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.
These are works that I’ve only glossed over and never delved deeper. Sometime in the future, I’d like to understand them better.
GP priors are unusually interesting. They lead to smooth interpolators with
uncertainty estimates. Some parts of the inference are embarrasingly
parallelizable. See references
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
There’s a comically truthful idea
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
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
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?
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