Related papers: FANOK: Knockoffs in Linear Time
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
We consider problems where many, somewhat redundant, hypotheses are tested and we are interested in reporting the most precise rejections, with false discovery rate (FDR) control. This is the case, for example, when researchers are…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
Quantifying how genomic features influence different parts of an outcome distribution requires statistical tools that go beyond mean regression, especially in ultrahigh-dimensional settings. Motivated by the study of LINE-1 activity in…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
We present a principled approach for detecting out-of-distribution (OOD) and adversarial samples in deep neural networks. Our approach consists in modeling the outputs of the various layers (deep features) with parametric probability…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…
The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
We study the problem of strongly refuting semirandom $k$-LIN$(\mathbb{F})$ instances: systems of $k$-sparse inhomogeneous linear equations over a finite field $\mathbb{F}$. For the case of $\mathbb{F} = \mathbb{F}_2$, this is the…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…
We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the…