Related papers: Scalable Sobolev IPM for Probability Measures on a…
We propose Slim Graph: the first programming model and framework for practical lossy graph compression that facilitates high-performance approximate graph processing, storage, and analytics. Slim Graph enables the developer to express…
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve…
In this paper, we propose to use the general $L^2$-based Sobolev norms, i.e., $H^s$ norms where $s\in \mathbb{R}$, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As…
We investigate the approximation of high-dimensional target measures as low-dimensional updates of a dominating reference measure. This approximation class replaces the associated density with the composition of: (i) a feature map that…
Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev…
The Smatch metric is a popular method for evaluating graph distances, as is necessary, for instance, to assess the performance of semantic graph parsing systems. However, we observe some issues in the metric that jeopardize meaningful…
The deployment of safe and trustworthy machine learning systems, and particularly complex black box neural networks, in real-world applications requires reliable and certified guarantees on their performance. The conformal prediction…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Estimating the uncertainty of a model's prediction on a test point is a crucial part of ensuring reliability and calibration under distribution shifts. A minimum description length approach to this problem uses the predictive normalized…
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between…
Medical imaging classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, which prevents their deployment in medical clinics. We present an algorithm that can modify any classifier…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
A standard method for designing randomized algorithms to approximately count the number of solutions of a problem in $\#$P, is by constructing a rapidly mixing Markov chain converging to the uniform distribution over this set of solutions.…
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…
By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…
This is the first of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several notions of metric Sobolev space and on their equivalence. More precisely, we give a systematic…