Related papers: New perspectives on knockoffs construction

Let $X$ be a $p$-variate random vector and $\widetilde{X}$ a knockoff copy of $X$ (in the sense of \cite{CFJL18}). A new approach for constructing $\widetilde{X}$ (henceforth, NA) has been introduced in \cite{JSPI}. NA has essentially three…

Let $X=(X_1,\ldots,X_p)$ be a $p$-variate random vector and $F$ a fixed finite set. In a number of applications, mainly in genetics, it turns out that $X_i\in F$ for each $i=1,\ldots,p$. Despite the latter fact, to obtain a knockoff…

The recent paper Cand\`es et al. (2018) introduced model-X knockoffs, a method for variable selection that provably and non-asymptotically controls the false discovery rate with no restrictions or assumptions on the dimensionality of the…

Consider a case-control study in which we have a random sample, constructed in such a way that the proportion of cases in our sample is different from that in the general population---for instance, the sample is constructed to achieve a…

We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_1, \ldots, X_p$. We wish to do so while offering finite-sample guarantees about the…

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…

As new Model-X knockoff construction techniques are developed, primarily concerned with determining the correct conditional distribution from which to sample, we focus less on deriving the correct multivariate distribution and instead ask…

Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…

While there is substantial need for dependence models in higher dimensions, most existing models quickly become rather restrictive and barely balance parsimony and flexibility. Hierarchical constructions may improve on that by grouping…

Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion…

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…

The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…

Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…

A $\widetilde{Q}-$representation of real numbers is introduced as a generalization of the $p-$adic and $Q-$representations. It is shown that the $\widetilde{Q}-$representation may be used as a convenient tool for the construction and study…

We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which…

A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…

Researchers in biomedical studies often work with samples that are not selected uniformly at random from the population of interest, a major example being a case-control study. While these designs are motivated by specific scientific…

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…

Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…