Related papers: Cartesian Linearly Distributive Categories: Revisi…
We briefly relate the existence of a middle-four interchange map in a category with two monoidal structures, to the standard Cockett and Seely notion of a weakly distributive category.
We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…
Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose…
Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join…
Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli…
We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can test for the presence of categorical structure, including community structure and…
Lenses are a mathematical structure for maintaining consistency between a pair of systems. In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetric lenses with spans of asymmetric lenses. This…
We define and investigate separable K-linear categories. We show that such a category C is locally finite and that every left C-module is projective. We apply our main results to characterize separable linear categories that are spanned by…
In this brief note, we revisit a class of crossed-product orders over discrete valuation rings introduced by D. E. Haile. We give simple but useful criteria, which involve only the two-cocycle associated with a given crossed-product order,…
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…
Generalized Category Discovery (GCD) utilizes labeled samples of known classes to discover novel classes in unlabeled samples. Existing methods show effective performance on artificial datasets with balanced distributions. However,…
Spatially coupled low-density parity-check (SC-LDPC) codes are a class of capacity approaching LDPC codes with low message recovery latency when a sliding window decoding is used. In this paper, we first present a new method for the…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out…
The main objective of this paper is to construct a symmetric monoidal closed model category of coherently commutative monoidal quasi-categories. We construct another model category structure whose fibrant objects are (essentially) those…
Tensor products are ubiquitous in algebra, topology, logic and category theory. The present paper explores the monoidal structure of the category $\mathcal{V}\hspace{0pt}\mbox{-}\hspace{.5pt}\mathbf{Sup}$ of separated cocomplete enriched…
We propose a novel structured discriminative block-diagonal dictionary learning method, referred to as scalable Locality-Constrained Projective Dictionary Learning (LC-PDL), for efficient representation and classification. To improve the…
The sorting and filtering capabilities offered by modern e-commerce platforms significantly impact customers' purchase decisions, as well as the resulting prices set by competing sellers on these platforms. Motivated by this practical…