We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution

The scientific process is a means for turning the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific process in a precise mathematical language. This paper outlines one such language. What is presented here is hardly new. The material leans much on great thinkers of times past as well as more modern contributions. The novel contributions of this paper are: A new, general data processing inequality, a bias variance decomposition for canonical losses, Streamlined proofs of the Blackwell-Sherman-Stein and Randomization Theorems, and Means to calculate deficiency via linear programming.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution f(x, y, z) of continuous random vectors X, Y and Z, we determine whether X? Y |Z. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing.

Transformer based large-language models (LLMs) display extreme proficiency with language yet a precise understanding of how they work remains elusive. One way of demystifying transformer predictions would be to describe how they depend on their context in terms of simple template functions. This paper takes a first step in this direction by considering families of functions (i.e. rules) formed out of simple N-gram based statistics of the training data. By studying how well these rulesets approximate transformer predictions, we obtain a variety of novel discoveries: a simple method to detect overfitting during training without using a holdout set, a quantitative measure of how transformers progress from learning simple to more complex statistical rules over the course of training, a model-variance criterion governing when transformer predictions tend to be described by N-gram rules, and insights into how well transformers can be approximated by N-gram rulesets in the limit where these rulesets become increasingly complex. In this latter direction, we find that for 78% of LLM next-token distributions on TinyStories, their top-1 predictions agree with those provided by our N-gram rulesets.

We consider the problem of learning control policies via trajectory preference queries to an expert. In particular, the agent presents an expert with short runs of a pair of policies originating from the same state and the expert indicates which trajectory is preferred. The agent's goal is to elicit a latent target policy from the expert with as few queries as possible. To tackle this problem we propose a novel Bayesian model of the querying process and introduce two methods that exploit this model to actively select expert queries. Experimental results on four benchmark problems indicate that our model can effectively learn policies from trajectory preference queries and that active query selection can be substantially more efficient than random selection.

It is essential for users to understand what their AI systems can and can't do in order to use them safely. However, the problem of enabling users to assess AI systems with sequential decision-making (SDM) capabilities is relatively understudied. This paper presents a new approach for modeling the capabilities of black-box AI systems that can plan and act, along with the possible effects and requirements for executing those capabilities in stochastic settings. We present an active-learning approach that can effectively interact with a black-box SDM system and learn an interpretable probabilistic model describing its capabilities. Theoretical analysis of the approach identifies the conditions under which the learning process is guaranteed to converge to the correct model of the agent; empirical evaluations on different agents and simulated scenarios show that this approach is few-shot generalizable and can effectively describe the capabilities of arbitrary black-box SDM agents in a sample-efficient manner.