Related papers: From Soft-Minoration to Information-Constrained Op…
We implement the Ising model on a structural connectivity matrix describing the brain at a coarse scale. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower…
In this paper we discuss Sudakov type minoration for the dependent setting. Sudakov minoration is a well known property first proved for centered Gaussian processes which states that for well separated points there is a natural lower bound…
Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable…
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis…
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…
We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…
The present work extends the randomized shortest-paths framework (RSP), interpolating between shortest-path and random-walk routing in a network, in three directions. First, it shows how to deal with equality constraints on a subset of…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
We characterize the communication complexity of the following distributed estimation problem. Alice and Bob observe infinitely many iid copies of $\rho$-correlated unit-variance (Gaussian or $\pm1$ binary) random variables, with unknown…
We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…