# Fragments

Raw unstructured thoughts

These are just raw keywords which may eventually evolve into their own pages if I dive deep enough. For now they are just disconnected "fragments", interesting directions that I may want to pursue.

# Three-Way Markets

Economy (and "micro-"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 (I'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?

# Bayesian Inference

• How do we utilize self-consistency from Bayes theorem. Can we create tractable formulations for the following divergence problem?

$\mathcal{D}\left( p(x)p(y|x) \Big|\Big| p(y)p(x|y) \right)$
• EM maximizes the log marginal directly instead of a lower bound in VI. Is it objectively better?

## Learned invariances

• It'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