Above are papers related to the following paper: [Paper_ID] Paper #35905. 	[Title] Equivalence of Linear Boltzmann Chains and Hidden Markov Models sequence L, is: where Z(; A; [Abstract] Several authors have made a link between hidden Markov models for time series and energy-based models (Luttrell 1989, Williams 1990, Saul and Jordan 1995). Saul and Jordan (1995) discuss a linear Boltzmann chain model with state-state transition energies A ii 0 (going from state i to state i 0 ) and symbol emission energies B ij , under which the probability of an entire state fi l ; j l g L Whilst any HMM can be written as a linear Boltzmann chain by setting exp(A ii 0 ) = a ii 0 , exp(B ij ) = b ij and exp( i ) = i , not all linear Boltzmann chains can be represented as HMMs (Saul and Jordan 1995). However, the difference between the two models is minimal. To be precise, if the final hidden Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1118848. 	[Title] A Sparse Representation for Function Approximation [Abstract] We derive a new general representation for a function as a linear combination of local correlation kernels at optimal sparse locations (and scales) and characterize its relation to PCA, regularization, sparsity principles and Support Vector Machines. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #576257. 	[Title] Genetic Programming of Minimal Neural Nets Using Occam's Razor [Abstract] A genetic programming method is investigated for optimizing both the architecture and the connection weights of multilayer feedforward neural networks. The genotype of each network is represented as a tree whose depth and width are dynamically adapted to the particular application by specifically defined genetic operators. The weights are trained by a next-ascent hillclimb-ing search. A new fitness function is proposed that quantifies the principle of Occam's razor. It makes an optimal trade-off between the error fitting ability and the parsimony of the network. We discuss the results for two problems of differing complexity and study the convergence and scaling properties of the algorithm. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1114118. 	[Title] Power System Security Margin Prediction Using Radial Basis Function Networks [Abstract] Dr. McCalley's research is partially supported through grants from National Science Foundation and Pacific Gas and Electric Company. Dr. Honavar's research is partially supported through grants from National Science Foundation and the John Deere Foundation. This paper will appear in: Proceedings of the 29th Annual North American Power Symposium, Oct. 13-14. 1997, Laramie, Wyoming. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #300806. 	[Title] Learning in Boltzmann Trees [Abstract] We introduce a large family of Boltzmann machines that can be trained using standard gradient descent. The networks can have one or more layers of hidden units, with tree-like connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resort to simulated or mean-field annealing. The stochastic averages that yield the gradients in weight space are computed by the technique of decimation. We present results on the problems of N -bit parity and the detection of hidden symmetries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152904. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #906. 	[Title] Regularization Theory and Neural Networks Architectures [Abstract] We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, some forms of Projection Pursuit Regression and several types of neural networks. We propose to use the term Generalized Regularization Networks for this broad class of approximation schemes that follow from an extension of regularization. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In summary, different multilayer networks with one hidden layer, which we collectively call Generalized Regularization Networks, correspond to different classes of priors and associated smoothness functionals in a classical regularization principle. Three broad classes are a) Radial Basis Functions that can be generalized to Hyper Basis Functions, b) some tensor product splines, and c) additive splines that can be generalized to schemes of the type of ridge approximation, hinge functions and several perceptron-like neural networks with one-hidden layer. 1 This paper will appear on Neural Computation, vol. 7, pages 219-269, 1995. An earlier version of Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #910. 	[Title] Learning networks for face analysis and synthesis [Abstract] This paper presents an overview of the face-related projects in our group. The unifying theme underlying our work is the use of example-based learning methods for both analyzing and synthesizing face images. We label the example face images (and for the problem of face detection, "near miss" faces as well) with descriptive parameters for pose, expression, identity, and face vs. non-face. Then, by using example-based learning techniques, we develop networks for performing analysis tasks such as pose and expression estimation, face recognition, and face detection in cluttered scenes. In addition to these analysis applications, we show how the example-based technique can also be used as a novel method for image synthesis that is for computer graphics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152272. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #755217. 	[Title] Active Gesture Recognition using Partially Observable Markov Decision Processes [Abstract] M.I.T Media Laboratory Perceptual Computing Section Technical Report No. 367 Appeared 13th IEEE Intl. Conference on Pattern Recognition (ICPR '96), Vienna, Austria. Abstract We present a foveated gesture recognition system that guides an active camera to foveate salient features based on a reinforcement learning paradigm. Using vision routines previously implemented for an interactive environment, we determine the spatial location of salient body parts of a user and guide an active camera to obtain images of gestures or expressions. A hidden-state reinforcement learning paradigm based on the Partially Observable Markov Decision Process (POMDP) is used to implement this visual attention. The attention module selects targets to foveate based on the goal of successful recognition, and uses a new multiple-model Q-learning formulation. Given a set of target and distractor gestures, our system can learn where to foveate to maximally discriminate a particular gesture. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12946. 	[Title] Learning from incomplete data [Abstract] Real-world learning tasks often involve high-dimensional data sets with complex patterns of missing features. In this paper we review the problem of learning from incomplete data from two statistical perspectives|the likelihood-based and the Bayesian. The goal is two-fold: to place current neural network approaches to missing data within a statistical framework, and to describe a set of algorithms, derived from the likelihood-based framework, that handle clustering, classification, and function approximation from incomplete data in a principled and efficient manner. These algorithms are based on mixture modeling and make two distinct appeals to the Expectation-Maximization (EM) principle (Dempster et al., 1977)|both for the estimation of mixture components and for coping with the missing data. 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. The authors were supported in part by a grant from ATR Auditory and Visual Perception Research Laboratories, by a grant from Siemens Corporation, by grant IRI-9013991 from the National Science Foundation, and by grant N00014-90-J-1942 from the Office of Naval Research. Zoubin Ghahramani was supported by a grant from the McDonnell-Pew Foundation. 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 #1129111. 	[Title] TABLE DES MATI ERES 1 Apprentissage et approximation les techniques de regularisation 3 1.1 Introduction [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12439. 	[Title] Improving the Performance of Radial Basis Function Networks by Learning Center Locations [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1116569. 	[Title] Gaussian Regression and Optimal Finite Dimensional Linear Models [Abstract]  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 #1122460. 	[Title] Learning Controllers from Examples  a motivation for searching alternative, empirical techniques for generating controllers. [Abstract] Today there is a great interest in discovering methods that allow a faster design and development of real-time control software. Control theory helps when linear controllers have to be developed but it does not support the generation In this paper, it is discussed how Machine Learning has been applied to the Function, and Locally Receptive Field Function Approximators. Three integrated learning algorithms, two of which are original, are described and then tried on two experimental test cases. The first test case is provided by an industrial robot KUKA IR-361 engaged into the "peg-into-hole" task, while the second is a classical prediction task on the Mackey-Glass chaotic series. From the experimental comparison, it appears that both Fuzzy Controllers and RBFNs synthesised from examples are excellent approximators, and that they can be even more accurate than MLPs. of non-linear controllers, which in many cases (such as in compliant motion control) Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1126044. 	[Title] A Brief History of Connectionism [Abstract] Connectionist research is firmly established within the scientific community, especially within the multi-disciplinary field of cognitive science. This diversity, however, has created an environment which makes it difficult for connectionist researchers to remain aware of recent advances in the field, let alone understand how the field has developed. This paper attempts to address this problem by providing a brief guide to connectionist research. The paper begins by defining the basic tenets of connectionism. Next, the development of connectionist research is traced, commencing with connectionism's philosophical predecessors, moving to early psychological and neuropsychological influences, followed by the mathematical and computing contributions to connectionist research. Current research is then reviewed, focusing specifically on the different types of network architectures and learning rules in use. The paper concludes by suggesting that neural network research|at least in cognitive science|should move towards models that incorporate the relevant functional principles inherent in neurobiological systems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1135137. 	[Title] Temporal Compositional Processing by a DSOM Hierarchical Model [Abstract] Any intelligent system, whether human or robotic, must be capable of dealing with patterns over time. Temporal pattern processing can be achieved if the system has a short-term memory capacity (STM) so that different representations can be maintained for some time. In this work we propose a neural model wherein STM is realized by leaky integrators in a self-organizing system. The model exhibits composition-ality, that is, it has the ability to extract and construct progressively complex and structured associations in an hierarchical manner, starting with basic and primitive (temporal) elements. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152162. 	[Title] GIBBS-MARKOV MODELS [Abstract] In this paper we present a framework for building probabilistic automata parameterized by context-dependent probabilities. Gibbs distributions are used to model state transitions and output generation, and parameter estimation is carried out using an EM algorithm where the M-step uses a generalized iterative scaling procedure. We discuss relations with certain classes of stochastic feedforward neural networks, a geometric interpretation for parameter estimation, and a simple example of a statistical language model constructed using this methodology. 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 #48550. 	[Title] Identification and Control of Nonlinear Systems Using Neural Network Models: Design and Stability Analysis [Abstract] Report 91-09-01 September 1991 (revised) May 1994 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 #34355. 	[Title] PRIOR KNOWLEDGE AND THE CREATION OF "VIRTUAL" EXAMPLES FOR RBF NETWORKS 1 [Abstract] We consider the problem of how to incorporate prior knowledge in supervised learning techniques. We set the problem in the framework of regularization theory, and consider the case in which we know that the approximated function has radial symmetry. The problem can be solved in two alternative ways: 1) use the invariance as a constraint in the regularization theory framework to derive a rotation invariant version of Radial Basis Functions; 2) use the radial symmetry to create new, "virtual" examples from a given data set. We show that these two apparently different methods of learning from "hints" (Abu-Mostafa, 1993) lead to exactly the same analyt ical solution. