Related papers: Generalizations of Maximal Inequalities to Arbitra…
Selective rationalization improves neural network interpretability by identifying a small subset of input features -- the rationale -- that best explains or supports the prediction. A typical rationalization criterion, i.e. maximum mutual…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
The idea of maximizing the likelihood of the observed range for a set of jointly realized counts has been employed in a variety of contexts. The applicability of the MLE introduced in [1] has been extended to the general case of a…
Continuing the study reported in Satheesh (2001),(math.PR/0304499 dated 01 May 2003) and Satheesh (2002)(math.PR/0305030 dated 02May 2003), here we study generalizations of infinitely divisible (ID) and max-infinitely divisible (MID) laws.…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
Given p independent normal populations, we consider the problem of estimating the mean of those populations, that based on the observed data, give the strongest signals. We explicitly condition on the ranking of the sample means, and…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Effective machine learning models can automatically learn useful information from a large quantity of data and provide decisions in a high accuracy. These models may, however, lead to unfair predictions in certain sense among the population…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…