Probabilistic Reasoning across the Causal Hierarchy

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning -- including conditional independence and Bayesian inference -- the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.Comment: AAAI-2

Discovery of Linguistic Relations Using Lexical Attraction

This work has been motivated by two long term goals: to understand how humans learn language and to build programs that can understand language. Using a representation that makes the relevant features explicit is a prerequisite for successful learning and understanding. Therefore, I chose to represent relations between individual words explicitly in my model. Lexical attraction is defined as the likelihood of such relations. I introduce a new class of probabilistic language models named lexical attraction models which can represent long distance relations between words and I formalize this new class of models using information theory. Within the framework of lexical attraction, I developed an unsupervised language acquisition program that learns to identify linguistic relations in a given sentence. The only explicitly represented linguistic knowledge in the program is lexical attraction. There is no initial grammar or lexicon built in and the only input is raw text. Learning and processing are interdigitated. The processor uses the regularities detected by the learner to impose structure on the input. This structure enables the learner to detect higher level regularities. Using this bootstrapping procedure, the program was trained on 100 million words of Associated Press material and was able to achieve 60% precision and 50% recall in finding relations between content-words. Using knowledge of lexical attraction, the program can identify the correct relations in syntactically ambiguous sentences such as ``I saw the Statue of Liberty flying over New York.''Comment: dissertation, 56 page

On the Tractability of Neural Causal Inference

Roth (1996) proved that any form of marginal inference with probabilistic graphical models (e.g. Bayesian Networks) will at least be NP-hard. Introduced and extensively investigated in the past decade, the neural probabilistic circuits known as sum-product network (SPN) offers linear time complexity. On another note, research around neural causal models (NCM) recently gained traction, demanding a tighter integration of causality for machine learning. To this end, we present a theoretical investigation of if, when, how and under what cost tractability occurs for different NCM. We prove that SPN-based causal inference is generally tractable, opposed to standard MLP-based NCM. We further introduce a new tractable NCM-class that is efficient in inference and fully expressive in terms of Pearl's Causal Hierarchy. Our comparative empirical illustration on simulations and standard benchmarks validates our theoretical proofs.Comment: Main paper: 8 pages, References: 2 pages, Appendix: 5 pages. Figures: 5 main, 2 appendi

Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning

A General Neural Causal Model for Interactive Recommendation

Survivor bias in observational data leads the optimization of recommender systems towards local optima. Currently most solutions re-mines existing human-system collaboration patterns to maximize longer-term satisfaction by reinforcement learning. However, from the causal perspective, mitigating survivor effects requires answering a counterfactual problem, which is generally unidentifiable and inestimable. In this work, we propose a neural causal model to achieve counterfactual inference. Specifically, we first build a learnable structural causal model based on its available graphical representations which qualitatively characterizes the preference transitions. Mitigation of the survivor bias is achieved though counterfactual consistency. To identify the consistency, we use the Gumbel-max function as structural constrains. To estimate the consistency, we apply reinforcement optimizations, and use Gumbel-Softmax as a trade-off to get a differentiable function. Both theoretical and empirical studies demonstrate the effectiveness of our solution

Reasoning about Independence in Probabilistic Models of Relational Data

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related wor