Variational inference for robust sequential learning of multilayered perceptron neural network

U radu je prikazan i izveden novi sekvencijalni algoritam za obučavanje višeslojnog perceptrona u prisustvu autlajera. Autlajeri predstavljaju značajan problem, posebno ukoliko sprovodimo sekvencijalno obučavanje ili obučavanje u realnom vremenu. Linearizovani Kalmanov filtar robustan na autlajere (LKF-RA), je statistički generativni model u kome je matrica kovarijansi šuma merenja modelovana kao stohastički proces, a apriorna informacija usvojena kao inverzna Višartova raspodela. Izvođenje svih jednakosti je bazirano na prvim principima Bajesovske metodologije. Da bi se rešio korak modifikacije primenjen je varijacioni metod, u kome rešenje problema tražimo u familiji raspodela odgovarajuće funkcionalne forme. Eksperimentalni rezultati primene LKF-RA, dobijeni korišćenjem stvarnih vremenskih serija, pokazuju da je LKF-RA bolji od konvencionalnog linearizovanog Kalmanovog filtra u smislu generisanja niže greške na test skupu podataka. Prosečna vrednost poboljšanja određena u eksperimentalnom procesu je 7%.We derive a new sequential learning algorithm for Multilayered Perceptron (MLP) neural network robust to outliers. Presence of outliers in data results in failure of the model especially if data processing is performed on-line or in real time. Extended Kalman filter robust to outliers (EKF-OR) is probabilistic generative model in which measurement noise covariance is modeled as stochastic process over the set of symmetric positive-definite matrices in which prior is given as inverse Wishart distribution. Derivation of expressions comes straight form first principles, within Bayesian framework. Analytical intractability of Bayes' update step is solved using Variational Inference (VI). Experimental results obtained using real world stochastic data show that MLP network trained with proposed algorithm achieves low error and average improvement rate of 7% when compared directly to conventional EKF learning algorithm

Variational inference for robust sequential learning of multilayered perceptron neural network

U radu je prikazan i izveden novi sekvencijalni algoritam za obučavanje višeslojnog perceptrona u prisustvu autlajera. Autlajeri predstavljaju značajan problem, posebno ukoliko sprovodimo sekvencijalno obučavanje ili obučavanje u realnom vremenu. Linearizovani Kalmanov filtar robustan na autlajere (LKF-RA), je statistički generativni model u kome je matrica kovarijansi šuma merenja modelovana kao stohastički proces, a apriorna informacija usvojena kao inverzna Višartova raspodela. Izvođenje svih jednakosti je bazirano na prvim principima Bajesovske metodologije. Da bi se rešio korak modifikacije primenjen je varijacioni metod, u kome rešenje problema tražimo u familiji raspodela odgovarajuće funkcionalne forme. Eksperimentalni rezultati primene LKF-RA, dobijeni korišćenjem stvarnih vremenskih serija, pokazuju da je LKF-RA bolji od konvencionalnog linearizovanog Kalmanovog filtra u smislu generisanja niže greške na test skupu podataka. Prosečna vrednost poboljšanja određena u eksperimentalnom procesu je 7%.We derive a new sequential learning algorithm for Multilayered Perceptron (MLP) neural network robust to outliers. Presence of outliers in data results in failure of the model especially if data processing is performed on-line or in real time. Extended Kalman filter robust to outliers (EKF-OR) is probabilistic generative model in which measurement noise covariance is modeled as stochastic process over the set of symmetric positive-definite matrices in which prior is given as inverse Wishart distribution. Derivation of expressions comes straight form first principles, within Bayesian framework. Analytical intractability of Bayes' update step is solved using Variational Inference (VI). Experimental results obtained using real world stochastic data show that MLP network trained with proposed algorithm achieves low error and average improvement rate of 7% when compared directly to conventional EKF learning algorithm

Robust artificial neural networks and outlier detection. Technical report

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks to contaminated data using least trimmed squares criterion. We introduce a penalized least trimmed squares criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression