相关论文: Algebraic Properties of Wyner Common Information S…

Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…

Copulas have gained widespread popularity as statistical models to represent dependence structures between multiple variables in various applications. The minimum information copula, given a finite number of constraints in advance, emerges…

We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs…

We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by…

We take a closer look at the structure of bivariate dependency induced by a pair of predictor random variables $(X_1, X_2)$ trying to synergistically, redundantly or uniquely encode a target random variable $Y$. We evaluate a recently…

Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…

We pose the fine-grained hardness hypothesis that the textbook algorithm for the NFA Acceptance problem is optimal up to subpolynomial factors, even for dense NFAs and fixed alphabets. We show that this barrier appears in many variations…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

We propose a novel classification model for weak signal data, building upon a recent model for Bayesian multi-view learning, Group Factor Analysis (GFA). Instead of assuming all data to come from a single GFA model, we allow latent…

The Weber problem consists of finding a point in $\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of…

In a compound decision problem, consisting of $n$ statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule $\delta$ satisfies a natural symmetry…

Most existing debiasing methods for multimodal models, including causal intervention and inference methods, utilize approximate heuristics to represent the biases, such as shallow features from early stages of training or unimodal features…

We propose a notion of common information that allows one to quantify and separate the information that is shared between two random variables from the information that is unique to each. Our notion of common information is defined by an…

Amid growing demands for data privacy and advances in computational infrastructure, federated learning (FL) has emerged as a prominent distributed learning paradigm. Nevertheless, differences in data distribution (such as covariate and…

We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…

Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter…

In the traditional Katz-Vafa method, matter representations are determined by decomposing the adjoint representation of a parent simple Lie algebra $\mathfrak{m}$ as the direct sum of irreducible representations of a semisimple subalgebra…

Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $\mu_k \in R^k$…

We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, practical…

The input in the Minimum-Cost Constraint Satisfaction Problem (MinCSP) over the Point Algebra contains a set of variables, a collection of constraints of the form $x < y$, $x = y$, $x \leq y$ and $x \neq y$, and a budget $k$. The goal is to…