The statistical learning theory of risk minimization depends heavily on probability bounds for uniform deviations of the empirical risks. Classical probability bounds using Hoeffding’s inequality cannot accommodate more general situations with unbounded loss and dependent data. The current paper introduces an inequality that extends Hoeffding’s inequality to handle these more general situations...

The Wasserstein metric is an important measure of distance between probability distributions, with several applications in machine learning, statistics, probability theory, and data analysis. In this paper, we upper and lower bound minimax rates for the problem of estimating a probability distribution underWasserstein loss, in terms of metric properties, such as covering and packing numbers, of...

Probability distributions produced by the crossentropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate this approach in the context of deep learning on two large ordinal image datas...

The city of Kolkata, the State Capital of West Bengal is jolted by earthquakes time and again from the tectonic regimes of the Central Himalaya, highly seismogenic Northeast India and the active tectonics of Bengal Basin which is a pericratonic tertiary basin on which the City is located. Earthquake disaster mitigation and management necessitates seismic hazard assessment for the generation of ...