Artificial Neural Networks

Such mappings have been found to exist, for example in the perception process of the human eye where properties of an image are mapped directly to an area of the brain (figure 1). A form of cognition can thus be simulated by replicating the behaviour of the brain and its massively parallel architecture. Some Artificial Neural Networks attempt to artificially recreate this by mapping complex inputs into a lower dimensional space.

[1]  V. Fabian.  On Asymptotic Normality in Stochastic Approximation , 1968 .

[2]  Héctor J. Sussmann,et al.  Uniqueness of the weights for minimal feedforward nets with a given input-output map , 1992, Neural Networks.

[3]  Chung-Ming Kuan,et al.  Strong Convergence of Recursive M-Estimators for Models with Dynamic Latent Variables , 1991 .

[4]  X. Xu,et al.  Effective neural algorithms for the traveling salesman problem , 1991, Neural Networks.

[5]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[6]  T. Amemiya.  QUALITATIVE RESPONSE MODELS: A SURVEY , 1981 .

[7]  H. White,et al.  A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models , 1988 .

[8]  M. Metivier,et al.  Applications of a Kushner and Clark lemma to general classes of stochastic algorithms , 1984, IEEE Trans. Inf. Theory.

[9]  D. Andrews,et al.  Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors , 1991 .

[10]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[11]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[12]  Andrew R. Barron,et al.  Complexity Regularization with Application to Artificial Neural Networks , 1991 .

[13]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[14]  H. White,et al.  Misspecified models with dependent observations , 1982 .

[15]  Bernd Fritzke,et al.  Kohonen Feature Maps and Growing Cell Structures - a Performance Comparison , 1992, NIPS.

[16]  Kunihiko Fukushima,et al.  Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position , 1982, Pattern Recognit..

[17]  Robin Sibson,et al.  What is projection pursuit , 1987 .

[18]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[19]  Robert V. Foutz,et al.  The Performance of the Likelihood Ratio Test When the Model is Incorrect , 1977 .

[20]  A. Lapedes,et al.  Nonlinear signal processing using neural networks: Prediction and system modelling , 1987 .

[21]  Whitney K. Newey,et al.  Maximum Likelihood Specification Testing and Conditional Moment Tests , 1985 .

[22]  A. Ronald Gallant,et al.  Inference for nonlinear models , 1975 .

[23]  Eduardo D. Sontag,et al.  Feedback Stabilization Using Two-Hidden-Layer Nets , 1991, 1991 American Control Conference.

[24]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[25]  Benedikt M. Pötscher,et al.  Basic structure of the asymptotic theory in dynamic nonlinear econometric models , 1991 .

[26]  George Tauchen.  Diagnostic testing and evaluation of maximum likelihood models , 1985 .

[27]  A. Gallant.  Testing a Subset of the Parameters of a Nonlinear Regression Model , 1975 .

[28]  David F. Hendry,et al.  Likelihood Evaluation for Dynamic Latent Variables Models , 1992 .

[29]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[30]  R. Davies.  Hypothesis Testing when a Nuisance Parameter is Present Only Under the Alternatives , 1987 .

[31]  L. Jones.  A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training , 1992 .

[32]  Herman J. Bierens,et al.  A consistent conditional moment test of functional form , 1990 .

[33]  Donald W. K. Andrews,et al.  An empirical process central limit theorem for dependent non-identically distributed random variables , 1989 .

[34]  D. McLeish.  A Maximal Inequality and Dependent Strong Laws , 1975 .

[35]  M. Woodford.  Learning to Believe in Sunspots , 1990 .

[36]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[37]  Kurt Hornik,et al.  Convergence of learning algorithms with constant learning rates , 1991, IEEE Trans. Neural Networks.

[38]  H. White,et al.  An additional hidden unit test for neglected nonlinearity in multilayer feedforward networks , 1989, International 1989 Joint Conference on Neural Networks.

[39]  H. Kushner,et al.  Asymptotic Properties of Stochastic Approximations with Constant Coefficients. , 1981 .

[40]  Hong Wang,et al.  Recursive estimation and time-series analysis , 1986, IEEE Trans. Acoust. Speech Signal Process..