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #58552. 	[Title] Differential theory of learning for efficient neural network pattern recognition [Abstract] We describe a new theory of differential learning by which a broad family of pattern classifiers (including many well-known neural network paradigms) can learn stochastic concepts efficiently. We describe the relationship between a classifier's ability to generalize well to unseen test examples and the efficiency of the strategy by which it learns. We list a series of proofs that differential learning is efficient in its information and computational resource requirements, whereas traditional probabilistic learning strategies are not. The proofs are illustrated by a simple example that lends itself to closed-form analysis. We conclude with an optical character recognition task for which three different types of differentially generated classifiers generalize significantly better than their probabilistically generated counterparts. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #436796. 	[Title] Some Extensions of the K-Means Algorithm for Image Segmentation and Pattern Classification [Abstract] In this paper we present some extensions to the k-means algorithm for vector quantization that permit its efficient use in image segmentation and pattern classification tasks. It is shown that by introducing state variables that correspond to certain statistics of the dynamic behavior of the algorithm, it is possible to find the representative centers of the lower dimensional manifolds that define the boundaries between classes, for clouds of multi-dimensional, multi-class data; this permits one, for example, to find class boundaries directly from sparse data (e.g., in image segmentation tasks) or to efficiently place centers for pattern classification (e.g., with local Gaussian classifiers). The same state variables can be used to define algorithms for determining adaptively the optimal number of centers for clouds of data with space-varying density. Some examples of the application of these extensions are also given. This report describes research done within CIMAT (Guanajuato, Mexico), the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences, and at the Artificial Intelligence Laboratory. This research is sponsored by grants from the Office of Naval Research under contracts N00014-91-J-1270 and N00014-92-J-1879; by a grant from the National Science Foundation under contract ASC-9217041; and by a grant from the National Institutes of Health under contract NIH 2-S07-RR07047. Additional support is provided by the North Atlantic Treaty Organization, ATR Audio and Visual Perception Research Laboratories, Mitsubishi Electric Corporation, Sumitomo Metal Industries, and Siemens AG. Support for the A.I. Laboratory's artificial intelligence research is provided by ONR contract N00014-91-J-4038. J.L. Marroquin was supported in part by a grant from the Consejo Nacional de Ciencia y Tecnologia, Mexico. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #77758. 	[Title] Parzen. On estimation of a probability density function and mode. Annual Mathematical Statistics, 33:1065-1076, 1962. [Abstract] To apply the algorithm for classification we assign each class a separate set of codebook Gaussians. Each set is only trained with patterns from a single class. After having trained the codebook Gaussians, each set provides an estimate of the probability function of one class; just as with Parzen window estimation, we take as the estimate of the pattern distribution the average of all Gaussians in the set. Classification of a pattern may now be done by calculating the probability of each class at the respective sample point, and assigning to the pattern the class with the highest probability. Hence the whole codebook plays a role in the classification of patterns. This is not the case with regular classification schemes using codebooks. We have tested the classification scheme on several classification tasks including the two spiral problem. We compared our algorithm to various other classification algorithms and it came out second; the best algorithm for the applications is the Parzen window estimation. However, the computing time and memory for Parzen window estimation are excessive when compared to our algorithm, and hence, in practical situations, our algorithm is to be preferred. We have developed a fast algorithm which combines attractive properties of both Parzen window estimation and vector quantization. The scale parameter is tuned adaptively and, therefore, is not set in an ad hoc manner. It allows a classification strategy in which all the codebook vectors are taken into account. This yields better results than the standard vector quantization techniques. An interesting topic for further research is to use radially non-symmetric Gaussians. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105344. 	[Title] In Advances in Neural Information Processing Systems 8  Gaussian Processes for Regression [Abstract] The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152194. 	[Title]  [Abstract] Draft A Brief Introduction to Neural Networks Richard D. De Veaux Lyle H. Ungar Williams College University of Pennsylvania Abstract Artificial neural networks are being used with increasing frequency for high dimensional problems of regression or classification. This article provides a tutorial overview of neural networks, focusing on back propagation networks as a method for approximating nonlinear multivariable functions. We explain, from a statistician's vantage point, why neural networks might be attractive and how they compare to other modern regression techniques. KEYWORDS: nonparametric regression; function approximation; backpropagation. 1 Introduction Networks that mimic the way the brain works; computer programs that actually LEARN patterns; forecasting without having to know statistics. These are just some of the many claims and attractions of artificial neural networks. Neural networks (we will henceforth drop the term artificial, unless we need to distinguish them from biological neural networks) seem to be everywhere these days, and at least in their advertising, are able to do all that statistics can do without all the fuss and bother of having to do anything except buy a piece of software. Neural networks have been successfully used for many different applications including robotics, chemical process control, speech recognition, optical character recognition, credit card fraud detection, interpretation of chemical spectra and vision for autonomous navigation of vehicles. (Pointers to the literature are given at the end of this article.) In this article we will attempt to explain how one particular type of neural network, feedforward networks with sigmoidal activation functions ("backpropagation networks") actually works, how it is "trained", and how it compares with some more well known statistical techniques. As an example of why someone would want to use a neural network, consider the problem of recognizing hand written ZIP codes on letters. This is a classification problem, where the 1 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #675649. 	[Title] Modeling Volatility using State Space Models [Abstract] In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict their time evolution adequately, we estimate state space models that explicitly include observational noise. We obtain relaxation times for shocks in the logarithm of volatility ranging from three weeks (for foreign exchange) to three to five months (for stock indices). In most cases, a two-dimensional hidden state is required to yield residuals that are consistent with white noise. We compare these results with ordinary autoregressive models (without a hidden state) and find that autoregressive models underestimate the relaxation times by about two orders of magnitude due to their ignoring the distinction between observational and dynamic noise. This new interpretation of the dynamics of volatility in terms of relaxators in a state space model carries over to stochastic volatility models and to GARCH models, and is useful for several problems in finance, including risk management and the pricing of derivative securities. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31043. 	[Title] FONN: Combining First Order Logic with Connectionist Learning [Abstract] This paper presents a neural network architecture that can manage structured data and refine knowledge bases expressed in a first order logic language. The presented framework is well suited to classification problems in which concept de scriptions depend upon numerical features of the data. In fact, the main goal of the neural architecture is that of refining the numerical part of the knowledge base, without changing its structure. In particular, we discuss a method to translate a set of classification rules into neural computation units. Here, we focus our attention on the translation method and on algorithms to refine network weights on struc tured data. The classification theory to be refined can be manually handcrafted or automatically acquired by a symbolic relational learning system able to deal with numerical features. As a matter of fact, the primary goal is to bring into a neural network architecture the capability of dealing with structured data of unrestricted size, by allowing to dynamically bind the classification rules to different items occur ring in the input data. An extensive experimentation on a challenging artificial case study shows that the network converges quite fastly and generalizes much better than propositional learners on an equivalent task definition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #160705. 	[Title] Receptive Fields for Vision: from Hyperacuity to Object Recognition [Abstract] Many of the lower-level areas in the mammalian visual system are organized retinotopically, that is, as maps which preserve to a certain degree the topography of the retina. A unit that is a part of such a retinotopic map normally responds selectively to stimulation in a well-delimited part of the visual field, referred to as its receptive field (RF). Receptive fields are probably the most prominent and ubiquitous computational mechanism employed by biological information processing systems. This paper surveys some of the possible computational reasons behind the ubiquity of RFs, by discussing examples of RF-based solutions to problems in vision, from spatial acuity, through sensory coding, to object recognition. fl Weizmann Institute CS-TR 95-29, 1995; to appear in Vision, R. J. Watt, ed., MIT Press, 1996. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1140040. 	[Title] for Projective Basis Function Networks 2m1 Global Form 2m Local Form With appropriate constant factors, [Abstract] OGI CSE Technical Report 96-006 Abstract: Smoothing regularizers for radial basis functions have been studied extensively, but no general smoothing regularizers for projective basis functions (PBFs), such as the widely-used sigmoidal PBFs, have heretofore been proposed. We derive new classes of algebraically-simple m th -order smoothing regularizers for networks of projective basis functions f (W; x) = P N fi fl + u 0 ; with general transfer functions g[]. These simple algebraic forms R(W; m) enable the direct enforcement of smoothness without the need for costly Monte Carlo integrations of S(W; m). The regularizers are tested on illustrative sample problems and compared to quadratic weight decay. The new regularizers are shown to yield better generalization errors than Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #242637. 	[Title] A Delay Damage Model Selection Algorithm for NARX Neural Networks [Abstract] Recurrent neural networks have become popular models for system identification and time series prediction. NARX (Nonlinear AutoRegressive models with eXogenous inputs) neural network models are a popular subclass of recurrent networks and have been used in many applications. Though embedded memory can be found in all recurrent network models, it is particularly prominent in NARX models. We show that using intelligent memory order selection through pruning and good initial heuristics significantly improves the generalization and predictive performance of these nonlinear systems on problems as diverse as grammatical inference and time series prediction. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #13136. 	