Related papers: Relational Marginal Problems: Theory and Estimatio…
Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…
Probabilities of Causation play a fundamental role in decision making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions such as monotonicity. In the absence of such…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
An econometric or statistical model may undergo a marginal gain if we admit a new variable to the model, and a marginal loss if we remove an existing variable from the model. Assuming equality of opportunity among all candidate variables,…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Bayesian hierarchical models are frequently used in practical data analysis contexts. One interpretation of these models is that they provide an indirect way of assigning a prior for unknown parameters, through the introduction of…
Given a matrix $A$, a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem $w: A^Tw > \textbf{0}$ or a certificate for the dual problem which is a probability distribution…
Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the…
This paper deals with the problem of measurable lifting modification for stochastic processes in its most general form and with the 'product lifting problem'. Solutions to the positive are reduced to the existence of marginals with respect…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The…
We study computational aspects of relational marginal polytopes which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and…
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the…
We present a probabilistic model that simultaneously learns alignments and distributed representations for bilingual data. By marginalizing over word alignments the model captures a larger semantic context than prior work relying on hard…