Related papers: A Reverse Jensen Inequality Result with Applicatio…
The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts,…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
Convex functions have played a major role in the field of Mathematical inequalities. In this paper, we introduce a new concept related to convexity, which proves better estimates when the function is somehow more convex than another. In…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…
The primary goal of this paper is to improve the operator version of Jensen inequality. As an application, we provide an improvement for the celebrated Ando's inequality. Additionally, we give a tight bound for the operator H\"older…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
In this paper, we first provide a better estimate of the second inequality in Hermite-Hadamard inequality. Next, we study the reverse of the celebrated Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for…
In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…
Information distances like the Hellinger distance and the Jensen-Shannon divergence have deep roots in information theory and machine learning. They are used extensively in data analysis especially when the objects being compared are high…
Cognitive biases are widespread in humans and animals alike, and can sometimes be reinforced by social interactions. One prime bias in judgment and decision-making is the human tendency to underestimate large quantities. Previous research…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…
We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability…
We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.