Above are papers related to the following paper: [Paper_ID] Paper #6814. 	[Title] Factorial Hidden Markov Models [Abstract] One of the basic probabilistic tools used for time series modeling is the hidden Markov model (HMM). In an HMM, information about the past of the time series is conveyed through a single discrete variable|the hidden state. We present a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. Both inference and learning in this model depend critically on computing the posterior probabilities of the hidden state variables given the observations. We present an exact algorithm for inference in this model, and relate it to the Forward-Backward algorithm for HMMs and to algorithms for more general belief networks. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or mean field theory. We also present a structured approximation in which the the state variables are decoupled, based on which we derive a tractable learning algorithm. Empirical comparisons suggest that these approximations are efficient and accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that it outperforms HMMs in capturing the complex temporal patterns in this dataset. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #37888. 	[Title] Stochastic simulation algorithms for dynamic probabilistic networks [Abstract] Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special characteristics of dynamic probabilistic networks (DPNs), which are used to represent stochastic temporal processes, mean that standard simulation algorithms perform very poorly. In essence, the simulation trials diverge further and further from reality as the process is observed over time. In this paper, we present simulation algorithms that use the evidence observed at each time step to push the set of trials back towards reality. The first algorithm, "evidence reversal" (ER) restructures each time slice of the DPN so that the evidence nodes for the slice become ancestors of the state variables. The second algorithm, called "survival of the fittest" sampling (SOF), "repopulates" the set of trials at each time step using a stochastic reproduction rate weighted by the likelihood of the evidence according to each trial. We compare the performance of each algorithm with likelihood weighting on the original network, and also investigate the benefits of combining the ER and SOF methods. The ER/SOF combination appears to maintain bounded error independent of the number of time steps in the simulation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #315266. 	[Title] Speech Recognition with Dynamic Bayesian Networks [Abstract] 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. This is the first successful application of DBNs to a large-scale speech recognition problem. Investigation of the learned models indicates that the hidden state variables are strongly correlated with acoustic properties of the speech signal. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #202639. 	[Title] PREDICTING SUNSPOTS AND EXCHANGE RATES WITH CONNECTIONIST NETWORKS [Abstract] We investigate the effectiveness of connectionist networks for predicting the future continuation of temporal sequences. The problem of overfitting, particularly serious for short records of noisy data, is addressed by the method of weight-elimination: a term penalizing network complexity is added to the usual cost function in back-propagation. The ultimate goal is prediction accuracy. We analyze two time series. On the benchmark sunspot series, the networks outperform traditional statistical approaches. We show that the network performance does not deteriorate when there are more input units than needed. Weight-elimination also manages to extract some part of the dynamics of the notoriously noisy currency exchange rates and makes the network solution interpretable. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #446610. 	[Title] Coupled hidden Markov models for modeling interacting processes [Abstract] c flMIT Media Lab Perceptual Computing / Learning and Common Sense Technical Report 405 3nov96, revised 3jun97 Abstract We present methods for coupling hidden Markov models (hmms) to model systems of multiple interacting processes. The resulting models have multiple state variables that are temporally coupled via matrices of conditional probabilities. We introduce a deterministic O(T (CN ) 2 ) approximation for maximum a posterior (MAP) state estimation which enables fast classification and parameter estimation via expectation maximization. An "N-heads" dynamic programming algorithm samples from the highest probability paths through a compact state trellis, minimizing an upper bound on the cross entropy with the full (combinatoric) dynamic programming problem. The complexity is O(T (CN ) 2 ) for C chains of N states apiece observing T data points, compared with O(T N 2C ) for naive (Cartesian product), exact (state clustering), and stochastic (Monte Carlo) methods applied to the same inference problem. In several experiments examining training time, model likelihoods, classification accuracy, and robustness to initial conditions, coupled hmms compared favorably with conventional hmms and with energy-based approaches to coupled inference chains. We demonstrate and compare these algorithms on synthetic and real data, including interpretation of video. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #29723. 	[Title] Boltzmann Chains and Hidden Markov Models [Abstract] We propose a statistical mechanical framework for the modeling of discrete time series. Maximum likelihood estimation is done via Boltzmann learning in one-dimensional networks with tied weights. We call these networks Boltzmann chains and show that they contain hidden Markov models (HMMs) as a special case. Our framework also motivates new architectures that address particular shortcomings of HMMs. We look at two such architectures: parallel chains that model feature sets with disparate time scales, and looped networks that model long-term dependencies between hidden states. For these networks, we show how to implement the Boltzmann learning rule exactly, in polynomial time, without resort to simulated or mean-field annealing. The necessary computations are done by exact decimation procedures from statistical mechanics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6818. 	