Abstract: Slow feature analysis (SFA), as a method for learning slowly varying features in classification and signal analysis, has attracted increasing attention in recent years. It is guaranteed to find the optimal solution within a family of transformations and can learn to extract a large number of such “slow” features that are additionally orthogonal. While being effective, SFA suffers from three major shortcomings. First, it is not adaptive, in that the notion of “slowness” is fixed to be the average of the squared derivative of a signal. Second, its formulation assumes deterministic features/observations, which renders it ineffective for applications involving stochastic features/measurement uncertainties. Third, SFA is not necessarily suited for nonlinear processes. In this work, all these issues are addressed by proposing adaptive SFA and its probabilistic version, termed the ASFA and probabilistic ASFA (PASFA), respectively. The ASFA essentially introduces an optimally tunable filter that accommodates task-dependent slowness. We provide guidelines and a procedure for tuning the ASFA filter for a given application. We prove that linear SFA is a special case of ASFA for a specific choice of filter and demonstrate that it outperforms the standard SFA. PASFA extends ASFA to accommodate measurement and process noises, wherein the features are modeled as filtered Gaussian white noise (GWN) sequences, and the measurement noise is assumed to be GWN. Furthermore, it accommodates nonlinear generative models. A variational expectation-maximization (EM) algorithm is used for estimating the filter parameters and the statistical properties of noise sequences. Frequency-domain interpretations of ASFA are also provided to enhance interpretability. Case studies involving applications to signal analysis and classification are presented to demonstrate the effectiveness and superiority of the proposed methods.

Abstract: In the wake of the outbreak of COVID-19, the unprecedented policy response and the heightened uncertainty worldwide, large swings in prices of various asset classes such as currency, bond, equity and credit were observed. Emerging market currencies in particular, witnessed considerable volatility, beginning with large risk-off outflows in March 2020 exerting massive depreciation pressure, including on the Indian Rupee (INR). In this article, we analyse the USD-INR exchange rate data spanning from 2019 to 2021 and quantify the structural changes brought about by the pandemic on the USD-INR exchange rates in the temporal dimension using autoregressive time series models.

Abstract: In machine learning, support-vector machines (SVMs, also support-vector networks) are supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier. SVM maps training examples to points in space so as to maximise the width of the gap between the two categories. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces. In this article, we use the SVM classifier to classify whether a neutron star is a pulsar or not from simple statistics computed from the integrated pulse profile and the Dispersion measure - Signal to Noise ratio (DM-SNR) curve.