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

Comparative Analysis of Different Classes of On-line State Estimators for Aerodynamics Angles and True Airspeed Sensors for Applications to the Sensor Failure Problem

Throughout aviation history, there have been numerous incidents due to sensor failure that have caused a range of issues from loss of control of the aircraft to crashes resulting in loss of human life. Although there are many hardware-based solutions to this problem, the threat of control hardware failure still exists. This work investigates the efficacy of implementing neural networks (NN) and Kalman filters (KF) to solve the accommodation portion of the sensor failure detection, identification, and accommodation (SFDIA) problem through on-line real-time estimation of specific aircraft dynamic parameters. The implementation of on-line estimation architectures into the aircraft flight control system provides multiple advantages such as cost effectiveness and drastic decrease in weight. The multilayer perceptron (MLP) NN, extended minimal resource allocation (neural) network (EMRAN), extended KF (EKF), and unscented KF (UKF) have been evaluated in this effort for the purpose of providing analytical redundancy (AR) for estimating the parameter of the ‘failed’ sensor in lieu of physical redundancy. Each NN-based and KF-based estimator was compared using preset criteria including estimation accuracy, time to perform, and complexity of the model. The overall results have shown that the NN-based sensor failure accommodation (SFA) schemes outperform the KF-based SFA schemes with no undetected faults nor false alarms and significantly smaller estimation errors. More specifically, the EMRAN-based neural estimator has the best performance of all four schemes followed by the MLP NN, UKF, and EKF, respectively. This research shows the great potential of analytical redundancy-based approaches as opposed to physical or hardware redundancy to improved aviation safety for preventing future crashes due to sensor failures

Imitating Driver Behavior with Generative Adversarial Networks

The ability to accurately predict and simulate human driving behavior is critical for the development of intelligent transportation systems. Traditional modeling methods have employed simple parametric models and behavioral cloning. This paper adopts a method for overcoming the problem of cascading errors inherent in prior approaches, resulting in realistic behavior that is robust to trajectory perturbations. We extend Generative Adversarial Imitation Learning to the training of recurrent policies, and we demonstrate that our model outperforms rule-based controllers and maximum likelihood models in realistic highway simulations. Our model both reproduces emergent behavior of human drivers, such as lane change rate, while maintaining realistic control over long time horizons.Comment: 8 pages, 6 figure

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era