Above are papers related to the following paper: [Paper_ID] Paper #1115790. 	[Title] Adaptive Wavelet Control of Nonlinear Systems [Abstract] This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semi-global stability results are obtained under the key assumption that the system uncertainty satisfies a "matching" condition. The localization properties of adaptive networks are discussed and formal definitions of interference and localization measures are proposed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #31489. 	[Title] Minimax Estimation via Wavelet Shrinkage  a pleasure to acknowledge friendly conversations with Gerard Kerkyacharian, [Abstract] We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel- and Besov-type smoothness constraints, and asymptotically minimax over Besov bodies with p q. Linear estimates cannot achieve even the minimax rates over Triebel and Besov classes with p &lt; 2, so our method can significantly outperform every linear method (kernel, smoothing spline, sieve, : : : ) in a minimax sense. Variants of our method based on simple threshold nonlinearities are nearly minimax. Our method possesses the interpretation of spatial adaptivity: it reconstructs using a kernel which may vary in shape and bandwidth from point to point, depending on the data. Least favorable distributions for certain of the Triebel and Besov scales generate objects with sparse wavelet transforms. Many real objects have similarly sparse transforms, which suggests that these minimax results are relevant for practical problems. Sequels to this paper discuss practical implementation, spatial adaptation properties and applications to inverse problems. Acknowledgements. This work was completed while the first author was on leave from U.C. Berkeley, where his research was supported by NSF DMS 88-10192, by NASA Contract NCA2-488, and by a grant from ATT Foundation. The second author was supported in part by NSF grants DMS 84-51750, 86-00235, and NIH PHS grant GM21215-12. Supersedes an earlier version, titled "Wavelets and Optimal Function Estimation", dated November 10, 1990, and issued as Technical reports by the Departments of Statistics at both Stanford and at U.C. Berkeley. 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 #1106568. 	[Title] Local Feedforward Networks [Abstract] Although feedforward neural networks are well suited to function approximation, in some applications networks experience problems when learning a desired function. One problem is interference which occurs when learning in one area of the input space causes unlearning in another area. Networks that are less susceptible to interference are referred to as spatially local networks. To understand these properties, a theoretical framework, consisting of a measure of interference and a measure of network localization, is developed that incorporates not only the network weights and architecture but also the learning algorithm. Using this framework to analyze sigmoidal multi-layer perceptron (MLP) networks that employ the back-prop learning algorithm, we address a familiar misconception that sigmoidal networks are inherently non-local by demonstrating that given a sufficiently large number of adjustable parameters, sigmoidal MLPs can be made arbitrarily local while retaining the ability to represent any continuous function on a compact domain. 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 #75983. 	[Title] An Analytical Framework for Local Feedforward Networks [Abstract] Interference in neural networks occurs when learning in one area of the input space causes unlearning in another area. Networks that are less susceptible to interference are referred to as spatially local networks. To understand these properties, a theoretical framework, consisting of a measure of interference and a measure of network localization, is developed. These measures incorporate not only the network weights and architecture but also the learning algorithm. Using this framework to analyze sigmoidal, multi-layer perceptron (MLP) networks that employ the back-propagation learning algorithm, we address a familiar misconception that single-hidden-layer sigmoidal networks are inherently non-local by demonstrating that given a sufficiently large number of adjustable weights, single-hidden-layer sigmoidal MLPs can be made arbitrarily local while retaining the ability to approximate any continuous function on a compact domain. fl Partially supported under Task 2312 R1 by the United States Air Force Office of Scientific Research. 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 #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.

Paper #1115790 has the title `Adaptive Wavelet Control of Nonlinear Systems  
` and the abstract `This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semi-global stability results are obtained under the key assumption that the system uncertainty satisfies a "matching" condition. The localization properties of adaptive networks are discussed and formal definitions of interference and localization measures are proposed. 
`.
Question: Which category should Paper #1115790 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1115790 has the title `Adaptive Wavelet Control of Nonlinear Systems  
` and the abstract `This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semi-global stability results are obtained under the key assumption that the system uncertainty satisfies a "matching" condition. The localization properties of adaptive networks are discussed and formal definitions of interference and localization measures are proposed. 
`.
Question: Which category should Paper #1115790 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