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Computing multi-source partial information decomposition (PID) for continuous data is hard: existing closed-form Gaussian estimators are restricted to two source variables, while continuous arbitrary-source estimators are typically…

We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by…

In this paper, I present three closed-form approximations of the two-sample Pearson Bayes factor, a recently developed index of evidential value for data in two-group designs. The techniques rely on some classical asymptotic results about…

One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node,…

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…

We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…

The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…

The ability to learn new visual concepts from limited examples is a hallmark of human cognition. While traditional category learning models represent each example as an unstructured feature vector, compositional concept learning is thought…

Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…

Under suitable conditions, with respect to some property on a random iterated function system(RIFS), it is shown how the system satisfies in this property almost surely.

The strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which…

The class of word-representable graphs, introduced in connection with the study of the Perkins semigroup by Kitaev and Seif, has attracted significant attention in combinatorics and theoretical computer science due to its deep connections…

Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…

This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic $0$. Our most general result determines the top component in total degree, which we…

Several explanation methods such as Integrated Gradients (IG) can be characterised as path-based methods, as they rely on a straight line between the data and an uninformative baseline. However, when applied to language models, these…

If $S$ is a cofinite set of positive integers, an "$S$-restricted composition of $n$" is a sequence of elements of $S$, denoted $\vec{\lambda}=(\lambda_1,\lambda_2,...)$, whose sum is $n$. For uniform random $S$-restricted compositions, the…

Stochastic Interpolants (SI) is a powerful framework for generative modeling, capable of flexibly transforming between two probability distributions. However, its use in jointly optimized latent variable models remains unexplored as it…

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…