The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...
Lakes are a fundamental feature of nature with brilliance, profoundness and complexity. Various of physical, chemical and biological changes take place three dimensionally in deep lakes, regulated by complicated boundary conditions. To understand and predi ...
Bioaccumulation is defined as the enrichment of a compound in an organism relative to the surrounding water or its food, and is an important endpoint in chemical risk assessment. Under laboratory conditions, bioaccumulation is measured as bioconcentration ...
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...
Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...
The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...
We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...
This article presents the Lightning Performance (LP) assessment of a realistic portion of the Italian distribution network with the use of probability distributions for lightning parameters inferred from local data recorded by a Lightning Location System ( ...
