Online Natural Gradient as a Kalman Filter

We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the "information filter" phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.Comment: 3rd version: expanded intr

Application Of Cascade-Correlation Neural Networks In Developing Stock Selection Models For Global Equities

We investigate the potential of artificial neural networks (ANN) in the stock selection process of actively managed funds. Two ANN models are constructed to perform stock selection, using the Dow Jones (DJ) Sector Titans as the research database. The cascade-correlation algorithm of Fahlman and Lebiere (1990/1991) is combined with embedded learning rules, namely the backpropagation learning rule and the extended Kalman filter learning rule to forecast the cross-section of global equity returns. The main findings support the use of artificial neural networks for financial forecasting as an active portfolio management tool. In particular, fractile analysis and risk-adjusted return performance metrics provide evidence that the model trained via the extended Kalman filter rule had greater strength in identifying future top performers for global equities than the model trained via the backpropagation learning rule. There is no distinguishable difference between the performances of the bottom quartiles formed by both ANN models. The zero-investment portfolios formed by longing the top quartiles and simultaneously shorting the bottom quartiles or the market proxy exhibit statistically significant Jensen’s alpha and continues to accumulate positive returns over the out-of-sample period for both ANN models. On the other hand, the zero-investment portfolios formed by longing the bottom quartiles and simultaneously shorting the market proxy exhibit statistically significant Jensen’s alpha and continues to accumulate losses over the out-of-sample period for both ANN models. The implementation of the extended Kalman filter rule in training artificial neural networks for applications involving noisy financial data is recommended

Query-Based Learning for Aerospace Applications

Models of real-world applications often include a large number of parameters with a wide dynamic range, which contributes to the difficulties of neural network training. Creating the training data set for such applications becomes costly, if not impossible. In order to overcome the challenge, one can employ an active learning technique known as query-based learning (QBL) to add performance-critical data to the training set during the learning phase, thereby efficiently improving the overall learning/generalization. The performance-critical data can be obtained using an inverse mapping called network inversion (discrete network inversion and continuous network inversion) followed by oracle query. This paper investigates the use of both inversion techniques for QBL learning, and introduces an original heuristic to select the inversion target values for continuous network inversion method. Efficiency and generalization was further enhanced by employing node decoupled extended Kalman filter (NDEKF) training and a causality index (CI) as a means to reduce the input search dimensionality. The benefits of the overall QBL approach are experimentally demonstrated in two aerospace applications: a classification problem with large input space and a control distribution problem

Incremental least squares methods and the extended Kalman filter

Caption titleIncludes bibliographical references (leaves 16-18).Supported by the NSF. 9300494-DMIby Dimitri P. Bertsekas

A Feed-Forward Neural Network Approach for Energy-Based Acoustic Source Localization

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Sensorimotor neural systems for a predatory stealth behaviour camouflaging motion

A thesis submitted to the University of London in partial fulfillment of the requirements for the admission to the degree of Doctor of Philosophy