This paper addresses the problem of iterative optimization of the Kullback-Leibler (KL) divergence on discrete (finite) probability spaces. Traditionally, the problem is formulated in the constrained optimization framework and is tackled by gradient like methods. Here, it is shown that performing the KL optimization in a Riemannian space equipped with the Fisher metric provides three major advantages over the standard methods: 1. The Fisher metric turns the original constrained optimization into an unconstrained optimization problem; 2. The optimization using a Fisher metric behaves asymptotically as a Newton method and shows very fast convergence near the optimum; 3. The Fisher metric is an intrinsic property of the space of probability distributions and allows a formally correct interpretation of a (natural) gradient as the steepest-descent method. Simulation results are presented.

This paper presents an algorithm for nonlinear adaptive control of the viral load in HIV-1 infection. The infection model considered is a reduced complexity nonlinear state-space model with two state variables, that represent the plasma concentration of uninfected and infected CD4+ T-cells of the human immune system. The viral load is assumed to be proportional to the concentration of infected cells. First, a change of variables that exactly linearizes the system is obtained. For the resulting linear system the manipulated variable is obtained by state feedback. To compensate for the uncertainty in the infection parameter of the model an estimator based on a Control Lyapunov Function is designed.

Over the years, due to the enrichment of paired-label datasets, supervised machine learning has become a prime component of any problem-solving. Examples include building classifiers for applications such as image/speech recognition, traffic prediction, product recommendation, virtual personal assistant (VPA), online fraud detection and many more. The performance of these developed classifiers is highly dependent upon the training dataset, and subsequently, without human intervention or true labels, the evaluation over unseen observations remains unknown. Using a statistical distance researchers did try to assess the model’s goodness-of-fit and compared multiple independent models. Nonetheless, given a train-test split and different classifiers built over the training set, the question ‘is it possible to find a prediction error using the relation between training and test set?’ remains unsolved. In this article, we propose a generalized statistical distance-based method measuring the prediction uncertainty at a new query point. To be specific, we propose a Mahalanobis distance-based Evidence Function Model to measure the misclassification caused by K-Nearest Neighbours (KNN), Extra Trees (ET), and Convolutional Neural Network (CNN) models when classifying Sentinel-2 image into six scene classes (Water, Shadow, Cirrus, Cloud, Snow, Other). The performance of the proposed method was assessed over two different datasets: (i) the test set, with an overall mean prediction uncertainty detection of 62.99%, 29.80% and 31.51%, leading to a mean micro-F1 performance of 67.89%, 39.30%, and 38.29% for KNN, ET, and CNN, respectively; (ii) a water-body set, with prediction uncertainty detection of 22.27%, 42.08%, and 27.67%, leading to a micro-F1 performance of 34.70%, 58.96%, and 43.32%, respectively.