diff --git a/docs/examples/constrained.ipynb b/docs/examples/constrained.ipynb index 0623bbe2..610eae8a 100644 --- a/docs/examples/constrained.ipynb +++ b/docs/examples/constrained.ipynb @@ -88,7 +88,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can define a transform to map between the unbounded spaces and constrained space. \n", + "We can define a bijection to map between the unbounded space and constrained space. \n", "In this case, we use tanh to map the first dimension to $[-1, 1]$, and the identity\n", "transformation to leave the second dimension unchanged." ] @@ -100,7 +100,7 @@ "outputs": [], "source": [ "to_constrained = bij.Stack([\n", - " bij.Chain([bij.Tanh(), bij.Affine(0.5, 0.5)]), # x1: maps real -> [-1, 1] -> [0, 1]\n", + " bij.Sigmoid(), # x_1: maps real -> [0, 1]\n", " bij.Identity(), # x_2: maps real -> real\n", " ]) " ] @@ -110,7 +110,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can now create and train the flows, using both options outlined above, in addition to naively training without contraints." + "We can now create and train the flows, using the options outlined above." ] }, { @@ -192,12 +192,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] diff --git a/flowjax/bijections/__init__.py b/flowjax/bijections/__init__.py index c0ea525b..7880b007 100644 --- a/flowjax/bijections/__init__.py +++ b/flowjax/bijections/__init__.py @@ -12,6 +12,7 @@ from .planar import Planar from .power import Power from .rational_quadratic_spline import RationalQuadraticSpline +from .sigmoid import Sigmoid from .softplus import SoftPlus from .tanh import LeakyTanh, Tanh from .utils import EmbedCondition, Flip, Identity, Invert, Partial, Permute, Reshape @@ -40,6 +41,7 @@ "Reshape", "Scale", "Scan", + "Sigmoid", "SoftPlus", "Stack", "Tanh", diff --git a/flowjax/bijections/sigmoid.py b/flowjax/bijections/sigmoid.py new file mode 100644 index 00000000..d090bf8b --- /dev/null +++ b/flowjax/bijections/sigmoid.py @@ -0,0 +1,36 @@ +"""Sigmoid bijection.""" + +from typing import ClassVar + +import jax.numpy as jnp +from jax import nn +from jax.scipy.special import logit + +from flowjax.bijections.bijection import AbstractBijection + + +class Sigmoid(AbstractBijection): + r"""Sigmoid bijection :math:`y = \sigma(x) = \frac{1}{1 + \exp(-x)}`. + + Args: + shape: The shape of the transform. + """ + + shape: tuple[int, ...] = () + cond_shape: ClassVar[None] = None + + def transform(self, x, condition=None): + return nn.sigmoid(x) + + def transform_and_log_det(self, x, condition=None): + y = nn.sigmoid(x) + log_det = jnp.sum(nn.log_sigmoid(x) + nn.log_sigmoid(-x)) + return y, log_det + + def inverse(self, y, condition=None): + return logit(y) + + def inverse_and_log_det(self, y, condition=None): + x = logit(y) + log_det = -jnp.sum(nn.log_sigmoid(x) + nn.log_sigmoid(-x)) + return x, log_det diff --git a/flowjax/distributions.py b/flowjax/distributions.py index 45a441ef..e0de13cb 100644 --- a/flowjax/distributions.py +++ b/flowjax/distributions.py @@ -780,3 +780,29 @@ def __init__(self, concentration: ArrayLike, scale: ArrayLike): concentration, scale = jnp.broadcast_arrays(concentration, scale) self.base_dist = _StandardGamma(concentration) self.bijection = Scale(scale) + + +class Beta(AbstractDistribution): + """Beta distribution. + + Args: + alpha: The alpha shape parameter. + beta: The beta shape parameter. + """ + + alpha: Array | AbstractUnwrappable[Array] + beta: Array | AbstractUnwrappable[Array] + shape: tuple[int, ...] + cond_shape: ClassVar[None] = None + + def __init__(self, alpha: ArrayLike, beta: ArrayLike): + alpha, beta = jnp.broadcast_arrays(alpha, beta) + self.alpha = Parameterize(softplus, inv_softplus(alpha)) + self.beta = Parameterize(softplus, inv_softplus(beta)) + self.shape = alpha.shape + + def _sample(self, key, condition=None): + return jr.beta(key, self.alpha, self.beta) + + def _log_prob(self, x, condition=None): + return jstats.beta.logpdf(x, self.alpha, self.beta).sum() diff --git a/tests/test_bijections/test_bijections.py b/tests/test_bijections/test_bijections.py index 6b548f00..f9268ac2 100644 --- a/tests/test_bijections/test_bijections.py +++ b/tests/test_bijections/test_bijections.py @@ -30,6 +30,7 @@ Reshape, Scale, Scan, + Sigmoid, SoftPlus, Stack, Tanh, @@ -67,6 +68,7 @@ "LeakyTanh (broadcast max_val)": lambda: LeakyTanh(1, (2, 3)), "Loc": lambda: Loc(jnp.arange(DIM)), "Exp": lambda: Exp((DIM,)), + "Sigmoid": lambda: Sigmoid((DIM,)), "SoftPlus": lambda: SoftPlus((DIM,)), "TriangularAffine (lower)": lambda: TriangularAffine( jnp.arange(DIM), diff --git a/tests/test_distributions.py b/tests/test_distributions.py index 966040f5..04142b58 100644 --- a/tests/test_distributions.py +++ b/tests/test_distributions.py @@ -13,6 +13,7 @@ from flowjax.distributions import ( AbstractDistribution, AbstractTransformed, + Beta, Cauchy, Exponential, Gamma, @@ -62,6 +63,7 @@ eqx.filter_vmap(Normal)(jnp.arange(3 * prod(shape)).reshape(3, *shape)), weights=jnp.arange(3) + 1, ), + "Beta": lambda shape: Beta(jnp.ones(shape), jnp.ones(shape)), }