[Title] Exploiting Tractable Substructures in Intractable Networks [Abstract] We develop a refined mean field approximation for inference and learning in probabilistic neural networks. Our mean field theory, unlike most, does not assume that the units behave as independent degrees of freedom; instead, it exploits in a principled way the existence of large substructures that are computationally tractable. To illustrate the advantages of this framework, we show how to incorporate weak higher order interactions into a first-order hidden Markov model, treating the corrections (but not the first order structure) within mean field theory. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117348. 	[Title] MIXED MEMORY MARKOV MODELS FOR TIME SERIES ANALYSIS [Abstract] This paper presents a method for analyzing coupled time series using Markov models in a domain where the state space is immense. To make the parameter estimation tractable, the large state space is represented as the Cartesian product of smaller state spaces, a paradigm known as factorial Markov models. The transition matrix for this model is represented as a mixture of the transition matrices of the underlying dynamical processes. This formulation is know as mixed memory Markov models. Using this framework, we analyze the daily exchange rates for five currencies - British pound, Canadian dollar, Deutsch mark, Japanese yen, and Swiss franc as measured against the U.S. dollar. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #300071. 	[Title] Coupled hidden Markov models for complex action recognition [Abstract] c flMIT Media Lab Perceptual Computing / Learning and Common Sense Technical Report 407 20nov96 Abstract We present algorithms for coupling and training hidden Markov models (HMMs) to model interacting processes, and demonstrate their superiority to conventional HMMs in a vision task classifying two-handed actions. HMMs are perhaps the most successful framework in perceptual computing for modeling and classifying dynamic behaviors, popular because they offer dynamic time warping, a training algorithm, and a clear Bayesian semantics. However, the Markovian framework makes strong restrictive assumptions about the system generating the signalthat it is a single process having a small number of states and an extremely limited state memory. The single-process model is often inappropriate for vision (and speech) applications, resulting in low ceilings on model performance. Coupled HMMs provide an efficient way to resolve many of these problems, and offer superior training speeds, model likelihoods, and robustness to initial conditions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #108974. 	[Title] Global Conditioning for Probabilistic Inference in Belief Networks [Abstract] In this paper we propose a new approach to probabilistic inference on belief networks, global conditioning, which is a simple generalization of Pearl's (1986b) method of loop-cutset conditioning. We show that global conditioning, as well as loop-cutset conditioning, can be thought of as a special case of the method of Lauritzen and Spiegelhalter (1988) as refined by Jensen et al (1990a; 1990b). Nonetheless, this approach provides new opportunities for parallel processing and, in the case of sequential processing, a tradeoff of time for memory. We also show how a hybrid method (Suermondt and others 1990) combining loop-cutset conditioning with Jensen's method can be viewed within our framework. By exploring the relationships between these methods, we develop a unifying framework in which the advantages of each approach can be combined successfully. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35778. 	[Title] Context-Specific Independence in Bayesian Networks [Abstract] Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation schemetree-structured CPTs for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33231. 	[Title] Probabilistic Independence Networks for Hidden Markov Probability Models [Abstract] Graphical techniques for modeling the dependencies of random variables have been explored in a variety of different areas including statistics, statistical physics, artificial 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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35922. 	[Title] Mean Field Theory for Sigmoid Belief Networks [Abstract] We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition|the classification of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #293974. 	[Title] Tractable Inference for Complex Stochastic Processes [Abstract] The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief statea probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18777. 	[Title] A Tutorial on Learning With Bayesian Networks [Abstract] Technical Report MSR-TR-95-06 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #158172. 	[Title] Space-efficient inference in dynamic probabilistic networks [Abstract] Dynamic probabilistic networks (DPNs) are a useful tool for modeling complex stochastic processes. The simplest inference task in DPNs is monitoring | that is, computing a posterior distribution for the state variables at each time step given all observations up to that time. Recursive, constant-space algorithms are well-known for monitoring in DPNs and other models. This paper is concerned with hindsight | that is, computing a posterior distribution given both past and future observations. Hindsight is an essential subtask of learning DPN models from data. Existing algorithms for hindsight in DPNs use O(SN ) space and time, where N is the total length of the observation sequence and S is the state space size for each time step. They are therefore impractical for hindsight in complex models with long observation sequences. This paper presents an O(S log N ) space, O(SN log N ) time hindsight algorithm. We demonstrates the effectiveness of the algorithm in two real-world DPN learning problems. We also discuss the possibility of an O(S)-space, O(SN )-time algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1125469. 	