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Given a finite set $K$, we denote by $X=\Delta(K)$ the set of probabilities on $K$ and by $Z=\Delta_f(X)$ the set of Borel probabilities on $X$ with finite support. Studying a Markov Decision Process with partial information on $K$…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We consider the higher-order Markov Chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
We define integer multimodal sequences, which are generalizations of unimodal sequences having multiple local peaks of equal size. The generating functions for multimodal sequences represent novel types of $q$-series that combine generating…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
New theoretical results are presented here on the recently introduced model called mixed states MRF. Such models were introduced in the context of image motion analysis and are useful to represent information which can take both discrete…
A parametrization of hypergraphs based on the geometry of points in $\mathbf{R}^d$ is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…
Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categories of discrete and Gaussian probabilistic processes have…
We extend Deligne's notion of determinant functor to tensor triangulated categories. Specifically, to account for the multiexact structure of the tensor, we define a determinant functor on the 2-multicategory of triangulated categories and…
We provide a new approach to categorical graph and hypergraph theory by using categorical syntax and semantics. For each monoid $M$ and action on a set $X$, there is an associated presheaf topos of $(X,M)$-graphs where each object can be…
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…