Above are papers related to the following paper: [Paper_ID] Paper #50381. 	[Title] Training Algorithms for Hidden Markov Models Using Entropy Based Distance Functions [Abstract] We present new algorithms for parameter estimation of HMMs. By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay close to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative training algorithms which are similar to the EM (Baum-Welch) algorithm for training HMMs. The proposed algorithms are composed of a step similar to the expectation step of Baum-Welch and a new update of the parameters which replaces the maximization (re-estimation) step. The algorithm takes only negligibly more time per iteration and an approximated version uses the same expectation step as Baum-Welch. We evaluate experimentally the new algorithms on synthetic and natural speech pronunciation data. For sparse models, i.e. models with relatively small number of non-zero parameters, the proposed algorithms require significantly fewer iterations. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6913. 	[Title] On Convergence of the EM Algorithm and the Gibbs Sampler  SUMMARY [Abstract] In this article we investigate the relationship between the two popular algorithms, the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference which uses proper prior distributions. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1135108. 	[Title] A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian [Abstract] We describe the maximum-likelihood parameter estimation problem and how the Expectation-Maximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the parameters of a hidden Markov model (HMM) (i.e., the Baum-Welch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical rigor. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32260. 	[Title] On-Line Portfolio Selection Using Multiplicative Updates [Abstract] We present an on-line investment algorithm which achieves almost the same wealth as the best constant-rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New York Stock Exchange accumulated during a 22-year period. On this data, our algorithm clearly outperforms the best single stock as well as Cover's universal portfolio selection algorithm. We also present results for the situation in which the investor has access to additional "side information." Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1115291. 	[Title] How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis 1 [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12195. 	[Title] Efficient Learning of Typical Finite Automata from Random Walks (Extended Abstract) [Abstract] This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the "typical" labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning non-trivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that makes an expected polynomial number of mistakes in this model. Next, we show how this first algorithm can be used as a subroutine by a second algorithm that also makes a polynomial number of mistakes even in the absence of a reset. Along the way, we prove a number of combinatorial results for randomly labeled automata. We also show that the labeling of the states and the bits of the input sequence need not be truly random, but merely semi-random. Finally, we discuss an extension of our results to a model in which automata are used to represent distributions over binary strings. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1116336. 	[Title] On Computing the Largest Fraction of Missing Information for the EM Algorithm and the Worst [Abstract] We address the problem of computing the largest fraction of missing information for the EM algorithm and the worst linear function for data augmentation. These are the largest eigenvalue and its associated eigenvector for the Jacobian of the EM operator at a maximum likelihood estimate, which are important for assessing convergence in iterative simulation. An estimate of the largest fraction of missing information is available from the EM iterates; this is often adequate since only a few figures of accuracy are needed. In some instances the EM iteration also gives an estimate of the worst linear function. We show that the power method for eigencomputation can be used to compute efficient and accurate estimates of both quantities. Unlike eigenvalue decomposition, the power method computes only the largest eigenvalue and eigenvector of a matrix, it can take advantage of a good eigenvector estimate as an initial value and it can be terminated after only a few figures of accuracy are obtained. Moreover, the matrix products needed in the power method can be computed by extrapolation, obviating the need to form the Jacobian of the EM operator. We give results of simultation studies on multivariate normal data showing this approach becomes more efficient as the data dimension increases than methods that use a finite-difference approximation to the Jacobian, which is the only general-purpose alternative available. fl Funded by National Institutes of Health Small Business Innovation Reseach Grant 5R44CA65147-03, and by Office of Naval Research contracts N00014-96-1-0192 and N00014-96-1-0330. We are indebted to Tim Hesterberg, Jim Schimert, Doug Clarkson, Anne Greenbaum, and Adrian Raftery for comments and discussion that helped advance this research and improve this paper. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #32688. 	[Title] CLASSIFICATION USING HIERARCHICAL MIXTURES OF EXPERTS [Abstract] There has recently been widespread interest in the use of multiple models for classification and regression in the statistics and neural networks communities. The Hierarchical Mixture of Experts (HME) [1] has been successful in a number of regression problems, yielding significantly faster training through the use of the Expectation Maximisation algorithm. In this paper we extend the HME to classification and results are reported for three common classification benchmark tests: Exclusive-Or, N-input Parity and Two Spirals. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1717. 	[Title] On Convergence Properties of the EM Algorithm for Gaussian Mixtures [Abstract] We build up the mathematical connection between the "Expectation-Maximization" (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix P , and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of P and provide new results analyzing the effect that P has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models. This report describes research done at the Center for Biological and Computational Learning and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the Center is provided in part by a grant from the National Science Foundation under contract ASC-9217041. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00000-00-A-0000. The authors were also supported by the HK RGC Earmarked Grant CUHK250/94E, by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, and by grant N00014-90-1-0777 from the Office of Naval Research. Michael I. Jordan is an NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12350. 	[Title] Cryptographic Limitations on Learning Boolean Formulae and Finite Automata [Abstract] In this paper we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are representation independent, in that they hold regardless of the syntactic form in which the learner chooses to represent its hypotheses. Our methods reduce the problems of cracking a number of well-known public-key cryptosys- tems to the learning problems. We prove that a polynomial-time learning algorithm for Boolean formulae, deterministic finite automata or constant-depth threshold circuits would have dramatic consequences for cryptography and number theory: in particular, such an algorithm could be used to break the RSA cryptosystem, factor Blum integers (composite numbers equivalent to 3 modulo 4), and detect quadratic residues. The results hold even if the learning algorithm is only required to obtain a slight advantage in prediction over random guessing. The techniques used demonstrate an interesting duality between learning and cryptography. We also apply our results to obtain strong intractability results for approximating a gener - alization of graph coloring. fl This research was conducted while the author was at Harvard University and supported by an A.T.& T. Bell Laboratories scholarship. y Supported by grants ONR-N00014-85-K-0445, NSF-DCR-8606366 and NSF-CCR-89-02500, DAAL03-86-K-0171, DARPA AFOSR 89-0506, and by SERC. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #38722. 	[Title] Learning Probabilistic Automata with Variable Memory Length [Abstract] We propose and analyze a distribution learning algorithm for variable memory length Markov processes. These processes can be described by a subclass of probabilistic finite automata which we name Probabilistic Finite Suffix Automata. The learning algorithm is motivated by real applications in man-machine interaction such as handwriting and speech recognition. Conventionally used fixed memory Markov and hidden Markov models have either severe practical or theoretical drawbacks. Though general hardness results are known for learning distributions generated by sources with similar structure, we prove that our algorithm can indeed efficiently learn distributions generated by our more restricted sources. In Particular, we show that the KL-divergence between the distribution generated by the target source and the distribution generated by our hypothesis can be made small with high confidence in polynomial time and sample complexity. We demonstrate the applicability of our algorithm by learning the structure of natural English text and using our hy pothesis for the correction of corrupted text. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #62274. 	[Title] A Comparison of New and Old Algorithms for A Mixture Estimation Problem [Abstract] We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple derivations for many of the standard iterative algorithms like gradient projection and EM. In this framework, the distance between the new and old proportion vectors is used as a penalty term. The square distance leads to the gradient projection update, and the relative entropy to a new update which we call the exponentiated gradient update (EG ). Curiously, when a second order Taylor expansion of the relative entropy is used, we arrive at an update EM which, for = 1, gives the usual EM update. Experimentally, both the EM -update and the EG -update for &gt; 1 outperform the EM algorithm and its variants. We also prove a polynomial bound on the rate of convergence of the EG algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #67415. 	[Title] On the Learnability of Discrete Distributions (extended abstract) [Abstract]  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 #51180. 	[Title] On the Learnability and Usage of Acyclic Probabilistic Finite Automata [Abstract] We propose and analyze a distribution learning algorithm for a subclass of Acyclic Probabilistic Finite Automata (APFA). This subclass is characterized by a certain distinguishability property of the automata's states. Though hardness results are known for learning distributions generated by general APFAs, we prove that our algorithm can efficiently learn distributions generated by the subclass of APFAs we consider. In particular, we show that the KL-divergence between the distribution generated by the target source and the distribution generated by our hypothesis can be made arbitrarily small with high confidence in polynomial time. We present two applications of our algorithm. In the first, we show how to model cursively written letters. The resulting models are part of a complete cursive handwriting recognition system. In the second application we demonstrate how APFAs can be used to build multiple-pronunciation models for spoken words. We evaluate the APFA based pronunciation models on labeled speech data. The good performance (in terms of the log-likelihood obtained on test data) achieved by the APFAs and the little time needed for learning suggests that the learning algorithm of APFAs might be a powerful alternative to commonly used probabilistic models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4335. 	[Title] A VIEW OF THE EM ALGORITHM THAT JUSTIFIES INCREMENTAL, SPARSE, AND OTHER VARIANTS [Abstract] The EM algorithm performs maximum likelihood estimation for data in which some variables are unobserved. We present a function that resembles negative free energy and show that the M step maximizes this function with respect to the model parameters and the E step maximizes it with respect to the distribution over the unobserved variables. From this perspective, it is easy to justify an incremental variant of the EM algorithm in which the distribution for only one of the unobserved variables is recalculated in each E step. This variant is shown empirically to give faster convergence in a mixture estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #733167. 	[Title] Soft Vector Quantization and the EM Algorithm Running Title: Soft Vector Quantization and EM Section: [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1107319. 	[Title] On Learning Bounded-Width Branching Programs [Abstract] In this paper, we study PAC-learning algorithms for specialized classes of deterministic finite automata (DFA). In particular, we study branching programs, and we investigate the influence of the width of the branching program on the difficulty of the learning problem. We first present a distribution-free algorithm for learning width-2 branching programs. We also give an algorithm for the proper learning of width-2 branching programs under uniform distribution on labeled samples. We then show that the existence of an efficient algorithm for learning width-3 branching programs would imply the existence of an efficient algorithm for learning DNF, which is not known to be the case. Finally, we show that the existence of an algorithm for learning width-3 branching programs would also yield an algorithm for learning a very restricted version of parity with noise. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #94713. 	[Title] Update rules for parameter estimation in Bayesian networks [Abstract] This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [12]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm [2, 3] and the EM algorithm [14] for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parame ters than does standard EM. Please summarise all the given information.

Paper #50381 has the title `Training Algorithms for Hidden Markov Models Using Entropy Based Distance Functions  
` and the abstract `We present new algorithms for parameter estimation of HMMs. By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay close to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative training algorithms which are similar to the EM (Baum-Welch) algorithm for training HMMs. The proposed algorithms are composed of a step similar to the expectation step of Baum-Welch and a new update of the parameters which replaces the maximization (re-estimation) step. The algorithm takes only negligibly more time per iteration and an approximated version uses the same expectation step as Baum-Welch. We evaluate experimentally the new algorithms on synthetic and natural speech pronunciation data. For sparse models, i.e. models with relatively small number of non-zero parameters, the proposed algorithms require significantly fewer iterations.
`.
Question: Which category should Paper #50381 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #50381 has the title `Training Algorithms for Hidden Markov Models Using Entropy Based Distance Functions  
` and the abstract `We present new algorithms for parameter estimation of HMMs. By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay close to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative training algorithms which are similar to the EM (Baum-Welch) algorithm for training HMMs. The proposed algorithms are composed of a step similar to the expectation step of Baum-Welch and a new update of the parameters which replaces the maximization (re-estimation) step. The algorithm takes only negligibly more time per iteration and an approximated version uses the same expectation step as Baum-Welch. We evaluate experimentally the new algorithms on synthetic and natural speech pronunciation data. For sparse models, i.e. models with relatively small number of non-zero parameters, the proposed algorithms require significantly fewer iterations.
`.
Question: Which category should Paper #50381 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: Theory