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.


Multiagent Stochastic Planning With Bayesian Policy Recognition

AAAI Conferences

When operating in stochastic, partially observable, multiagent settings, it is crucial to accurately predict the actions of other agents. In my thesis work, I propose methodologies for learning the policy of external agents from their observed behavior, in the form of finite state controllers. To perform this task, I adopt Bayesian learning algorithms based on nonparametric prior distributions, that provide the flexibility required to infer models of unknown complexity. These methods are to be embedded in decision making frameworks for autonomous planning in partially observable multiagent systems.


Gaussian-binary Restricted Boltzmann Machines on Modeling Natural Image Statistics

arXiv.org Machine Learning

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of Gaussians, which gives a much better insight into the model's capabilities and limitations. We show that GRBMs are capable of learning meaningful features both in a two-dimensional blind source separation task and in modeling natural images. Further, we show that reported difficulties in training GRBMs are due to the failure of the training algorithm rather than the model itself. Based on our analysis we are able to propose several training recipes, which allowed successful and fast training in our experiments. Finally, we discuss the relationship of GRBMs to several modifications that have been proposed to improve the model.


Efficient Bayesian analysis of multiple changepoint models with dependence across segments

arXiv.org Machine Learning

We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or out-performs, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.


Neural Networks for Determining Protein Specificity and Multiple Alignment of Binding Sites

AAAI Conferences

Regulation of gene expression often involves proteins that bind to particular regions of DNA. Determining the binding sites for a protein and its specificity usually requires extensive biochemical and/or genetic experimentation. In this paper we illustrate the use of a neural network to obtain the desired information with much less experimental effort. It is often fairly easy to obtain a set of moderate length sequences, perhaps one or two hundred base-pairs, that each contain binding sites for the protein being studied. For example, the upstream regions of a set of genes that are all regulated by the same protein should each contain binding sites for that protein.