# ML Fragments

Raw unstructured thoughts and ideas.

These are just raw keywords which may eventually evolve into their own pages if I dive deep enough. For now they are just disconnected âfragmentsâ, interesting directions that I may want to pursue. These are intentionally abstract. Please donât hesitate to reach out if youâd like to discuss more!

There is non-trivial chance that prior work has already posed questions similar but then I havenât spent enough time studying these in detail.

## Three-Way Markets

Economy (and âmicro-âeconomies if you will) seem to be running on three-way markets. i) The stock market ii) Gig economy - the likes of Uber, AirBnB. Each transaction can most likely be modeled as consisting of three components - a buyer, a seller and a mediator where each component could be an individual or an institution.

Much like the reward hypothesis in RL, there appears to be a similar hypothesis in stock markets - stock price contains all the information one needs (Iâm still trying to understand the nuance involved in this hypothesis). We certainly would want to model the micro and macro dynamics. What tools does machine learning provide?

## Reinforcement Learning

### Model-Based

• Fixing objective mismatch in MBRL using Expectation Maximization.
• Connections to classic control theory

## Bayesian Inference

$\mathcal{D}\left( p(x)p(y|x) \Big|\Big| p(y)p(x|y) \right)$

### Learned invariances

• Itâs probably become more important now than ever to have priors in Neural Networks that satisfy invariances we care about instead of just using $\mathcal{N}(\mathbf{0}, \mathbf{I})$. how do we do this? e.g. Learning Invariances using the Marginal Likelihood

## Linear Algebra

• Circulant (in general Toeplitz) matrices allow much faster matrix-vector multiplications. For non-Toeplitz ones, we have a notion of âasymptotically Toeplitzâ under the weak matrix norm (Frobenius). What problems families afford such a structure? If they do, can we leverage non-asymptotic guarantees?