[Title] Models of perceptual learning in vernier hyperacuity [Abstract] Performance of human subjects in a wide variety of early visual processing tasks improves with practice. HyperBF networks (Poggio and Girosi, 1990) constitute a mathematically well-founded framework for understanding such improvement in performance, or perceptual learning, in the class of tasks known as visual hyperacuity. The present article concentrates on two issues raised by the recent psychophysical and computational findings reported in (Poggio et al., 1992b; Fahle and Edelman, 1992). First, we develop a biologically plausible extension of the HyperBF model that takes into account basic features of the functional architecture of early vision. Second, we explore various learning modes that can coexist within the HyperBF framework and focus on two unsupervised learning rules which may be involved in hyperacuity learning. Finally, we report results of psychophysical experiments that are consistent with the hypothesis that activity-dependent presynaptic amplification may be involved in perceptual learning in hyperacuity. 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 #684372. 	[Title] Incremental Polynomial Model-Controller Network: a self organising non-linear controller [Abstract] The aim of this study is to present the "Incremental Polynomial Model-Controller Network" (IPMCN). This network is composed of controllers each one attached to a model used for its indirect design. At each instant the controller connected to the model performing the best is selected. An automatic network construction algorithm is discribed in this study. It makes the IPMCN a self-organising non-linear controller. However the emphasis is on the polynomial controllers that are the building blocks of the IPMCN. From an analysis of the properties of polynomial functions for system modelling it is shown that multiple low order odd polynomials are very suitable to model non-linear systems. A closed loop reference model method to design a controller from a odd polynomial model is then described. The properties of the IPMCN are illustrated according to a second order system having both system states y and _y involving non-linear behaviour. It shows that as a component of a network or alone, a low order odd polynomial controller performs much better than a linear adaptive controller. Moreover, the number of controllers is significantly reduced with the increase of the polynomial order of the controllers and an improvement of the control performance is proportional to the decrease of the number of controllers. In addition, the clustering free approach, applied for the selection of the controllers, makes the IPMCN insensitive to the number of quantities involving nonlinearity in the system. The use of local controllers capable of handling systems with complex dynamics will make this scheme one of the most effective approaches for the control of non-linear systems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5462. 	[Title] Priors, Stabilizers and Basis Functions: from regularization to radial, tensor and additive splines [Abstract] We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular we had discussed how standard smoothness functionals lead to a subclass of regularization networks, the well-known Radial Basis Functions approximation schemes. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same extension that leads from Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions and some forms of Projection Pursuit Regression. We propose to use the term Generalized Regularization Networks for this broad class of approximation schemes that follow from an extension of regularization. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we show the relation between activation functions of the Gaussian and sigmoidal type by considering the simple case of the kernel G(x) = jxj. In summary, different multilayer networks with one hidden layer, which we collectively call Generalized Regularization Networks, correspond to different classes of priors and associated smoothness functionals in a classical regularization principle. Three broad classes are a) Radial Basis Functions that generalize into Hyper Basis Functions, b) some tensor product splines, and c) additive splines that generalize into schemes of the type of ridge approximation, hinge functions and one-hidden-layer perceptrons. This paper describes research done within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences and at the Artificial Intelligence Laboratory. This research is sponsored by grants from the Office of Naval Research under contracts N00014-91-J-1270 and N00014-92-J-1879; by a grant from the National Science Foundation under contract ASC-9217041 (which includes funds from DARPA provided under the HPCC program); and by a grant from the National Institutes of Health under contract NIH 2-S07-RR07047. Additional support is provided by the North Atlantic Treaty Organization, ATR Audio and Visual Perception Research Laboratories, Mitsubishi Electric Corporation, Sumitomo Metal Industries, and Siemens AG. Support for the A.I. Laboratory's artificial intelligence research is provided by ONR contract N00014-91-J-4038. Tomaso Poggio is supported by the Uncas and Helen Whitaker Chair at the Whitaker College, Massachusetts Institute of Technology. c fl Massachusetts Institute of Technology, 1993 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #227286. 	[Title] Space-Frequency Localized Basis Function Networks for Nonlinear System Estimation and Control [Abstract] Stable neural network control and estimation may be viewed formally as a merging of concepts from nonlinear dynamic systems theory with tools from multivariate approximation theory. This paper extends earlier results on adaptive control and estimation of nonlinear systems using gaussian radial basis functions to the on-line generation of irregularly sampled networks, using tools from multiresolution analysis and wavelet theory. This yields much more compact and efficient system representations while preserving global closed-loop stability. Approximation models employing basis functions that are localized in both space and spatial frequency admit a measure of the approximated function's spatial frequency content that is not directly dependent on reconstruction error. As a result, these models afford a means of adaptively selecting basis functions according to the local spatial frequency content of the approximated function. An algorithm for stable, on-line adaptation of output weights simultaneously with node configuration in a class of non-parametric models with wavelet basis functions is presented. An asymptotic bound on the error in the network's reconstruction is derived and shown to be dependent solely on the minimum approximation error associated with the steady state node configuration. In addition, prior bounds on the temporal bandwidth of the system to be identified or controlled are used to develop a criterion for on-line selection of radial and ridge wavelet basis functions, thus reducing the rate of increase in network's size with the dimension of the state vector. Experimental results obtained by using the network to predict the path of an unknown light bluff object thrown through air, in an active-vision based robotic catching system, are given to illustrate the network's performance in a simple real-time application. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120858. 	[Title] Three-Dimensional Object Recognition Using an Unsupervised BCM Network: The Usefulness of Distinguishing Features [Abstract] We propose an object recognition scheme based on a method for feature extraction from gray level images that corresponds to recent statistical theory, called projection pursuit, and is derived from a biologically motivated feature extracting neuron. To evaluate the performance of this method we use a set of very detailed psychophysical 3D object recognition experiments (Bulthoff and Edelman, 1992). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #67292. 	[Title] Radial Basis Functions for Process Control [Abstract] Radial basis function (RBFs) neural networks provide an attractive method for high dimensional nonparametric estimation for use in nonlinear control. They are faster to train than conventional feedforward networks with sigmoidal activation networks ("backpropagation nets"), and provide a model structure better suited for adaptive control. This article gives a brief survey of the use of RBFs and then introduces a new statistical interpretation of radial basis functions and a new method of estimating the parameters, using the EM algorithm. This new statistical interpretation allows us to provide confidence limits on predictions made using the networks. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #636511. 	[Title] Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers [Abstract] The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by k-means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well-founded, but also superior in a practical application. This report describes research done at the Center for Biological and Computational Learning, the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology, and at AT&T Bell Laboratories (now AT&T Research, and Lucent Technologies Bell Laboratories). Support for the Center is provided in part by a grant from the National Science Foundation under contract ASC-9217041. BS thanks the M.I.T. for hospitality during a three-week visit in March 1995, where this work was started. At the time of the study, BS, CB, and VV were with AT&T Bell Laboratories, NJ; KS, FG, PN, and TP were with the Massachusetts Institute of Technology. KS is now with the Department of Information Systems and Computer Science at the National University of Singapore, Lower Kent Ridge Road, Singapore 0511; CB and PN are with Lucent Technologies, Bell Laboratories, NJ; VV is with AT&T Research, NJ. BS was supported by the Studienstiftung des deutschen Volkes; CB was supported by ARPA under ONR contract number N00014-94-C-0186. We thank A. Smola for useful discussions. Please direct correspondence to Bernhard Scholkopf, bs@mpik-tueb.mpg.de, Max-Planck-Institut fur biologische Kybernetik, Spemannstr. 38, 72076 Tubingen, Germany. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #42847. 	[Title] GROWING RADIAL BASIS FUNCTION NETWORKS [Abstract] This paper presents and evaluates two algorithms for incrementally constructing Radial Basis Function Networks, a class of neural networks which looks more suitable for adtaptive control applications than the more popular backpropagation networks. The first algorithm has been derived by a previous method developed by Fritzke, while the second one has been inspired by the CART algorithm developed by Breiman for generation regression trees. Both algorithms proved to work well on a number of tests and exhibit comparable performances. An evaluation on the standard case study of the Mackey-Glass temporal series is reported. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1108834. 	[Title] ce: [39] <author> Yoda, M. </author> <year> (1994). </year> <title> Predicting the Tokyo stock market. </title> <editor> In Deboeck, G.J. (Ed.) </editor> <year> (1994). </year> <title> Trading on the Edge. </title> <address> New York: </address> <publisher> Wiley., </publisher> <pages> 66-79. </pages> <institution> VITA Graduate School Southern Illinois University Daniel Nikolaev Nikovski Date of Birth: </institution> <address> April 13, 1969 606 West College Street, Apt.4, Rm. 6, Carbondale, Illinois 62901 150 Hristo Botev Boulevard, Apt. </address> <month> 54, </month> <title> 4004 Plovdiv, Bulgaria Technical University - Sofia, Bulgaria Engineer of Computer Systems and Control Thesis Title: Adaptive Computation Techniques for Time Series Analysis Major Professor: </title> <journal> Dr. Mehdi Zargham </journal> [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #131042. 	[Title] Efficient Implementation of Gaussian Processes [Abstract] Neural networks and Bayesian inference provide a useful framework within which to solve regression problems. However their parameterization means that the Bayesian analysis of neural networks can be difficult. In this paper, we investigate a method for regression using Gaussian process priors which allows exact Bayesian analysis using matrix manipulations. We discuss the workings of the method in detail. We will also detail a range of mathematical and numerical techniques that are useful in applying Gaussian processes to general problems including efficient approximate matrix inversion methods developed by Skilling. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25702. 	[Title] Nonlinear Prediction of Chaotic Time Series Using Support Vector Machines [Abstract] A novel method for regression has been recently proposed by V. Vapnik et al. [8, 9]. The technique, called Support Vector Machine (SVM), is very well founded from the mathematical point of view and seems to provide a new insight in function approximation. We implemented the SVM and tested it on the same data base of chaotic time series that was used in [1] to compare the performances of different approximation techniques, including polynomial and rational approximation, local polynomial techniques, Radial Basis Functions, and Neural Networks. The SVM performs better than the approaches presented in [1]. We also study, for a particular time series, the variability in performance with respect to the few free parameters of SVM. