I’ve decided to maintain a wishlist of things I’d like to work on whenever my interest peaks. Clearly, this is a weakly organized scratchpad.

# Theory

These are works that I’ve only glossed over and never delved deeper. Sometime in the future, I’d like to understand them better.

### Gaussian Processes

GP priors are unusually interesting. They lead to smooth interpolators with uncertainty estimates. Some parts of the inference are embarrasingly parallelizable. See references for my readings. The background section of Exact GPs on a Million Points is also full of great references.

### Kernels

Kernels can be applied to almost any kind of data and provide a notion of “similarity”. They are like the grand-old-daddy of feature representation (and quite powerful at that). The famous Representer Theorem and its generalizations provide a powerful list of results, many of which I don’t fully understand. See references for my readings.

### MCMC Diagnostics

There’s a comically truthful idea This is the idea behind Importance Sampling

any sample can come from any distribution

How do we evaluate goodness-of-fit? How do we ascribe samples belong to a particular distribution? These are very interesting and hard questions. See reference for my readings.

### Statistical Learning Theory

For this topic, I don’t have a particularly defined scope. My primary qualm with most treatment on this topic is the reliance on plenty of obscure sounding inqualities (except for a few popular ones like Markov’s, Hoeffding’s, Chebychev’s, Azuma’s). Often times, I think this is more of an art of posing the question what to put a bound on? and then put out some results in terms of a function of error tolerance $\epsilon$ and confidence $\delta$. I might have a myopic view on this and still looking for big-picture treatment. See references for my readings. I’m looking for a general attack recipe for such kind of bounds analysis.

# Questions

Most of these are gaps in my knowledge. Looking for resources and perspectives to improve my understanding. I hope to summarize answers to these as blog posts.

• To my knowledge, there is no way to prove convergence in MCMC sampling algorithms. All we have are diagnostics like Effective Sample Size and Gelman-Rubin Diagnostic to show chains have diverged. What is the recommended way to verify convergence?

• How do we scale Gaussian Processes to large data? Matrix computations involve operations of the order of $$O(N^3)$$. Isn’t this terribly slow?