Graphical techniques for modeling the dependencies of random variables have been explored in a variety of di erent areas including statistics, statistical physics, arti-cial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a self-contained review of the basic principles of PINs. It is shown that the well-known forward-backward (F-B) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach. 1

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

. Probabilistic networks (also known as Bayesian belief networks) allow a compact description of complex stochastic relationships among several random variables. They are rapidly becoming the tool of choice for uncertain reasoning in artificial intelligence. In this paper, we investigate the problem of learning probabilistic networks with known structure and hidden variables. This is an important problem, because structure is much easier to elicit from experts than numbers, and the world is rarely fully observable. We present a gradient-based algorithmand show that the gradient can be computed locally, using information that is available as a byproduct of standard probabilistic network inference algorithms. Our experimental results demonstrate that using prior knowledge about the structure, even with hidden variables, can significantly improve the learning rate of probabilistic networks. We extend the method to networks in which the conditional probability tables are described using a ...

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts. 1

We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models -- hidden Markov models and linear dynamical systems -- and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward-backward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

Machine Learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up supervised learning algorithms, (c) reinforcement learning, and (d) learning complex stochastic models.

Bayesian networks are directed acyclic graphs that represent dependencies between variables in a probabilistic model. Many time series models, including the hidden Markov models (HMMs) used in speech recognition and Kalman filter models used in filtering and control applications, can be viewed as examples of dynamic Bayesian networks. We first provide a brief tutorial on learning and Bayesian networks. We then present some dynamic Bayesian networks that can capture much richer structure than HMMs and Kalman filters, including spatial and temporal multiresolution structure, distributed hidden state representations, and multiple switching linear regimes. While exact probabilistic inference is intractable in these networks, one can obtain tractable variational approximations which call as subroutines the forward-backward and Kalman filter recursions. These approximations can be used to learn the model parameters...

Dynamic Bayesian networks (DBNs) are a useful tool for representing complex stochastic processes. Recent developments in inference and learning in DBNs allow their use in real-world applications. In this paper, we apply DBNs to the problem of speech recognition. The factored state representation enabled by DBNs allows us to explicitly represent long-term articulatory and acoustic context in addition to the phonetic-state information maintained by hidden Markov models (HMMs). Furthermore, it enables us to model the short-term correlations among multiple observation streams within single time-frames. Given a DBN structure capable of representing these long- and short-term correlations, we applied the EM algorithm to learn models with up to 500,000 parameters. The use of structured DBN models decreased the error rate by 12 to 29% on a large-vocabulary isolated-word recognition task, compared to a discrete HMM; it also improved significantly on other published results for the same task. Th...

In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an ecient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.

In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linear-chain conditional random fields (CRFs) in which each time slice contains a set of state variables and edges---a distributed state representation as in dynamic Bayesian networks (DBNs)---and parameters are tied across slices. Since exact