Related papers: Common Information, Matroid Representation, and Se…

In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…

Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

Pretrained transformers achieve the state of the art across tasks in natural language processing, motivating researchers to investigate their inner mechanisms. One common direction is to understand what features are important for…

In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…

Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…

Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…

Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…

We consider the problem of learning an unknown partition of an $n$ element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple…

Independently trained machine learning models tend to learn similar features. Given an ensemble of independently trained models, this results in correlated predictions and common failure modes. Previous attempts focusing on decorrelation of…

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive…

The information theoretic quantity known as mutual information finds wide use in classification and community detection analyses to compare two classifications of the same set of objects into groups. In the context of classification…

Networks such as social networks, airplane networks, and citation networks are ubiquitous. The adjacency matrix is often adopted to represent a network, which is usually high dimensional and sparse. However, to apply advanced machine…

A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation for many real-world systems. However, due to a variety of potential factors, such as limited budget and…

Fairness constitutes a concern within machine learning (ML) applications. Currently, there is no study on how disparities in classification complexity between privileged and unprivileged groups could influence the fairness of solutions,…

Contention resolution schemes have proven to be a useful and unifying abstraction for a variety of constrained optimization problems, in both offline and online arrival models. Much of prior work restricts attention to product distributions…

Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the…

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…

Matrix inequalities that extend certain scalar ones have been at the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed…

Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…