Related papers: Enumerating Independent Linear Inferences
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…
An integer linear system (ILS) is a linear system with integer constraints. The solution graph of an ILS is defined as an undirected graph defined on the set of feasible solutions to the ILS. A pair of feasible solutions is connected by an…
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable ``interlace polynomial'' for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and…
Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
We propose a linear independence criterion, and outline an application of it. Down to its simplest case, it aims at solving this problem: given three real numbers, typically as special values of analytic functions, how to prove that the…
We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current…
In this paper, a linear model with grouped explanatory variables is considered. The idea is to perform an automatic detection of different successive groups of the unknown coefficients under the assumption that the number of groups is of…
In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…
The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…
We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…
In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true…
Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on…