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #94953. 	[Title] Convergence Rates of Approximation by Translates [Abstract] In this paper we consider the problem of approximating a function belonging to some function space by a linear combination of n translates of a given function G. Using a lemma by Jones (1990) and Barron (1991) we show that it is possible to define function spaces and functions G for which the rate of convergence to zero of the error is O( 1 p n ) in any number of dimensions. The apparent avoidance of the "curse of dimensionality" is due to the fact that these function spaces are more and more constrained as the dimension increases. Examples include spaces of the Sobolev type, in which the number of weak derivatives is required to be larger than the number of dimensions. We give results both for approximation in the L 2 norm and in the L 1 norm. The interesting feature of these results is that, thanks to the constructive nature of Jones' and Barron's lemma, an iterative procedure is defined that can achieve this rate. This paper describes research done within the Center for Biological Information Processing, in the Department of Brain and Cognitive Sciences, at the Artificial Intelligence Laboratory and at the Department of Mathematics, University of Trento, Italy. Gabriele Anzellotti is with the Department of Mathematics, University of Trento, Italy. This research is sponsored by a grant from the Office of Naval Research (ONR), Cognitive and Neural Sciences Division; by the Artificial Intelligence Center of Hughes Aircraft Corporation (S1-801534-2). Support for the A. I. Laboratory's artificial intelligence research is provided by the Advanced Research Projects Agency of the Department of Defense under Army contract DACA76-85-C-0010, and in part by ONR contract N00014-85-K-0124. c fl Massachusetts Institute of Technology, 1992 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #340075. 	[Title] Comparison of Kernel Estimators, Perceptrons, and Radial-Basis Functions for OCR and Speech Classification [Abstract] We compare kernel estimators, single and multi-layered perceptrons and radial-basis functions for the problems of classification of handwritten digits and speech phonemes. By taking two different applications and employing many techniques, we report here a two-dimensional study whereby a domain-independent assessment of these learning methods can be possible. We consider a feed-forward network with one hidden layer. As examples of the local methods, we use kernel estimators like k-nearest neighbor (k-nn), Parzen windows, generalized k-nn, and Grow and Learn (Condensed Nearest Neighbor). We have also considered fuzzy k-nn due to its similarity. As distributed networks, we use linear perceptron, pairwise separating linear perceptron, and multilayer perceptrons with sigmoidal hidden units. We also tested the radial-basis function network which is a combination of local and distributed networks. Four criteria are taken for comparison: Correct classification of the test set, network size, learning time, and the operational complexity. We found that perceptrons when the architecture is suitable, generalize better than local, memory-based kernel estimators but require longer training and more precise computation. Local networks are simple, learn very quickly and acceptably, but use more memory. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5869. 	[Title] Observations on Cortical Mechanisms for Object Recognition and Learning [Abstract] This paper sketches several aspects of a hypothetical cortical architecture for visual object recognition, based on a recent computational model. The scheme relies on modules for learning from examples, such as Hyperbf-like networks, as its basic components. Such models are not intended to be precise theories of the biological circuitry but rather to capture a class of explanations we call Memory-Based Models (MBM) that contains sparse population coding, memory-based recognition and codebooks of prototypes. Unlike the sigmoidal units of some artificial neural networks, the units of MBMs are consistent with the usual description of cortical neurons as tuned to multidimensional optimal stimuli. We will describe how an example of MBM may be realized in terms of cortical circuitry and biophysical mechanisms, consistent with psychophysical and physiological data. A number of predictions, testable with physiological techniques, are made. This memo describes research done within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences and at the Artificial Intelligence Laboratory at the Massachusetts Institute of Technology. This research is sponsored by grants from the Office of Naval Research under contracts N00014-92-J-1879 and N00014-93-1-0385; and by a grant from the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program). Additional support is provided by the North Atlantic Treaty Organization, ATR Audio and Visual Perception Research Laboratories, Mitsubishi Electric Corporation, Sumitomo Metal Industries, and Siemens AG. Support for the A.I. Laboratory's artificial intelligence research is provided by ARPA contract N00014-91-J-4038. Tomaso Poggio is supported by the Uncas and Helen Whitaker Chair at MIT's Whitaker College. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #340078. 	[Title] Evaluation of Pattern Classifiers for Fingerprint and OCR Applications [Abstract] In this paper we evaluate the classification accuracy of four statistical and three neural network classifiers for two image based pattern classification problems. These are fingerprint classification and optical character recognition (OCR) for isolated handprinted digits. The evaluation results reported here should be useful for designers of practical systems for these two important commercial applications. For the OCR problem, the Karhunen-Loeve (K-L) transform of the images is used to generate the input feature set. Similarly for the fingerprint problem, the K-L transform of the ridge directions is used to generate the input feature set. The statistical classifiers used were Euclidean minimum distance, quadratic minimum distance, normal, and k-nearest neighbor. The neural network classifiers used were multilayer perceptron, radial basis function, and probabilistic. The OCR data consisted of 7,480 digit images for training and 23,140 digit images for testing. The fingerprint data consisted of 2,000 training and 2,000 testing images. In addition to evaluation for accuracy, the multilayer perceptron and radial basis function networks were evaluated for size and generalization capability. For the evaluated datasets the best accuracy obtained for either problem was provided by the probabilistic neural network, where the minimum classification error was 2.5% for OCR and 7.2% for fingerprints. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #131315. 	[Title] Hierarchical Recurrent Neural Networks for Long-Term Dependencies [Abstract] We have already shown that extracting long-term dependencies from sequential data is difficult, both for deterministic dynamical systems such as recurrent networks, and probabilistic models such as hidden Markov models (HMMs) or input/output hidden Markov models (IOHMMs). In practice, to avoid this problem, researchers have used domain specific a-priori knowledge to give meaning to the hidden or state variables representing past context. In this paper, we propose to use a more general type of a-priori knowledge, namely that the temporal dependencies are structured hierarchically. This implies that long-term dependencies are represented by variables with a long time scale. This principle is applied to a recurrent network which includes delays and multiple time scales. Experiments confirm the advantages of such structures. A similar approach is proposed for HMMs and IOHMMs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28278. 	[Title] Chapter 1 Reinforcement Learning for Planning and Control [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1110520. 	[Title] Generalization to local remappings of the visuomotor coordinate transformation [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31353. 	[Title] Hidden Markov Models in Computational Biology: Applications to Protein Modeling UCSC-CRL-93-32 Keywords: Hidden Markov Models, [Abstract] Hidden Markov Models (HMMs) are applied to the problems of statistical modeling, database searching and multiple sequence alignment of protein families and protein domains. These methods are demonstrated on the globin family, the protein kinase catalytic domain, and the EF-hand calcium binding motif. In each case the parameters of an HMM are estimated from a training set of unaligned sequences. After the HMM is built, it is used to obtain a multiple alignment of all the training sequences. It is also used to search the SWISS-PROT 22 database for other sequences that are members of the given protein family, or contain the given domain. The HMM produces multiple alignments of good quality that agree closely with the alignments produced by programs that incorporate three-dimensional structural information. When employed in discrimination tests (by examining how closely the sequences in a database fit the globin, kinase and EF-hand HMMs), the HMM is able to distinguish members of these families from non-members with a high degree of accuracy. Both the HMM and PRO-FILESEARCH (a technique used to search for relationships between a protein sequence and multiply aligned sequences) perform better in these tests than PROSITE (a dictionary of sites and patterns in proteins). The HMM appears to have a slight advantage Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1105530. 	[Title] EMRBF: A Statistical Basis for Using Radial Basis Functions for Process Control [Abstract] Radial Basis Function (RBF) neural networks offer an attractive equation form for use in model-based control because they can approximate highly nonlinear plants and yet are well suited for linear adaptive control. We show how interpreting RBFs as mixtures of Gaussians allows the application of many statistical tools including the EM algorithm for parameter estimation. The resulting EMRBF models give uncertainty estimates and warn when they are extrapolating beyond the region where training data was available. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104379. 	[Title] GA-RBF: A Self-Optimising RBF Network [Abstract] The effects of a neural network's topology on its performance are well known, yet the question of finding optimal configurations automatically remains largely open. This paper proposes a solution to this problem for RBF networks. A self- optimising approach, driven by an evolutionary strategy, is taken. The algorithm uses output information and a computationally efficient approximation of RBF networks to optimise the K-means clustering process by co-evolving the two determinant parameters of the network's layout: the number of centroids and the centroids' positions. Empirical results demonstrate promise. Please summarise all the given information.

Paper #35905 has the title `Equivalence of Linear Boltzmann Chains and Hidden Markov Models sequence L, is: where Z(; A;
` and the abstract `Several authors have made a link between hidden Markov models for time series and energy-based models (Luttrell 1989, Williams 1990, Saul and Jordan 1995). Saul and Jordan (1995) discuss a linear Boltzmann chain model with state-state transition energies A ii 0 (going from state i to state i 0 ) and symbol emission energies B ij , under which the probability of an entire state fi l ; j l g L Whilst any HMM can be written as a linear Boltzmann chain by setting exp(A ii 0 ) = a ii 0 , exp(B ij ) = b ij and exp( i ) = i , not all linear Boltzmann chains can be represented as HMMs (Saul and Jordan 1995). However, the difference between the two models is minimal. To be precise, if the final hidden 
`.
Question: Which category should Paper #35905 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #35905 has the title `Equivalence of Linear Boltzmann Chains and Hidden Markov Models sequence L, is: where Z(; A;
` and the abstract `Several authors have made a link between hidden Markov models for time series and energy-based models (Luttrell 1989, Williams 1990, Saul and Jordan 1995). Saul and Jordan (1995) discuss a linear Boltzmann chain model with state-state transition energies A ii 0 (going from state i to state i 0 ) and symbol emission energies B ij , under which the probability of an entire state fi l ; j l g L Whilst any HMM can be written as a linear Boltzmann chain by setting exp(A ii 0 ) = a ii 0 , exp(B ij ) = b ij and exp( i ) = i , not all linear Boltzmann chains can be represented as HMMs (Saul and Jordan 1995). However, the difference between the two models is minimal. To be precise, if the final hidden 
`.
Question: Which category should Paper #35905 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: Neural_Networks