On the Difficulty of Achieving Equilibrium in Interactive POMDPs

AAAI Conferences

We analyze the asymptotic behavior of agents engaged in an infinite horizon partially observable stochastic game as formalized by the interactive POMDP framework. We show that when agents' initial beliefs satisfy a truth compatibility condition, their behavior converges to a subjective ɛ-equilibrium in a finite time, and subjective equilibrium in the limit. This result is a generalization of a similar result in repeated games, to partially observable stochastic games. However, it turns out that the equilibrating process is difficult to demonstrate computationally because of the difficulty in coming up with initial beliefs that are both natural and satisfy the truth compatibility condition. Our results, therefore, shed some negative light on using equilibria as a solution concept for decision making in partially observable stochastic games.

RNA Modeling Using Gibbs Sampling and Stochastic Context Free Grammars

AAAI Conferences

Leslie Grate and Mark Herbster and Richard Hughey and David Haussler Baskin (;enter for Computer Engineering and Computer and Information Sciences University of California Santa Cruz, CA 95064 Keywords: RNA secondary structure, Gibbs sampler, Expectation Maximization, stochastic contextfree grammars, hidden Markov models, tP NA, snRNA, 16S rRNA, linguistic methods Abstract A new method of discovering the common secondary structure of a family of homologous RNA sequences using Gibbs sampling and stochastic context-free grammars is proposed. These parameters describe a statistical model of the family. After the Gibbs sampling has produced a crude statistical model for the family, this model is translated into a stochastic context-free grammar, which is then refined by an Expectation Maximization (EM) procedure produce a more complete model. A prototype implementation of the method is tested on tRNA, pieces of 16S rRNA and on U5 snRNA with good results. I. Saira Mian and Harry Noller Sinsheimer Laboratories University of California Santa Cruz, CA 95064 Introduction Tools for analyzing RNA are becoming increasingly important as in vitro evolution and selection techniques produce greater numbers of synthesized RNA families to supplement those related by phylogeny. Two principal methods have been established for predicting RNA secondary structure base pairings. The second technique employs thermodynamics to compare the free energy changes predicted for formation of possible s,'covdary structure and relies on finding the structure with the lowest free energy (Tinoco Jr., Uhlenbeck, & Levine 1971: Turner, Sugimoto, & Freier 1988; *This work was supported in part by NSF grants C,I)A-9115268 and IR1-9123692, and NIIt gratnt (.;M17129. When several related sequences are available that all share a common secondary structure, combinations of different approaches have been used to obtain improved results (Waterman 1989; Le & Zuker 1991; Han& Kim 1993; Chiu & Kolodziejczak 1991; Sankoff 1985; Winker et al. 1990; Lapedes 1992; Klinger & Brutlag 1993; Gutell et aL 1992). Recent efforts have applied Stochastic Context-Free Grammars (SCFGs) to the problems of statistical modeling, multiple alignment, discrimination and prediction of the secondary structure of RNA families (Sakakibara el al. 1994; 1993; Eddy & Durbin 1994; Searls 1993).

Bayesian Non-Homogeneous Markov Models via Polya-Gamma Data Augmentation with Applications to Rainfall Modeling

arXiv.org Machine Learning

Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal non-homogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional non-homogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this we extend the recently-proposed Polya-Gamma data augmentation approach to handle non-homogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.

Differentially Private Markov Chain Monte Carlo

arXiv.org Machine Learning

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the R\'enyi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests.

Feature Correspondence: A Markov Chain Monte Carlo Approach

Neural Information Processing Systems

When trying to recover 3D structure from a set of images, the most difficult problem is establishing the correspondence between the measurements. Most existing approaches assume that features can be tracked across frames, whereas methods that exploit rigidity constraints to facilitate matching do so only under restricted camera motion.In this paper we propose a Bayesian approach that avoids the brittleness associated with singling out one "best" correspondence, andinstead consider the distribution over all possible correspondences. We treat both a fully Bayesian approach that yields a posterior distribution, and a MAP approach that makes use of EM to maximize this posterior. We show how Markov chain Monte Carlo methods can be used to implement these techniques in practice, and present experimental results on real data.