Related papers: A Note on Reverse Pinsker Inequalities
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
In the classical many normal means with different variances, we consider the situation when the observer is allowed to allocate the available measurement budget over the coordinates of the parameter of interest. The benchmark is the minimax…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks,…
The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
Variance regularized counterfactual risk minimization (VRCRM) has been proposed as an alternative off-policy learning (OPL) method. VRCRM method uses a lower-bound on the $f$-divergence between the logging policy and the target policy as…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…