwtixYykoKKBt27bcd9995YclHo+GDRvy1FNP8R//8R88/vjjnHvuufz4xz/+2N7qn+aee+4hJSWFH/3oR2zcuJEWLVpw2223AWFF+UMPPcRPf/pTfvSjHzFs2DByc3M/9jl+8YtfEI/Hueaaa9izZw99+/bln//8Z4Xs+a2aLZb49w11qriCggKysrLIz8+nXr16UceRJEmVSGFJGc/NW8djk1eyYfcBAOqmp3DNoLbcMKQ9Teoeez9HSZIUjcLCQlatWkX79u3JyMiIOo4k6QQc63v4iXS5rsiWJEnVXkFhCX+YuYaJ01exfW8xAI3rpHHDkPZcM6gt9TJSP+UzSJIkSZKiZJEtSZKqrW17ivjd9FU8NXMNe4pKAWhVP5Nbh3fgG32zyUhN/pTPIEmSVLk8/fTT3HrrrUe9rW3btixZsuQUJ5KkU8MiW5IkVTvrdu7nN1NW8ty8dRSVxgHo1LQOI0fkcEnPlqQmJ0WcUJIk6bP58pe/zIABA456W2qqV5lJqr4ssiVJUrXxwZY9TMjN+//bu/+4mu/+f+CPd+mXOpWTpDgpSfKjECoWaW1q06XN77VV1xJSWRcR25Qf29hofrXM2KptWdduI1xjxoVizW/LhVKTONf8mIykuIrT+f7h0/vrTFpRvc/hcb/dut2c8/71OO9zXuH5fp3nG1tOXIKq9v5tQPoqLDHN1wn+rjbQ0xMkTkhERET0ZGQyGWQymdQxiIhaHQvZREREpPN+Ud5Aak4JdhX8Lj7n49weUb5O8O5qBUFgAZuIiIiIiEiXsZBNREREOkmtVuOns9eQurcEB879AQAQBGBEz46YNtwJbp0tpQ1IREREREREzYaFbCIiItIptbVq7Cy4gk/2luDkxZsAgDZ6AoL7dcLUYU7o1sFM4oRERERERETU3FjIJiIiIp1wV1WLzb9cxKe5JSgpqwIAGBvoYcJAe0QO7YpOliYSJyQiIiIiIqKWwkI2ERERabU7NSpkHVFi3b5zuHTzfwAAmXEbhA92QPhgB1iZGUmckIiIiIiIiFoaC9lERESklW7euYuvDpzHF3nncb2qBgDQ3swIk3wcEeJpD5mxgcQJiYiIiIiIqLXoSR2AiIiI6EFXb/0Pi38oxJAle7BsZzGuV9VAITfBe8G98VPCcEwd5sQiNhERET0TfH19ERcX12rHS09Ph6WlZascq7leW3h4OIKDg594P3+lNc9NQ27fvo3Ro0fD3NwcgiCgvLy80dsKgoDNmze3WLYnlZOT0+TX9CRae3w9SK1WY/LkyZDL5RAEAfn5+ZLkAIDz589LnqGxWMgmIiIiraD84zbeyT6J5z7ci7W551BZfQ8uNjKsnNAXe2f64nWvLjA20Jc6JhEREVGr2bRpExYtWtQi+3ZwcMCKFStaZN+taeXKlUhPT2/WfdZ3bsaPH4/i4uJmPc7jyMjIwP79+/Hzzz/j8uXLsLCweGid+fPno2/fvq2Sp6Hi89PyGWsJO3bsQHp6Or7//ntcvnwZvXv3bpXj1nfhR6FQtGqGJ8HWIkRERCSpM1cqsCanBN//5zJUtWoAQH97S0zz7Qa/Hh2gpydInJCIiIhIGnK5XOoIWkulUkEQhHoLuS3BxMQEJibS31y8pKQErq6uOlF01BY1NTUwNDSUOoaGkpIS2NraYvDgwVJHgb6+Pjp27Ch1jEbhjGwiIiKSxLEL1xGRfgQBK/ZjS/4lqGrVGNrdGlmTvbAxajD8e9qwiE1ERET1U6uBmippftTqRsf09fVFTEwMYmJiYGFhgfbt22PevHlQP7CP1NRUODs7w9jYGDY2NhgzZozG9o1tfVBdXY2EhAQoFAoYGRmhW7du+Pzzzx+Z68KFC/jHP/4BQRAgCJr/5vrxxx/h6uoKMzMzBAQE4PLlyxrL169fD1dXVxgbG6NHjx5ITU1tMFtVVRVCQ0NhZmYGW1tbJCcn15s/Pj4enTp1gqmpKTw9PZGTkyMur2vtsXXrVvTs2RNGRkZQKpUaM0w/++wz2NnZoba2VmPfo0aNwptvvgngfgFx1KhRsLGxgZmZGQYOHIh///vff3luHmwtUlxcDEEQcObMGY3jLF++HE5OTuLjU6dOITAwEGZmZrCxscEbb7yBa9euNXiuNm7ciF69esHIyAgODg4a58rX1xfJycnYt28fBEGAr6/vQ9unp6djwYIFOHHihJj/wRnr165dwyuvvIK2bdvC2dkZW7du1dj+cTI3Rn3tK8rLyyEIgsb7DAB5eXlwc3ODsbExvLy8cOrUKY3lP/30E3x8fGBiYgKFQoHp06ejqqpKXO7g4IBFixYhNDQU5ubmmDx5cqMy3rhxA6GhoWjXrh3atm2LwMBA/Prrr+LyCxcuICgoCO3atYOpqSl69eqF7du3i9uGhITA2toaJiYmcHZ2RlpaWr3HCQ8PR2xsLJRKJQRBgIODg5j7zzPY+/bti/nz54uPBUHA+vXrG3wPT58+jZEjR8Lc3BwymQw+Pj4oKSnB/PnzkZGRgS1btoifjZycnHrfm9zcXAwaNAhGRkawtbXFnDlzcO/ePXG5r68vpk+fjtmzZ0Mul6Njx44aOVtKi83Ifv/997Ft2zbk5+fD0NCwUf1t1Go1kpKSsG7dOpSXl2PIkCFYs2YNnJ2dWyomERERtSK1Wo3c4jKk5pTgcOl1AIAgAC/1tkWUrxN6d2qdGTVERESk4+7eBj6wk+bYb18CDE0bvXpGRgYiIiJw+PBhHD16FJMnT4a9vT0iIyNx9OhRTJ8+HV999RUGDx6M69evY//+/Y8VKzQ0FAcOHMCqVavg7u6O0tLSRxYgN23aBHd3d0yePBmRkZEay27fvo1ly5bhq6++gp6eHl5//XXEx8cjMzMTAJCZmYnExESkpKSgX79++OWXXxAZGQlTU1OEhYXVe7xZs2YhNzcXW7ZsQYcOHfD222/j+PHjGu0vYmJiUFBQgKysLNjZ2SE7OxsBAQE4efKkWBe6ffs2PvzwQ6xfvx5WVlbo0KGDxnHGjh2L2NhY7N27F88//zwA4Pr169ixY4dYcKysrMRLL72E999/H0ZGRvjyyy8RFBSEoqIi2NvbN3hu6nTv3h0DBgxAZmamRuuXzMxMvPbaawDuF2n9/PwwadIkLF++HHfu3EFCQgLGjRuHPXv21LvfY8eOYdy4cZg/fz7Gjx+Pn3/+GdOmTYOVlRXCw8OxadMmzJkzB6dOncKmTZvqnWU8fvx4nDp1Cjt27BAL9A/OWl+wYAE++ugjLF26FKtXr0ZISAguXLgAuVz+WJlbwqxZs7By5Up07NgRb7/9NoKCglBcXAwDAwOUlJQgICAA7733Hr744guUlZWJF4seLBwvW7YMiYmJSEpKavRxw8PD8euvv2Lr1q0wNzdHQkICXnrpJRQUFMDAwADR0dGoqanBvn37YGpqioKCApiZmQEA5s2bh4KCAvzwww9o3749zp49izt37tR7nJUrV8LJyQmfffYZjhw5An39prVPbOg9vHjxIoYOHQpfX1/s2bMH5ubmyMvLw7179xAfH4/CwkJUVFSI50oul+PSpUsa+7948SJeeuklhIeH48svv8SZM2cQGRkJY2NjjWJ1RkYGZsyYgUOHDuHAgQMIDw/HkCFD8MILLzTp9TRFixWya2pqMHbsWHh7ez/yCuCfffTRR1i1ahUyMjLg6OiIefPmYcSIESgoKICxsXFLRSUiIqIWpqpV44dTl7EmpwSnL1UAAAz0BbzarzOmDOuKrtZmEickIiIiahkKhQLLly+HIAhwcXHByZMnsXz5ckRGRkKpVMLU1BQjR46ETCZDly5d0K9fvyYfo7i4GN9++y127doFf39/AEDXrl0fub5cLoe+vj5kMtlDLQXu3r2LTz/9VJxZHBMTg4ULF4rLk5KSkJycjFdffRUA4OjoiIKCAqxdu7beQnZlZSU+//xzfP3112JxOSMjA507dxbXUSqVSEtLg1KphJ3d/QsU8fHx2LFjB9LS0vDBBx+I2VJTU+Hu7l7v62rXrh0CAwOxYcMG8Vjfffcd2rdvj+HDhwMA3N3dNbZftGgRsrOzsXXrVsTExDR4bh4UEhKClJQUsZBdXFyMY8eO4euvvwYAsdBflx0AvvjiCygUChQXF6N79+4P7fPjjz/G888/j3nz5gG4XzAvKCjA0qVLER4eDrlcjrZt28LQ0PCR2UxMTGBmZoY2bdrUu054eDgmTpwIAPjggw+watUqHD58GAEBAY+Vuc6D72ed27dvP3L9hiQlJYnF0LrPSnZ2NsaNG4fFixcjJCRE/KaCs7MzVq1ahWHDhmHNmjVi/dDPzw8zZ85s9DHrCth5eXliu4/MzEwoFAps3rwZY8eOhVKpxOjRo9GnTx8AmmNMqVSiX79+GDBgAACIs6zrY2FhAZlM9tgtPRp6Dz/55BNYWFggKysLBgYGAKDxvpmYmKC6urrB46ampkKhUCAlJQWCIKBHjx64dOkSEhISkJiYCD29+w0+3NzcxAsFzs7OSElJwe7du3WzkL1gwQIAaHTDfbVajRUrVuDdd9/FqFGjAABffvklbGxssHnzZkyYMKGloj41rlfVoOD/igNERETa4sL1KqzfX4rSa/e/7mdioI/XPO0xyccRthbS9xkkIiIiHWTQ9v7MaKmO3QReXl4arTu8vb2RnJwMlUqFF154AV26dEHXrl0REBCAgIAAsWVAU+Tn50NfXx/Dhg1r0nb1adu2rUZ7DFtbW1y9ehXA/RYhJSUliIiI0JitfO/evUf2qi4pKUFNTQ08PT3F5+RyOVxcXMTHJ0+ehEqleqhQWl1dDSsrK/GxoaEh3NzcGswfEhKCyMhIpKamwsjICJmZmZgwYYJYfKusrMT8+fOxbds2XL58Gffu3cOdO3egVCr/6tRomDBhAuLj43Hw4EF4eXkhMzMT/fv3R48ePQAAJ06cwN69e8UZu38+J/UVhQsLC8WaWJ0hQ4ZgxYoVUKlUTZ65W58Hz5+pqSnMzc3F9/dxMtfZv38/ZDKZxnP1tT5pDG9vb/HPdZ+VwsJCMeN//vMf8RsCwP2aYm1tLUpLS+Hq6goAYkG5sQoLC9GmTRuNz6mVlZXGsadPn46oqCjs3LkT/v7+GD16tHg+o6KiMHr0aBw/fhwvvvgigoODW6z/dUPvYX5+Pnx8fMQi9uMoLCyEt7e3xu+tIUOGoLKyEr/99hvs7e0fygFo/q5oKVpzs8fS0lJcuXJFvHII3L9C4enpiQMHDjyykF1dXY3q6mrxcUXFs1vIPfFbOf6edkTqGERERPWyMDFA+GAHhA12gNxUu262QkRERDpGEJrU3kNbyWQyHD9+HDk5Odi5cycSExMxf/58HDlyROzH3BjNeRPCPxfABEEQe3pXVlYCANatW6dR8APwREXWyspK6Ovr49ixYw/t58GiqomJyUP9vP8sKCgIarUa27Ztw8CBA7F//34sX75cXB4fH49du3Zh2bJl6NatG0xMTDBmzBjU1NQ0KXPHjh3h5+eHDRs2wMvLCxs2bEBUVJTGawoKCsKHH3740La2trZNOlZzqu/9resp/iSZHR0dH/rMtmnz/8uOdRcSHuwPf/fu3SZlr8s4ZcoUTJ8+/aFldQVW4H6Bt7lNmjQJI0aMwLZt27Bz504sXrwYycnJiI2NRWBgIC5cuIDt27dj165deP755xEdHY1ly5Y1ev96enoa5weo/xw19B625g1JG8rRUrSmkH3lyhUAgI2NjcbzNjY24rL6LF68WJz9/awzM2qDHh1lf70iERFRKzJso4cgNztM9LSHmZHW/NODiIiIqFUcOnRI4/HBgwfh7OwsFmzbtGkDf39/+Pv7IykpCZaWltizZ4/YuqMx+vTpg9raWuTm5mpMEGyIoaEhVCpV418I7tdo7OzscO7cOYSEhDRqGycnJxgYGODQoUNiofHGjRsoLi4WZ5D369cPKpUKV69ehY+PT5My/ZmxsTFeffVVZGZm4uzZs3BxcUH//v3F5Xl5eQgPD8crr7wC4H5h9Pz58xr7aOy5CQkJwezZszFx4kScO3dOYxJm//79sXHjRjg4OGgUdBvi6uqKvLw8jefy8vLQvXv3Jl0oeJz3Fni8zI1lbW0NALh8+bLYPufBmws+6ODBgw99VupmWvfv3x8FBQXo1q1bs+ZzdXXFvXv3cOjQIXEm9R9//IGioiL07NlTXE+hUGDq1KmYOnUq5s6di3Xr1iE2NlZ8jWFhYQgLC4OPjw9mzZrVpEK2tbW1xo1VKyoqUFpa2qTX4ebmhoyMDNy9e7feWdmN+Wy4urpi48aNUKvV4oWjvLw8yGSyelvItKYmfSrnzJlT71WZBxUWFopfo2gNc+fOxYwZM8THFRUVUCgUrXZ8bTLQQY4dcUOljkFERERERERE/0epVGLGjBmYMmUKjh8/jtWrVyM5ORkA8P333+PcuXMYOnQo2rVrh+3bt6O2tlaj7UZjODg4ICwsDG+++aZ4s8cLFy7g6tWrGDdu3CO32bdvHyZMmAAjIyO0b9++UcdasGABpk+fDgsLCwQEBKC6uhpHjx7FjRs3NOozdczMzBAREYFZs2aJN2h85513xBm6wP0eviEhIQgNDUVycjL69euHsrIy7N69G25ubnj55ZebdD5CQkIwcuRInD59Gq+//rrGMmdnZ2zatAlBQUEQBAHz5s17aBZpY8/Nq6++iqioKERFRWH48OFif28AiI6Oxrp16zBx4kTMnj0bcrkcZ8+eRVZWFtavX19vYXrmzJkYOHAgFi1ahPHjx+PAgQNISUlBampqk16/g4MDSktLkZ+fj86dO0Mmk8HIyOgvt3uczI1lYmICLy8vLFmyBI6Ojrh69SrefffdetdduHAhrKysYGNjg3feeQft27dHcHAwACAhIQFeXl6IiYnBpEmTxJsu7tq1CykpKY+dz9nZGaNGjUJkZCTWrl0LmUyGOXPmoFOnTmK7l7i4OAQGBqJ79+64ceMG9u7dKxbYExMT4eHhgV69eqG6uhrff/+9uKyx/Pz8kJ6ejqCgIFhaWiIxMbHJ5zwmJgarV6/GhAkTMHfuXFhYWODgwYMYNGgQXFxc4ODggB9//BFFRUWwsrKqtyXQtGnTsGLFCsTGxiImJgZFRUVISkrCjBkzNMatFJp09JkzZ6KwsLDBn4ZuJtCQuibjv//+u8bzv//+e4MNyI2MjGBubq7xQ0RERERERESkDUJDQ3Hnzh0MGjQI0dHReOuttzB58mQAgKWlJTZt2gQ/Pz+4urri008/xTfffINevXo1+Thr1qzBmDFjMG3aNPTo0QORkZGoqqp65PoLFy7E+fPn4eTkJM6WbYxJkyZh/fr1SEtLQ58+fTBs2DCkp6fD0dHxkdssXboUPj4+CAoKgr+/P5577jl4eHhorJOWlobQ0FDMnDkTLi4uCA4OxpEjRzTaRTSWn58f5HI5ioqK8Nprr2ks+/jjj9GuXTsMHjwYQUFBGDFihMaMbaDx50YmkyEoKAgnTpx4aIa6nZ0d8vLyoFKp8OKLL6JPnz6Ii4uDpaXlI4uB/fv3x7fffousrCz07t0biYmJWLhwIcLDw5v0+kePHo2AgAAMHz4c1tbW+Oabbxq13eNkboovvvgC9+7dg4eHB+Li4vDee+/Vu96SJUvw1ltvwcPDA1euXMG//vUvGBreb03o5uaG3NxcFBcXw8fHB/369UNiYqLGRYTHlZaWBg8PD4wcORLe3t5Qq9XYvn27OLNZpVIhOjoarq6uCAgIQPfu3cWLDIaGhpg7dy7c3NwwdOhQ6OvrIysrq0nHnzt3LoYNG4aRI0fi5ZdfRnBwsEa/+sawsrLCnj17UFlZiWHDhsHDwwPr1q0TX0NkZCRcXFwwYMAAWFtbP/QNAADo1KkTtm/fjsOHD8Pd3R1Tp05FRETEIy88tCZB/efmK80sPT0dcXFxKC8vb3A9tVoNOzs7xMfHi3cVraioQIcOHZCent7omz1WVFTAwsICN2/eZFGbiIiIiIiI6Cnwv//9D6WlpXB0dISxsbHUcRrN19cXffv2xYoVK6SOQkQkmYZ+hzelltti88GVSiXy8/OhVCqhUqmQn5+P/Px88cYAANCjRw9kZ2cDuN8QvO5qzNatW3Hy5EmEhobCzs5O/PoAERERERERERERET17WuyOS4mJicjIyBAf1zVy37t3L3x9fQEARUVFuHnzprjO7NmzUVVVhcmTJ6O8vBzPPfccduzYoVNXW4mIiIiIiIiImtP+/fsRGBj4yOUPThokInpatXhrkdbG1iJERERERERETxddbS3SXO7cuYOLFy8+cnm3bt1aMQ0RUdM0V2uRFpuRTURERERERERET87ExITFaiJ65rVYj2wiIiIiIiIioub0lH2pnIjomdBcv7s5I5uIiIiIiIiItJqBgQEEQUBZWRmsra0hCILUkYiIqBHUajXKysogCAIMDAyeaF8sZBMRERERERGRVtPX10fnzp3x22+/4fz581LHISKiJhAEAZ07d4a+vv4T7YeFbCIiIiIiIiLSemZmZnB2dsbdu3eljkJERE1gYGDwxEVsgIVsIiIiIiIiItIR+vr6zVIMISIi3cObPRIRERERERERERGRVmMhm4iIiIiIiIiIiIi0GgvZRERERERERERERKTVnroe2Wq1GgBQUVEhcRIiIiIiIiIiIiIiepS6Gm5dTbchT10h+9atWwAAhUIhcRIiIiIiIiIiIiIi+iu3bt2ChYVFg+sI6saUu3VIbW0tLl26BJlMBkEQpI7T6ioqKqBQKPDf//4X5ubmUsch0lkcS0TNg2OJqPlwPBE1D44loubD8UTUPJ7lsaRWq3Hr1i3Y2dlBT6/hLthP3YxsPT09dO7cWeoYkjM3N3/mPvhELYFjiah5cCwRNR+OJ6LmwbFE1Hw4noiax7M6lv5qJnYd3uyRiIiIiIiIiIiIiLQaC9lEREREREREREREpNVYyH7KGBkZISkpCUZGRlJHIdJpHEtEzYNjiaj5cDwRNQ+OJaLmw/FE1Dw4lhrnqbvZIxERERERERERERE9XTgjm4iIiIiIiIiIiIi0GgvZRERERERERERERKTVWMgmIiIiIiIiIiIiIq3GQjYRERERERERERERaTUWsomIiIiIiIiIiIhIq7GQ/RT729/+Bnt7exgbG8PW1hZvvPEGLl26JHUsIp1y/vx5REREwNHRESYmJnByckJSUhJqamqkjkakk95//30MHjwYbdu2haWlpdRxiHTGJ598AgcHBxgbG8PT0xOHDx+WOhKRztm3bx+CgoJgZ2cHQRCwefNmqSMR6aTFixdj4MCBkMlk6NChA4KDg1FUVCR1LCKdtGbNGri5ucHc3Bzm5ubw9vbGDz/8IHUsrcVC9lNs+PDh+Pbbb1FUVISNGzeipKQEY8aMkToWkU45c+YMamtrsXbtWpw+fRrLly/Hp59+irffflvqaEQ6qaamBmPHjkVUVJTUUYh0xj//+U/MmDEDSUlJOH78ONzd3TFixAhcvXpV6mhEOqWqqgru7u745JNPpI5CpNNyc3MRHR2NgwcPYteuXbh79y5efPFFVFVVSR2NSOd07twZS5YswbFjx3D06FH4+flh1KhROH36tNTRtJKgVqvVUoeg1rF161YEBwejuroaBgYGUsch0llLly7FmjVrcO7cOamjEOms9PR0xMXFoby8XOooRFrP09MTAwcOREpKCgCgtrYWCoUCsbGxmDNnjsTpiHSTIAjIzs5GcHCw1FGIdF5ZWRk6dOiA3NxcDB06VOo4RDpPLpdj6dKliIiIkDqK1uGM7GfE9evXkZmZicGDB7OITfSEbt68CblcLnUMIiJ6BtTU1ODYsWPw9/cXn9PT04O/vz8OHDggYTIiIqL7bt68CQD8PxLRE1KpVMjKykJVVRW8vb2ljqOVWMh+yiUkJMDU1BRWVlZQKpXYsmWL1JGIdNrZs2exevVqTJkyReooRET0DLh27RpUKhVsbGw0nrexscGVK1ckSkVERHRfbW0t4uLiMGTIEPTu3VvqOEQ66eTJkzAzM4ORkRGmTp2K7Oxs9OzZU+pYWomFbB0zZ84cCILQ4M+ZM2fE9WfNmoVffvkFO3fuhL6+PkJDQ8FuMkRNH0sAcPHiRQQEBGDs2LGIjIyUKDmR9nmc8UREREREui86OhqnTp1CVlaW1FGIdJaLiwvy8/Nx6NAhREVFISwsDAUFBVLH0krska1jysrK8McffzS4TteuXWFoaPjQ87/99hsUCgV+/vlnfkWBnnlNHUuXLl2Cr68vvLy8kJ6eDj09XgckqvM4fzexRzZR49TU1KBt27b47rvvNHr5hoWFoby8nN+2I3pM7JFN9ORiYmKwZcsW7Nu3D46OjlLHIXpq+Pv7w8nJCWvXrpU6itZpI3UAahpra2tYW1s/1ra1tbUAgOrq6uaMRKSTmjKWLl68iOHDh8PDwwNpaWksYhP9yZP83UREDTM0NISHhwd2794tFtxqa2uxe/duxMTESBuOiIieSWq1GrGxscjOzkZOTg6L2ETNrLa2lrW7R2Ah+yl16NAhHDlyBM899xzatWuHkpISzJs3D05OTpyNTdQEFy9ehK+vL7p06YJly5ahrKxMXNaxY0cJkxHpJqVSievXr0OpVEKlUiE/Px8A0K1bN5iZmUkbjkhLzZgxA2FhYRgwYAAGDRqEFStWoKqqCn//+9+ljkakUyorK3H27FnxcWlpKfLz8yGXy2Fvby9hMiLdEh0djQ0bNmDLli2QyWTiPRssLCxgYmIicToi3TJ37lwEBgbC3t4et27dwoYNG5CTk4Mff/xR6mhaia1FnlInT57EW2+9hRMnTqCqqgq2trYICAjAu+++i06dOkkdj0hnpKenP7JQwF+fRE0XHh6OjIyMh57fu3cvfH19Wz8QkY5ISUnB0qVLceXKFfTt2xerVq2Cp6en1LGIdEpOTg6GDx/+0PNhYWFIT09v/UBEOkoQhHqfT0tLQ3h4eOuGIdJxERER2L17Ny5fvgwLCwu4ubkhISEBL7zwgtTRtBIL2URERERERERERESk1djolYiIiIiIiIiIiIi0GgvZRERERERERERERKTVWMgmIiIiIiIiIiIiIq3GQjYRERERERERERERaTUWsomIiIiIiIiIiIhIq7GQTURERERERERERERajYVsIiIiIiIiIiIiItJqLGQTERERERERERERkVZjIZuIiIiIiIiIiIiItBoL2URERERERERERESk1VjIJiIiIiIiIiIiIiKt9v8A9r56BbWYndEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here's an example of rho and psi\n",
    "import numpy as np; import matplotlib.pyplot as plt\n",
    "\n",
    "@np.vectorize\n",
    "def huber_loss(t,c):\n",
    "    if np.abs(t)<=c:\n",
    "        return t**2/2\n",
    "    return c*np.abs(t)-c**2/2\n",
    "\n",
    "@np.vectorize\n",
    "def huber_slope(t,c):\n",
    "    if t>c:\n",
    "        return c\n",
    "    elif t<-c:\n",
    "        return -c\n",
    "    else:\n",
    "        return t\n",
    "\n",
    "t = np.linspace(-3.,3.,100); plt.figure(figsize=(18,5)); plt.plot(t, huber_slope(t,1.), label=\"rho_c the Huber loss function\"); plt.plot(t, huber_loss(t,1.), label=\"psi_c the derivative of the Huber loss function\"); plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-quantile\"></a>\n",
    "\n",
