presentation_overview.txt

Project Presentation Overview:
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1. Introduction:
	- poisson point process examples + expl
		-> malaria examples
	- explain (/semi-derive) formula (1)
	- illustrate importance of the rate function
		-> different rate function sample plots

2. Problem:
	- explain our setting: learn the intensity function with bayesian inference
	- problem: doubly intractable integral (3)
	- present different solution ideas? 
		-> MCMC approach, problems with it
	- paper approach:
		-> sparse GP prior
		-> variational inference

3. Background:
	- General Ideas behind the 
	- Sparse GP
		-> (why? explain difference, problem with integration)
	- Variational inference 
		-> derive general bound? 
		-> explain why the optimized dist approximates the posterior

4. Modell:
	- lambda(x) = f(x)**2
	- inducing points U, prior f|u ~GP
	- location fix (grid), one could also optimize
	- show kernel (only state it)
	- show model formula (8)
	- show parameters (\Omega) (only state which parts contain parameters?)

5. Lower Bound:
	- introduce variational distribution(model depends only on p(u))
	- derive variational lower bound
	- explain why this approximates the posterior

	- idea: max L => get q(u) => calc q(f) 
		-> then it would be possible to sample an f, square it and get a rate function

	- decompose the formula, show depencencies and give intuitions why certain parts are tractable
	- describe problem with the high res lookup table
		-> what does this mean for the TF implementation

6. Evaluation:
	- show loglikelihood plots
	- what do we want to reproduce (goal)
	- show kenya plot, hoping to reproduce sth similar

7. Concolusion + Discussion

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Todo:
	- finish smapling plot and include it somewhere (thinning with real model)

Questions:
	- why exactly helps the sparse formulation in the integration?
		-> take a look at general gaussian prior + posterior
	- VI: best solution for model class?