[41]  H. White.  Nonparametric Estimation of Conditional Quantiles Using Neural Networks , 1990 .

[42]  Richard S. Sutton,et al.  Training and Tracking in Robotics , 1985, IJCAI.

[43]  I. Badawi.  An elasticity can be estimated consistently without a priori knowledge of functional form , 1983 .

[44]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[45]  H. Kushner,et al.  RATES OF CONVERGENCE FOR STOCHASTIC APPROXIMATION TYPE ALGORITHMS , 1979 .

[46]  J. Blum.  Approximation Methods which Converge with Probability one , 1954 .

[47]  H. Kushner.  Asymptotic global behavior for stochastic approximation and diffusions with slowly decreasing noise effects: Global minimization via Monte Carlo , 1987 .

[48]  Y S Abu-Mostafa,et al.  Neural networks for computing , 1987 .

[49]  R. Hecht-Nielsen,et al.  Theory of the Back Propagation Neural Network , 1989 .

[50]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

[51]  D. Meeter.  Stochastic Approximation and Nonlinear Regression , 1969 .

[52]  Edward K. Blum,et al.  Approximation theory and feedforward networks , 1991, Neural Networks.

[53]  H. White,et al.  Universal approximation using feedforward networks with non-sigmoid hidden layer activation functions , 1989, International 1989 Joint Conference on Neural Networks.

[54]  Jack David Cowan,et al.  A mathematical theory of central nervous activity , 1967 .

[55]  Efraim Turban,et al.  Neural Networks in Finance and Investing: Using Artificial Intelligence to Improve Real-World Performance , 1992 .

[56]  Gerald Tesauro,et al.  Neurogammon Wins Computer Olympiad , 1989, Neural Computation.

[57]  S. M. Carroll,et al.  Construction of neural nets using the radon transform , 1989, International 1989 Joint Conference on Neural Networks.

[58]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[59]  L. Goldstein.  On the choice of step size in the Robbins-Monro procedure , 1988 .

[60]  A. Gallant,et al.  On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form , 1981 .

[61]  C. Gourieroux,et al.  Pseudo Maximum Likelihood Methods: Applications to Poisson Models , 1984 .

[62]  Bernd Fritzke,et al.  A Growing Neural Gas Network Learns Topologies , 1994, NIPS.

[63]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[64]  D. Duffie,et al.  Simulated Moments Estimation of Markov Models of Asset Prices , 1990 .

[65]  H. White,et al.  There exists a neural network that does not make avoidable mistakes , 1988, IEEE 1988 International Conference on Neural Networks.

[66]  David Ruppert.  Convergence of Stochastic Approximation Algorithms with Non-Additive Dependent Disturbances and Applications , 1983 .

[67]  S. Geman,et al.  Nonparametric Maximum Likelihood Estimation by the Method of Sieves , 1982 .

[68]  H. White.  Some Asymptotic Results for Learning in Single Hidden-Layer Feedforward Network Models , 1989 .

[69]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[70]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[71]  T. Sargent,et al.  Convergence of Least Squares Learning Mechanisms in Self- Referential Linear Stochastic Models* , 1989 .

[72]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[73]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[74]  Halbert White,et al.  Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings , 1990, Neural Networks.

[75]  X. Xu,et al.  Constructing associative memories using neural networks , 1990, Neural Networks.

[76]  Frank Rosenblatt,et al.  PRINCIPLES OF NEURODYNAMICS. PERCEPTRONS AND THE THEORY OF BRAIN MECHANISMS , 1963 .

[77]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

[78]  D. Ruppert,et al.  Recursive M-estimators of location and Scale for Dependent Sequences , 1988 .

[79]  Terrence J. Sejnowski,et al.  NETtalk: a parallel network that learns to read aloud , 1988 .

[80]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[81]  Truman F. Bewley.  Advances in econometrics, Fifth World Congress , 1987 .

[82]  Halbert White,et al.  On learning the derivatives of an unknown mapping with multilayer feedforward networks , 1992, Neural Networks.

[83]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[84]  Harro Walk.  An invariance principle for the Robbins-Monro process in a Hilbert space , 1977 .

[85]  Ker-Chau Li,et al.  Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set , 1987 .

[86]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.