    "## 8.6.B Quantile Regression with Quantile Loss ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "$$\\text{For quantile } q \\quad \\rho_q(t) = \\left\\{\\begin{array}{ll}(1-q) t &t \\leq 0\\\\ qt & t> 0 \\end{array}\\right. \\quad \\text{ then } \\quad \\psi_q(t) = \\left\\{\\begin{array}{ll}(1-q) &t \\leq 0\\\\ q & t > 0 \\end{array}\\right. \\quad \\text{ and } \\quad \\psi'_q(t) = 0  $$\n",
    "\n",
    "$$\\nabla_\\beta \\sum_{i=1}^n \\rho_q(y_i-x_i^T \\beta) = \\sum_{i=1}^n -\\psi_q(y_i-x_i^T \\beta)x_i = \\sum_{i=1}^n -\\psi_q(y-X\\beta)x_i = -X^T\\psi_q(y-X\\beta)$$\n",
    "\n",
    "\n",
    "and while there is no ***Hessian*** we can still use ***observed Fisher information*** (positive) ***Hessian*** approximation for ***M estimation***... \n",
    "\n",
    "\\begin{align*}\n",
    "\\mathcal{I}(\\beta) & = {} \\sum_{i=1}^n \\mathcal{I}_i(\\beta) = \\sum_{i=1}^n x_i\\psi_q(y_i-x_i^T \\beta)^2 x_i^T = X^T W X \\quad \\text{ with $W_{ij}=0$ and $W_{ij}=\\psi_q(y_i-x_i^T \\beta)^2$}\\\\\n",
    "\\beta^{(t+1)} & = {} \\beta^{(t)} + (X^TWX)^{-1} X^T\\psi(y-X\\beta^{(t)}) \\quad\\quad\\quad\\quad \\color{gray}{\\text{[subtraction and negative gradient cancel]}}\\\\\n",
    "& = {} (X^TWX)^{-1} X^TW \\overset{\\text{weighted least squares outcome variable}}{{\\left[X\\beta^{(t)}  +  W^{-1}\\psi(y-X\\beta^{(t)}) \\right]}}\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-quantile-1\"></a>\n",
    "\n",
    "## 8.6.B Quantile Regression with Quantile Loss\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "nndM1Rkp6U3a",
    "outputId": "b8e16183-163f-4819-8673-4037f5b30119"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@np.vectorize\n",
    "def quantile_loss(t,q):\n",
    "    if t<=0:\n",
    "        return (q-1)*t\n",
    "    return q*t\n",
    "\n",
    "@np.vectorize\n",
    "def quantile_gradient(t,q):\n",
    "    if t<=0:\n",
    "        return q-1\n",
    "    return q\n",
    "\n",
    "t = np.linspace(-3.,3.,100); plt.figure(figsize=(18,8)); plt.plot(t, quantile_loss(t,0.5), 'k', label=\"rho_q=0.5 the quantile loss function\"); plt.plot(t, quantile_gradient(t,0.5), 'k--', label=\"rho_q=0.5 the quantile loss function gradient\"); plt.plot(t, quantile_loss(t,0.33), 'b', label=\"rho_q=0.33 the quantile loss function\"); plt.plot(t, quantile_gradient(t,0.33), 'b--', label=\"rho_q=0.33 the quantile loss function gradient\"); plt.plot(t, quantile_loss(t,0.8), 'r', label=\"rho_q=0.80 the quantile loss function\"); plt.plot(t, quantile_gradient(t,0.8), 'r--', label=\"rho_q=0.8 the quantile loss function gradient\"); plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-quantile-2\"></a>\n",