[Title] Structured Representation of Complex Stochastic Systems [Abstract] This paper considers the problem of representing complex systems that evolve stochastically over time. Dynamic Bayesian networks provide a compact representation for stochastic processes. Unfortunately, they are often unwieldy since they cannot explicitly model the complex organizational structure of many real life systems: the fact that processes are typically composed of several interacting subprocesses, each of which can, in turn, be further decomposed. We propose a hierarchically structured representation language which extends both dynamic Bayesian networks and the object-oriented Bayesian network framework of [9], and show that our language allows us to describe such systems in a natural and modular way. Our language supports a natural representation for certain system characteristics that are hard to capture using more traditional frameworks. For example, it allows us to represent systems where some processes evolve at a different rate than others, or systems where the processes interact only intermittently. We provide a simple inference mechanism for our representation via translation to Bayesian networks, and suggest ways in which the inference algorithm can exploit the additional structure encoded in our representation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390896. 	[Title] IMPROVING THE MEAN FIELD APPROXIMATION VIA THE USE OF MIXTURE DISTRIBUTIONS [Abstract] Mean field methods provide computationally efficient approximations to posterior probability distributions for graphical models. Simple mean field methods make a completely factorized approximation to the posterior, which is unlikely to be accurate when the posterior is multimodal. Indeed, if the posterior is multi-modal, only one of the modes can be captured. To improve the mean field approximation in such cases, we employ mixture models as posterior approximations, where each mixture component is a factorized distribution. We describe efficient methods for optimizing the parameters in these models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #445938. 	[Title] Compositional Modeling With DPNs [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #37884. 	[Title] Hidden Markov decision trees [Abstract] We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence. We present simulation results for artificial data and the Bach chorales. Accepted for oral presentation at NIPS*96. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #77438. 	[Title] The BATmobile: Towards a Bayesian Automated Taxi [Abstract] The problem of driving an autonomous vehicle in highway traffic engages many areas of AI research and has substantial economic significance. We describe work in progress on a new approach to this problem based on a decision-theoretic architecture using dynamic probabilistic networks. The architecture provides a sound solution to the problems of sensor noise, sensor failure, and uncertainty about the behavior of other vehicles and about the effects of one's own actions. Our approach has been implemented in a computer simulation system, and the autonomous vehicle successfully negotiates a variety of difficult situations. Please summarise all the given information.

Paper #6814 has the title `Factorial Hidden Markov Models  
` and the abstract `One of the basic probabilistic tools used for time series modeling is the hidden Markov model (HMM). In an HMM, information about the past of the time series is conveyed through a single discrete variable|the hidden state. We present a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. Both inference and learning in this model depend critically on computing the posterior probabilities of the hidden state variables given the observations. We present an exact algorithm for inference in this model, and relate it to the Forward-Backward algorithm for HMMs and to algorithms for more general belief networks. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or mean field theory. We also present a structured approximation in which the the state variables are decoupled, based on which we derive a tractable learning algorithm. Empirical comparisons suggest that these approximations are efficient and accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that it outperforms HMMs in capturing the complex temporal patterns in this dataset.
`.
Question: Which category should Paper #6814 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #6814 has the title `Factorial Hidden Markov Models  
` and the abstract `One of the basic probabilistic tools used for time series modeling is the hidden Markov model (HMM). In an HMM, information about the past of the time series is conveyed through a single discrete variable|the hidden state. We present a generalization of HMMs in which this state is factored into multiple state variables and is therefore represented in a distributed manner. Both inference and learning in this model depend critically on computing the posterior probabilities of the hidden state variables given the observations. We present an exact algorithm for inference in this model, and relate it to the Forward-Backward algorithm for HMMs and to algorithms for more general belief networks. Due to the combinatorial nature of the hidden state representation, this exact algorithm is intractable. As in other intractable systems, approximate inference can be carried out using Gibbs sampling or mean field theory. We also present a structured approximation in which the the state variables are decoupled, based on which we derive a tractable learning algorithm. Empirical comparisons suggest that these approximations are efficient and accurate alternatives to the exact methods. Finally, we use the structured approximation to model Bach's chorales and show that it outperforms HMMs in capturing the complex temporal patterns in this dataset.
`.
Question: Which category should Paper #6814 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods