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.

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 #12165. 	[Title] The Power of Team Exploration: Two Robots Can Learn Unlabeled Directed Graphs [Abstract] We show that two cooperating robots can learn exactly any strongly-connected directed graph with n indistinguishable nodes in expected time polynomial in n. We introduce a new type of homing sequence for two robots, which helps the robots recognize certain previously-seen nodes. We then present an algorithm in which the robots learn the graph and the homing sequence simultaneously by actively wandering through the graph. Unlike most previous learning results using homing sequences, our algorithm does not require a teacher to provide counterexamples. Furthermore, the algorithm can use efficiently any additional information available that distinguishes nodes. We also present an algorithm in which the robots learn by taking random walks. The rate at which a random walk on a graph converges to the stationary distribution is characterized by the conductance of the graph. Our random-walk algorithm learns in expected time polynomial in n and in the inverse of the conductance and is more efficient than the homing-sequence algorithm for high-conductance graphs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #189577. 	[Title] Chain graphs for learning [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12182. 	[Title] How to Use Expert Advice (Extended Abstract) [Abstract] We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worst-case situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expectation is taken with respect to the randomization in the predictions. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We give implications of this result on the performance of batch learning algorithms in a PAC setting which improve on the best results currently known in this context. We also extend our analysis to the case in which log loss is used instead of the expected number of mistakes. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #159897. 	[Title] Robustness Analysis of Bayesian Networks with Finitely Generated Convex Sets of Distributions [Abstract] This paper presents exact solutions and convergent approximations for inferences in Bayesian networks associated with finitely generated convex sets of distributions. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. The paper presents exact inference algorithms and analyzes the circumstances where exact inference becomes intractable. Two classes of algorithms for numeric approximations are developed through transformations on the original model. The first transformation reduces the robust inference problem to the estimation of probabilistic parameters in a Bayesian network. The second transformation uses Lavine's bracketing algorithm to generate a sequence of maximization problems in a Bayesian network. The analysis is extended to the *-contaminated, the lower density bounded, the belief function, the sub-sigma, the density bounded, the total variation and the density ratio classes of distributions. c fl1996 Carnegie Mellon University Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28957. 	[Title] Operations for Learning with Graphical Models decomposition techniques and the demonstration that graphical models provide [Abstract] This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153183. 	[Title]  [Abstract] General convergence results for linear discriminant updates Abstract The problem of learning linear discriminant concepts can be solved by various mistake-driven update procedures, including the Winnow family of algorithms and the well-known Perceptron algorithm. In this paper we define the general class of quasi-additive algorithms, which includes Perceptron and Winnow as special cases. We give a single proof of convergence that covers much of this class, including both Perceptron and Winnow but also many novel algorithms. Our proof introduces a generic measure of progress that seems to capture much of when and how these algorithms converge. Using this measure, we develop a simple general technique for proving mistake bounds, which we apply to the new algorithms as well as existing algorithms. When applied to known algorithms, our technique automatically produces close variants of existing proofs (and we generally obtain the known bounds, to within constants) thus showing, in a certain sense, that these seem ingly diverse results are fundamentally isomorphic. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #88356. 	[Title] Learning Limited Dependence Bayesian Classifiers [Abstract] We present a framework for characterizing Bayesian classification methods. This framework can be thought of as a spectrum of allowable dependence in a given probabilistic model with the Naive Bayes algorithm at the most restrictive end and the learning of full Bayesian networks at the most general extreme. While much work has been carried out along the two ends of this spectrum, there has been surprising little done along the middle. We analyze the assumptions made as one moves along this spectrum and show the tradeoffs between model accuracy and learning speed which become critical to consider in a variety of data mining domains. We then present a general induction algorithm that allows for traversal of this spectrum depending on the available computational power for carrying out induction and show its application in a number of domains with different properties. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28964. 	[Title] Robust Parameter Learning in Bayesian Networks with Missing Data [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #173863. 	[Title] Learning Belief Networks in the Presence of Missing Values and Hidden Variables [Abstract] In recent years there has been a flurry of works on learning probabilistic belief networks. Current state of the art methods have been shown to be successful for two learning scenarios: learning both network structure and parameters from complete data, and learning parameters for a fixed network from incomplete datathat is, in the presence of missing values or hidden variables. However, no method has yet been demonstrated to effectively learn network structure from incomplete data. In this paper, we propose a new method for learning network structure from incomplete data. This method is based on an extension of the Expectation-Maximization (EM) algorithm for model selection problems that performs search for the best structure inside the EM procedure. We prove the convergence of this algorithm, and adapt it for learning belief networks. We then describe how to learn networks in two scenarios: when the data contains missing values, and in the presence of hidden variables. We provide experimental results that show the effectiveness of our procedure in both scenarios. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1118764. 	[Title] An Efficient Extension to Mixture Techniques for Prediction and Decision Trees [Abstract] We present a method for maintaining mixtures of prunings of a prediction or decision tree that extends the "node-based" prunings of [Bun90, WST95, HS97] to the larger class of edge-based prunings. The method includes an efficient online weight allocation algorithm that can be used for prediction, compression and classification. Although the set of edge-based prunings of a given tree is much larger than that of node-based prunings, our algorithm has similar space and time complexity to that of previous mixture algorithms for trees. Using the general on-line framework of Freund and Schapire [FS97], we prove that our algorithm maintains correctly the mixture weights for edge-based prunings with any bounded loss function. We also give a similar algorithm for the logarithmic loss function with a corresponding weight allocation algorithm. Finally, we describe experiments comparing node-based and edge-based mixture models for estimating the probability of the next word in English text, which show the ad vantages of edge-based models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5038. 	[Title] Using and combining predictors that specialize [Abstract] We study online learning algorithms that predict by combining the predictions of several subordinate prediction algorithms, sometimes called experts. These simple algorithms belong to the multiplicative weights family of algorithms. The performance of these algorithms degrades only logarithmically with the number of experts, making them particularly useful in applications where the number of experts is very large. However, in applications such as text categorization, it is often natural for some of the experts to abstain from making predictions on some of the instances. We show how to transform algorithms that assume that all experts are always awake to algorithms that do not require this assumption. We also show how to derive corresponding loss bounds. Our method is very general, and can be applied to a large family of online learning algorithms. We also give applications to various prediction models including decision graphs and switching experts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12210. 	[Title] Efficient Distribution-free Learning of Probabilistic Concepts [Abstract] In this paper we investigate a new formal model of machine learning in which the concept (boolean function) to be learned may exhibit uncertain or probabilistic behavior|thus, the same input may sometimes be classified as a positive example and sometimes as a negative example. Such probabilistic concepts (or p-concepts) may arise in situations such as weather prediction, where the measured variables and their accuracy are insufficient to determine the outcome with certainty. We adopt from the Valiant model of learning [27] the demands that learning algorithms be efficient and general in the sense that they perform well for a wide class of p-concepts and for any distribution over the domain. In addition to giving many efficient algorithms for learning natural classes of p-concepts, we study and develop in detail an underlying theory of learning p-concepts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12211. 	[Title] Learning From a Population of Hypotheses [Abstract] We introduce a new formal model in which a learning algorithm must combine a collection of potentially poor but statistically independent hypothesis functions in order to approximate an unknown target function arbitrarily well. Our motivation includes the question of how to make optimal use of multiple independent runs of a mediocre learning algorithm, as well as settings in which the many hypotheses are obtained by a distributed population of identical learning agents. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4660. 	[Title] Context-sensitive learning methods for text categorization [Abstract] Two recently implemented machine learning algorithms, RIPPER and sleeping experts for phrases, are evaluated on a number of large text categorization problems. These algorithms both construct classifiers that allow the "context" of a word w to affect how (or even whether) the presence or absence of w will contribute to a classification. However, RIPPER and sleeping experts differ radically in many other respects: differences include different notions as to what constitutes a context, different ways of combining contexts to construct a classifier, different methods to search for a combination of contexts, and different criteria as to what contexts should be included in such a combination. In spite of these differences, both RIPPER and sleeping experts perform extremely well across a wide variety of categorization problems, generally outperforming previously applied learning methods. We view this result as a confirmation of the usefulness of classifiers that represent contextual information. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #116790. 	[Title] Sequential Update of Bayesian Network Structure [Abstract] There is an obvious need for improving the performance and accuracy of a Bayesian network as new data is observed. Because of errors in model construction and changes in the dynamics of the domains, we cannot afford to ignore the information in new data. While sequential update of parameters for a fixed structure can be accomplished using standard techniques, sequential update of network structure is still an open problem. In this paper, we investigate sequential update of Bayesian networks were both parameters and structure are expected to change. We introduce a new approach that allows for the flexible manipulation of the tradeoff between the quality of the learned networks and the amount of information that is maintained about past observations. We formally describe our approach including the necessary modifications to the scoring functions for learning Bayesian networks, evaluate its effectiveness through and empirical study, and extend it to the case of missing data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #73146. 	[Title] LEARNING BAYESIAN NETWORKS WITH LOCAL STRUCTURE [Abstract] We examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional probability distributions (CPDs) that quantify these networks. This increases the space of possible models, enabling the representation of CPDs with a variable number of parameters. The resulting learning procedure induces models that better emulate the interactions present in the data. We describe the theoretical foundations and practical aspects of learning local structures and provide an empirical evaluation of the proposed learning procedure. This evaluation indicates that learning curves characterizing this procedure converge faster, in the number of training instances, than those of the standard procedure, which ignores the local structure of the CPDs. Our results also show that networks learned with local structures tend to be more complex (in terms of arcs), yet require fewer parameters. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #157761. 	[Title] On the Complexity of Function Learning [Abstract] The majority of results in computational learning theory are concerned with concept learning, i.e. with the special case of function learning for classes of functions with range f0; 1g. Much less is known about the theory of learning functions with a larger range such as IN or IR. In particular relatively few results exist about the general structure of common models for function learning, and there are only very few nontrivial function classes for which positive learning results have been exhibited in any of these models. We introduce in this paper the notion of a binary branching adversary tree for function learning, which allows us to give a somewhat surprising equivalent characterization of the optimal learning cost for learning a class of real-valued functions (in terms of a max-min definition which does not involve any "learning" model). Another general structural result of this paper relates the cost for learning a union of function classes to the learning costs for the individual function classes. Furthermore, we exhibit an efficient learning algorithm for learning convex piecewise linear functions from IR d into IR. Previously, the class of linear functions from IR d into IR was the only class of functions with multi-dimensional domain that was known to be learnable within the rigorous framework of a formal model for on-line learning. Finally we give a sufficient condition for an arbitrary class F of functions from IR into IR that allows us to learn the class of all functions that can be written as the pointwise maximum of k functions from F . This allows us to exhibit a number of further nontrivial classes of functions from IR into IR for which there exist efficient learning algorithms. 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 #1117249. 	[Title] Large Margin Classification Using the Perceptron Algorithm [Abstract] We introduce and analyze a new algorithm for linear classification which combines Rosenblatt's perceptron algorithm with Helmbold and Warmuth's leave-one-out method. Like Vapnik's maximal-margin classifier, our algorithm takes advantage of data that are linearly separable with large margins. Compared to Vapnik's algorithm, however, ours is much simpler to implement, and much more efficient in terms of computation time. We also show that our algorithm can be efficiently used in very high dimensional spaces using kernel functions. We performed some experiments using our algorithm, and some variants of it, for classifying images of handwritten digits. The performance of our algorithm is close to, but not as good as, the performance of maximal-margin classifiers on the same problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4804. 	[Title] Toward Efficient Agnostic Learning [Abstract] In this paper we initiate an investigation of generalizations of the Probably Approximately Correct (PAC) learning model that attempt to significantly weaken the target function assumptions. The ultimate goal in this direction is informally termed agnostic learning, in which we make virtually no assumptions on the target function. The name derives from the fact that as designers of learning algorithms, we give up the belief that Nature (as represented by the target function) has a simple or succinct explanation. We give a number of positive and negative results that provide an initial outline of the possibilities for agnostic learning. Our results include hardness results for the most obvious generalization of the PAC model to an agnostic setting, an efficient and general agnostic learning method based on dynamic programming, relationships between loss functions for agnostic learning, and an algorithm for a learning problem that involves hidden variables. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #321861. 	[Title] Gambling in a rigged casino: The adversarial multi-armed bandit problem [Abstract] In the multi-armed bandit problem, a gambler must decide which arm of K non-identical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff). Past solutions for the bandit problem have almost always relied on assumptions about the statistics of the slot machines. In this work, we make no statistical assumptions whatsoever about the nature of the process generating the payoffs of the slot machines. We give a solution to the bandit problem in which an adversary, rather than a well-behaved stochastic process, has complete control over the payoffs. In a sequence of T plays, we prove that the expected per-round payoff of our algorithm approaches that of the best arm at the rate O(T 1=2 ), and we give an improved rate of convergence when the best arm has fairly low payoff. We also prove a general matching lower bound on the best possible performance of any algorithm in our setting. In addition, we consider a setting in which the player has a team of experts advising him on which arm to play; here, we give a strategy that will guarantee expected payoff close to that of the best expert. Finally, we apply our result to the problem of learning to play an unknown repeated matrix game against an all-powerful adversary. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #79817. 	[Title] Bayesian and Information-Theoretic Priors for Bayesian Network Parameters [Abstract] We consider Bayesian and information-theoretic approaches for determining non-informative prior distributions in a parametric model family. The information-theoretic approaches are based on the recently modified definition of stochastic complexity by Rissanen, and on the Minimum Message Length (MML) approach by Wallace. The Bayesian alternatives include the uniform prior, and the equivalent sample size priors. In order to be able to empirically compare the different approaches in practice, the methods are instantiated for a model family of practical importance, the family of Bayesian networks. Please summarise all the given information.

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 #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 #429781. 	[Title] Mistake-Driven Learning in Text Categorization [Abstract] Learning problems in the text processing domain often map the text to a space whose dimensions are the measured features of the text, e.g., its words. Three characteristic properties of this domain are (a) very high dimensionality, (b) both the learned concepts and the instances reside very sparsely in the feature space, and (c) a high variation in the number of active features in an instance. In this work we study three mistake-driven learning algorithms for a typical task of this nature - text categorization. We argue that these algorithms which categorize documents by learning a linear separator in the feature space have a few properties that make them ideal for this domain. We then show that a quantum leap in performance is achieved when we further modify the algorithms to better address some of the specific characteristics of the domain. In particular, we demonstrate (1) how variation in document length can be tolerated by either normalizing feature weights or by using negative weights, (2) the positive effect of applying a threshold range in training, (3) alternatives in considering feature frequency, and (4) the benefits of discarding features while training. Overall, we present an algorithm, a variation of Littlestone's Winnow, which performs significantly better than any other algorithm tested on this task using a similar feature set. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18774. 	[Title] On the Sample Complexity of Learning Bayesian Networks [Abstract] In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown that this learning procedure is asymptotically successful: with probability one, it will converge to the target distribution, given a sufficient number of samples. However, the rate of this convergence has been hitherto unknown. In this work we examine the sample complexity of MDL based learning procedures for Bayesian networks. We show that the number of samples needed to learn an *-close approximation (in terms of entropy distance) with confidence ffi is O * ) 3 log 1 ffi log log 1 . This means that the sample complexity is a low-order polynomial in the error threshold and sub-linear in the confidence bound. We also discuss how the constants in this term depend on the complexity of the target distribution. Finally, we address questions of asymptotic minimality and propose a method for using the sample complexity results to speed up the learning process. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28632. 	[Title] Universal Portfolios With and Without Transaction Costs [Abstract] A constant rebalanced portfolio is an investment strategy which keeps the same distribution of wealth among a set of stocks from period to period. Recently there has been work on on-line investment strategies that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixed percentage transaction cost (commission), answering a question raised in (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). In addition, we present a simple randomized implementation that is significantly faster in practice. We conclude by explaining how these algorithms can be applied to other problems, such as combining the predictions of statistical language models, where the resulting guarantees are more striking. 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 #155736. 	[Title] Worst-case Quadratic Loss Bounds for Prediction Using Linear Functions and Gradient Descent [Abstract] In this paper we study the performance of gradient descent when applied to the problem of on-line linear prediction in arbitrary inner product spaces. We prove worst-case bounds on the sum of the squared prediction errors under various assumptions concerning the amount of a priori information about the sequence to predict. The algorithms we use are variants and extensions of on-line gradient descent. Whereas our algorithms always predict using linear functions as hypotheses, none of our results requires the data to be linearly related. In fact, the bounds proved on the total prediction loss are typically expressed as a function of the total loss of the best fixed linear predictor with bounded norm. All the upper bounds are tight to within constants. Matching lower bounds are provided in some cases. Finally, we apply our results to the problem of on-line prediction for classes of smooth functions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28640. 	[Title] Predicting a binary sequence almost as well as the optimal biased coin [Abstract] We apply the exponential weight algorithm, introduced and Littlestone and Warmuth [17] and by Vovk [24] to the problem of predicting a binary sequence almost as well as the best biased coin. We first show that for the case of the logarithmic loss, the derived algorithm is equivalent to the Bayes algorithm with Jeffrey's prior, that was studied by Xie and Barron under probabilistic assumptions [26]. We derive a uniform bound on the regret which holds for any sequence. We also show that if the empirical distribution of the sequence is bounded away from 0 and from 1, then, as the length of the sequence increases to infinity, the difference between this bound and a corresponding bound on the average case regret of the same algorithm (which is asymptotically optimal in that case) is only 1=2. We show that this gap of 1=2 is necessary by calculating the regret of the min-max optimal algorithm for this problem and showing that the asymptotic upper bound is tight. We also study the application of this algorithm to the square loss and show that the algorithm that is derived in this case is different from the Bayes algorithm and is better than it for prediction in the worst-case. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28641. 	[Title] Game Theory, On-line Prediction and Boosting [Abstract] We study the close connections between game theory, on-line prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the on-line prediction methods of Littlestone and War-muth. The analysis of this algorithm yields a simple proof of von Neumann's famous minmax theorem, as well as a provable method of approximately solving a game. We then show that the on-line prediction model is obtained by applying this game-playing algorithm to an appropriate choice of game and that boosting is obtained by applying the same algorithm to the dual of this game. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #309476. 	[Title] Adaptive Mixtures of Probabilistic Transducers [Abstract] We describe and analyze a mixture model for supervised learning of probabilistic transducers. We devise an on-line learning algorithm that efficiently infers the structure and estimates the parameters of each probabilistic transducer in the mixture. Theoretical analysis and comparative simulations indicate that the learning algorithm tracks the best transducer from an arbitrarily large (possibly infinite) pool of models. We also present an application of the model for inducing a noun phrase recognizer. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #219239. 	[Title] Simulating Access to Hidden Information while Learning [Abstract] We introduce a new technique which enables a learner without access to hidden information to learn nearly as well as a learner with access to hidden information. We apply our technique to solve an open problem of Maass and Turan [18], showing that for any concept class F , the least number of queries sufficient for learning F by an algorithm which has access only to arbitrary equivalence queries is at most a factor of 1= log 2 (4=3) more than the least number of queries sufficient for learning F by an algorithm which has access to both arbitrary equivalence queries and membership queries. Previously known results imply that the 1= log 2 (4=3) in our bound is best possible. We describe analogous results for two generalizations of this model to function learning, and apply those results to bound the difficulty of learning in the harder of these models in terms of the difficulty of learning in the easier model. We bound the difficulty of learning unions of k concepts from a class F in terms of the difficulty of learning F . We bound the difficulty of learning in a noisy environment for deterministic algorithms in terms of the difficulty of learning in a noise-free environment. We apply a variant of our technique to develop an algorithm transformation that allows probabilistic learning algorithms to nearly optimally cope with noise. A second variant enables us to improve a general lower bound of Turan [19] for the PAC-learning model (with queries). Finally, we show that logarithmically many membership queries never help to obtain computationally efficient learning algorithms. fl Supported by Air Force Office of Scientific Research grant F49620-92-J-0515. Most of this work was done while this author was at TU Graz supported by a Lise Meitner Fellowship from the Fonds zur Forderung der wissenschaftlichen Forschung (Austria). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28649. 	[Title] ON-LINE LEARNING OF LINEAR FUNCTIONS [Abstract] We present an algorithm for the on-line learning of linear functions which is optimal to within a constant factor with respect to bounds on the sum of squared errors for a worst case sequence of trials. The bounds are logarithmic in the number of variables. Furthermore, the algorithm is shown to be optimally robust with respect to noise in the data (again to within a constant factor). Key words. Machine learning; computational learning theory; on-line learning; linear functions; worst-case loss bounds; adaptive filter theory. Subject classifications. 68T05. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66794. 	[Title] Automated Decomposition of Model-based Learning Problems [Abstract] A new generation of sensor rich, massively distributed autonomous systems is being developed that has the potential for unprecedented performance, such as smart buildings, reconfigurable factories, adaptive traffic systems and remote earth ecosystem monitoring. To achieve high performance these massive systems will need to accurately model themselves and their environment from sensor information. Accomplishing this on a grand scale requires automating the art of large-scale modeling. This paper presents a formalization of decompositional, model-based learning (DML), a method developed by observing a modeler's expertise at decomposing large scale model estimation tasks. The method exploits a striking analogy between learning and consistency-based diagnosis. Moriarty, an implementation of DML, has been applied to thermal modeling of a smart building, demonstrating a significant improvement in learning rate. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1112686. 	[Title] Bayesian Finite Mixtures for Nonlinear Modeling of Educational data [Abstract] In this paper we discuss a Bayesian approach for finding latent classes in the data. In our approach we use finite mixture models to describe the underlying structure in the data, and demonstrate that the possibility to use full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated with a case study using a data set from a recent educational study. The Bayesian classification approach described has been implemented, and presents an appealing addition to the standard toolbox for exploratory data analysis of educational data. 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 #103537. 	[Title] Discovering Structure in Continuous Variables Using Bayesian Networks [Abstract] We study Bayesian networks for continuous variables using nonlinear conditional density estimators. We demonstrate that useful structures can be extracted from a data set in a self-organized way and we present sampling techniques for belief update based on 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 #1106418. 	[Title] Online Learning versus O*ine Learning [Abstract] We present an off-line variant of the mistake-bound model of learning. Just like in the well studied on-line model, a learner in the offline model has to learn an unknown concept from a sequence of elements of the instance space on which he makes "guess and test" trials. In both models, the aim of the learner is to make as few mistakes as possible. The difference between the models is that, while in the on-line model only the set of possible elements is known, in the off-line model the sequence of elements (i.e., the identity of the elements as well as the order in which they are to be presented) is known to the learner in advance. We give a combinatorial characterization of the number of mistakes in the off-line model. We apply this characterization to solve several natural questions that arise for the new model. First, we compare the mistake bounds of an off-line learner to those of a learner learning the same concept classes in the on-line scenario. We show that the number of mistakes in the on-line learning is at most a log n factor more than the off-line learning, where n is the length of the sequence. In addition, we show that if there is an off-line algorithm that does not make more than a constant number of mistakes for each sequence then there is an online algorithm that also does not make more than a constant number of mistakes. The second issue we address is the effect of the ordering of the elements on the number of mistakes of an off-line learner. It turns out that there are sequences on which an off-line learner can guarantee at most one mistake, yet a permutation of the same sequence forces him to err on many elements. We prove, however, that the gap, between the off-line mistake bounds on permutations of the same sequence of n-many elements, cannot be larger than a multiplicative factor of log n, and we present examples that obtain such a gap. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #65650. 	[Title] Machine Learning 27(1):51-68, 1997. Predicting nearly as well as the best pruning of a decision tree [Abstract] Many algorithms for inferring a decision tree from data involve a two-phase process: First, a very large decision tree is grown which typically ends up "over-fitting" the data. To reduce over-fitting, in the second phase, the tree is pruned using one of a number of available methods. The final tree is then output and used for classification on test data. In this paper, we suggest an alternative approach to the pruning phase. Using a given unpruned decision tree, we present a new method of making predictions on test data, and we prove that our algorithm's performance will not be "much worse" (in a precise technical sense) than the predictions made by the best reasonably small pruning of the given decision tree. Thus, our procedure is guaranteed to be competitive (in terms of the quality of its predictions) with any pruning algorithm. We prove that our procedure is very efficient and highly robust. Our method can be viewed as a synthesis of two previously studied techniques. First, we apply Cesa-Bianchi et al.'s [4] results on predicting using "expert advice" (where we view each pruning as an "expert") to obtain an algorithm that has provably low prediction loss, but that is com-putationally infeasible. Next, we generalize and apply a method developed by Buntine [3], [2] and Willems, Shtarkov and Tjalkens [20], [21] to derive a very efficient implementation of this procedure. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1059953. 	[Title] WORST CASE PREDICTION OVER SEQUENCES UNDER LOG LOSS [Abstract] We consider the game of sequentially assigning probabilities to future data based on past observations under logarithmic loss. We are not making probabilistic assumptions about the generation of the data, but consider a situation where a player tries to minimize his loss relative to the loss of the (with hindsight) best distribution from a target class for the worst sequence of data. We give bounds on the minimax regret in terms of the metric entropies of the target class with respect to suitable distances between distributions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #33013. 	[Title] Learning Conventions in Multiagent Stochastic Domains using Likelihood Estimates [Abstract] Fully cooperative multiagent systemsthose in which agents share a joint utility modelis of special interest in AI. A key problem is that of ensuring that the actions of individual agents are coordinated, especially in settings where the agents are autonomous decision makers. We investigate approaches to learning coordinated strategies in stochastic domains where an agent's actions are not directly observable by others. Much recent work in game theory has adopted a Bayesian learning perspective to the more general problem of equilibrium selection, but tends to assume that actions can be observed. We discuss the special problems that arise when actions are not observable, including effects on rates of convergence, and the effect of action failure probabilities and asymmetries. We also use likelihood estimates as a means of generalizing fictitious play learning models in our setting. Finally, we propose the use of maximum likelihood as a means of removing strategies from consideration, with the aim of convergence to a conventional equilibrium, at which point learning and deliberation can cease. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105531. 	[Title] Belief Networks, Hidden Markov Models, and Markov Random Fields: a Unifying View [Abstract] The use of graphs to represent independence structure in multivariate probability models has been pursued in a relatively independent fashion across a wide variety of research disciplines since the beginning of this century. This paper provides a brief overview of the current status of such research with particular attention to recent developments which have served to unify such seemingly disparate topics as probabilistic expert systems, statistical physics, image analysis, genetics, decoding of error-correcting codes, Kalman filters, and speech recognition with Markov models. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #345340. 	[Title] Generalized Prioritized Sweeping [Abstract] Prioritized sweeping is a model-based reinforcement learning method that attempts to focus an agent's limited computational resources to achieve a good estimate of the value of environment states. To choose effectively where to spend a costly planning step, classic prioritized sweeping uses a simple heuristic to focus computation on the states that are likely to have the largest errors. In this paper, we introduce generalized prioritized sweeping, a principled method for generating such estimates in a representation-specific manner. This allows us to extend prioritized sweeping beyond an explicit, state-based representation to deal with compact representations that are necessary for dealing with large state spaces. We apply this method for generalized model approximators (such as Bayesian networks), and describe preliminary experiments that compare our approach with classical prioritized sweeping. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #510718. 	[Title] Learning Bayesian Networks from Incomplete Data [Abstract] Much of the current research in learning Bayesian Networks fails to effectively deal with missing data. Most of the methods assume that the data is complete, or make the data complete using fairly ad-hoc methods; other methods do deal with missing data but learn only the conditional probabilities, assuming that the structure is known. We present a principled approach to learn both the Bayesian network structure as well as the conditional probabilities from incomplete data. The proposed algorithm is an iterative method that uses a combination of Expectation-Maximization (EM) and Imputation techniques. Results are presented on synthetic data sets which show that the performance of the new algorithm is much better than ad-hoc methods for handling missing data. Please summarise all the given information.

Paper #94713 has the title `Update rules for parameter estimation in Bayesian networks  
` and the 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.
`.
Question: Which category should Paper #94713 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #94713 has the title `Update rules for parameter estimation in Bayesian networks  
` and the 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.
`.
Question: Which category should Paper #94713 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