    "\n",
    "## 8.6.B Quantile Regression with Quantile Loss\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "n = 500; beta = np.ones((2,1)); X = 5*stats.uniform().rvs(size=(n,2)); X[:,0]=1; y = (X@beta)[:,0] + stats.norm.rvs(size = n)\n",
    "beta_ = np.ones((2,1))*0.5\n",
    "for i in range(10):\n",
    "    grad = -X.T.dot(quantile_gradient(y - (X@beta_)[:,0], 0.85)); grad = grad.reshape(2,1)\n",
    "    FI = X.T@np.diag(quantile_gradient(y - (X@beta_)[:,0], 0.85)**2)@X\n",
    "    #beta_ = beta_ - 0.001*grad \n",
    "    #beta_ = beta_ - np.linalg.inv(FI)@grad\n",
    "    beta_ = beta_ - np.linalg.solve(FI,grad) # beta_ = np.linalg.solve(FI,FI@beta_-grad)\n",
    "plt.figure(figsize=(18,9)); plt.plot(X[:,1], y, '.'); x = np.linspace(0,5,100); plt.plot(x, beta_[0]+beta_[1]*x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a name=\"cell-opt-fx-quantile-3\"></a>\n",
    "\n",
    "## 8.6.B Quantile Regression with Quantile Loss\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm \n",
    "# https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.WLS.html\n",
    "# https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.OLS.html\n",
    "beta_ = np.ones((2,1))*0.5\n",
    "for i in range(10):\n",
    "    gradient = quantile_gradient(y - (X@beta_)[:,0], 0.85)\n",
    "          # sm.WLS -> NOT sm.OLS\n",
    "    beta_ = sm.WLS((X@beta_)[:,0] + 1/gradient, X, weights = gradient**2).fit().params.reshape(2,1)\n",
    "    \n",
    "plt.figure(figsize=(18,9)); plt.plot(X[:,1], y, '.'); x = np.linspace(0,5,100); plt.plot(x, beta_[0]+beta_[1]*x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N2dkqvio-cv5",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<a name=\"cell-opt-fx-quasi\"></a>\n",
    "\n",
    "## 8.7 Quasi-Likelihood ([Return to TOC](#cell-TOC-opt)) \n",
    "\n",
    "---\n",
    "\n",
    "***Generalized linear models*** such as ***logistic regression*** and ***poisson regression*** parameterize specific ***log likelihood*** forms  \n",
    "\n",
    "$$\\text{with parameters } \\quad \\text{E}[y_i|x_i] = \\mu_i = \\phi^{-1}(\\theta_i = x_i^T \\beta) \\quad \\text{ and } \\quad \\text{Var}[y_i|x_i] = V(\\mu_i)$$\n",
