Multi-Modal Mean-Fields via Cardinality-Based Clamping

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the posterior probability distribution as a product of marginal probabilities, it may fail to properly account for important dependencies between variables. We therefore replace the fully factorized distribution of Mean Field by a weighted mixture of such distributions, that similarly minimizes the KL-Divergence to the true posterior. By introducing two new ideas, namely, conditioning on groups of variables instead of single ones and using a parameter of the conditional random field potentials, that we identify to the temperature in the sense of statistical physics to select such groups, we can perform this minimization efficiently. Our extension of the clamping method proposed in previous works allows us to both produce a more descriptive approximation of the true posterior and, inspired by the diverse MAP paradigms, fit a mixture of Mean Field approximations. We demonstrate that this positively impacts real-world algorithms that initially relied on mean fields.Comment: Submitted for review to CVPR 201

Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods

The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for a human's risk sensitivity. To this end, we propose a flexible class of models based on coherent risk measures, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient non-parametric algorithms based on linear programming and semi-parametric algorithms based on maximum likelihood for inferring a human's underlying risk measure and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively, especially in scenarios where catastrophic outcomes such as collisions can occur.Comment: Submitted to International Journal of Robotics Research; Revision 1: (i) Clarified minor technical points; (ii) Revised proof for Theorem 3 to hold under weaker assumptions; (iii) Added additional figures and expanded discussions to improve readabilit

Semantics for Probabilistic Inference

A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of nonmonotonic inferences in which the conclusion is supported only to a certain degree. Such inferences are clearly 'invalid' since they must allow the falsity of a conclusion even when the premises are true. Nevertheless, such inferences can be characterized both syntactically and semantically. The 'premises' of probabilistic arguments are sets of statements (as in a database or knowledge base), the conclusions categorical statements in the language. We provide standards for both this form of inference, for which high probability is required, and for an inference in which the conclusion is qualified by an intermediate interval of support.Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992

Authentication with Distortion Criteria

In a variety of applications, there is a need to authenticate content that has experienced legitimate editing in addition to potential tampering attacks. We develop one formulation of this problem based on a strict notion of security, and characterize and interpret the associated information-theoretic performance limits. The results can be viewed as a natural generalization of classical approaches to traditional authentication. Additional insights into the structure of such systems and their behavior are obtained by further specializing the results to Bernoulli and Gaussian cases. The associated systems are shown to be substantially better in terms of performance and/or security than commonly advocated approaches based on data hiding and digital watermarking. Finally, the formulation is extended to obtain efficient layered authentication system constructions.Comment: 22 pages, 10 figure

Demand Estimation under Uncertain Consideration Sets

To estimate customer demand, choice models rely both on what the individuals do and do not purchase. A customer may not purchase a product because it was not offered but also because it was not considered. To account for this behavior, existing literature has proposed the so-called consider-then-choose (CTC) models, which posit that customers sample a consideration set and then choose the most preferred product from the intersection of the offer set and the consideration set. CTC models have been studied quite extensively in the marketing literature. More recently, they have gained popularity within the operations management (OM) literature to make assortment and pricing decisions. Despite their richness, CTC models are difficult to estimate in practice because firms typically do not observe customers' consideration sets. Therefore, the common assumption in OM has been that customers consider everything on offer, so the consideration set is the same as the offer set. This raises the following question: When firms only collect transaction data, do CTC models provide any predictive advantage over classic choice models? More precisely, under what conditions do CTC models outperform (if ever) classic choice models in terms of prediction accuracy? In this work, we study a general class of CTC models. We propose techniques to estimate these models efficiently from sales transaction data. We then compare their performance against the classic approach. We find that CTC models outperform standard choice models when there is noise in the offer set information and the noise is asymmetric across the training and test offer sets but otherwise lead to no particular predictive advantage over the classic approach. We also demonstrate the benefits of using CTC models in real-world retail settings. In particular, we show that CTC models calibrated on retail transaction data are better at long-term and warehouse level sales forecasts. We also evaluate their performance in the context of an online platform setting: a peer-to-peer car sharing company. In this context, offer sets are even difficult to define. We observe a remarkable performance of CTC models over standard choice models therein.Este documento es la versión aceptada del artículo publicado en Operations Research (ISSN 0030-364X) en Septiembre de 202