Related papers: Pinsker bound under measurement budget constrain: …
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular,…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…
In natural perception, different items (objects) in a scene are rarely equally relevant to the observer. The brain improves performance by directing attention to the most relevant items, for example the ones most likely to be probed. For a…
We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost…
This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative constraint -- for a general linear second-order elliptic…
Parameter-elliptic boundary-value problems are investigated on the extended Sobolev scale. This scale consists of all Hilbert spaces that are interpolation spaces with respect to the Hilbert Sobolev scale. The latter are the H\"ormander…
Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = \{v_1, v_2,…
We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal…
We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…