    "\n",
    "\n",
    "- but $\\beta$ can be estimated implicitly (without explicit ***log likelihood***) through ***quasi-likehood*** $q(x|\\mu)$  \n",
    "\n",
    "$$\\text{via the differential equation } \\quad \\frac{d}{d\\mu_i} q(x|\\mu_i) = \\frac{y_i-\\mu_i}{V(\\mu_i)} \\quad \\text{ because then the }\\textbf{chain rule }\\text{evalutes to}$$\n",
    "\n",
    "$$\\nabla_{\\beta} q(x|\\mu_i) = \\frac{d}{d\\mu_i} q(x|\\mu_i) \\times \\!\\!\\!\\! \\underbrace{\\frac{d}{d\\theta} \\phi^{-1}(\\theta_i)}_{\\text{derivative of inverse}} \\!\\!\\!\\! \\times \\nabla_{\\beta} x_i^T \\beta = \\frac{y_i-\\mu_i}{V(\\mu_i)} \n",
    "\\left( \\phi'(\\phi^{-1}(x_i^T \\beta)) \\right)^{-1} x_i$$\n",
    "\n",
    "and subsequently the ***Fisher information*** of $\\beta$ for observation $i$ is\n",
    "\n",
    "$$\\mathcal{I}_i(\\beta) = \\text{E}_Y[\\nabla_{\\beta} q(x|\\mu_i) \\nabla_{\\beta} q(x|\\mu_i)^T] =\\frac{\\text{E}_Y[(y_i-\\mu_i)^2] x_ix_i^T}{V(\\mu_i)^2 \\left( \\phi'(\\phi^{-1}(x_i^T \\beta)) \\right)^{2}} =  \\frac{x_ix_i^T}{V(\\mu_i)\\left( \\phi'(\\phi^{-1}(x_i^T \\beta)) \\right)^{2}}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N2dkqvio-cv5",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 8.7 Quasi-Likelihood \n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "The ***Fisher scoring*** alternative to ***Newton's method*** to optimize the parameters $\\beta$ is\n",
    "\n",
    "$$\\beta^{(t+1)} = \\beta^{(t)} + \\mathcal{I}_i(\\beta)^{-1}\\nabla_{\\beta} q(x|\\mu_i=x_i^T \\beta)$$\n",
    "\n",
    "Setting $W$ as the diagonal matrix with $\\quad W_{ii}=\\frac{1}{V(\\mu_i)\\left( \\phi'(\\phi^{-1}(x_i^T \\beta)) \\right)^{2}}$ \n",
    "\n",
    "the ***Fisher scoring*** update can be generalized to the complete sample\n",
    "\n",
    "\\begin{align*}\n",
    "\\beta^{(t+1)} & = {} \\beta^{(t)} + (\\underbrace{X^TWX}_{\\mathcal{I}(\\beta)})^{-1}  X^TW \\left( \\phi'(\\mu) \\odot(y-\\mu) \\right)\\\\\n",
    "& = {} (X^TWX)^{-1}  X^TW \\underbrace{\\left(X\\beta^{(t)} + \\phi'(\\mu) \\odot(y-\\mu) \\right)}_{\\tilde y}\n",
    "\\end{align*}\n",
    "\n",
    "where $\\mu = \\phi^{-1}(X \\beta)$ and $\\odot$ indicates elementwise multiplication \n",
    "\n",
    "and this shows that (once again) $\\beta^{*}$ is found as a sequence of ***iteratively reweighted least squares*** problems "
   ]
  }
 ],
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