Related papers: Scalable Learning from Probability Measures with M…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…
We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points…
The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability…
Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a…
We propose a novel approach based on optimal transport (OT) for tackling the problem of highly mixed data in blind hyperspectral unmixing. Our method constrains the distribution of the estimated abundance matrix to resemble a targeted…
Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…
Quantization of neural networks provides benefits of inference in less compute and memory requirements. Previous work in quantization lack two important aspects which this work provides. First almost all previous work in quantization used a…
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…
We consider the problem of deep neural net compression by quantization: given a large, reference net, we want to quantize its real-valued weights using a codebook with $K$ entries so that the training loss of the quantized net is minimal.…