Related papers: Enumerating Independent Linear Inferences
We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…
In this paper we construct an entire function of two variables having the property that its values and its partial derivatives of any order at any distinct algebraic points are algebraically independent. Such an entire function is generated…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…
Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
A fundamental result in linear algebra states that if a homogenous linear equation system has only the trivial solution, then there are at most as many variables as equations. We prove the following generalisation of this phenomenon. If a…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…
In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic coefficients. For $m$ simultaneous inequalities we require at least $m+2$ variables,…
Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on…