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A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our…
This work presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the longitudinal axis of the filter. The model is formulated as a system of partial differential…
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…
In this paper, we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of (IBVPs) for some dispersive wave equations on a bounded domain corresponding to periodic forcing. The…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $4k+2$ dimensional manifolds, our results include the gravitational anomaly cancellation formulas of…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…
Continuous representation of words is a standard component in deep learning-based NLP models. However, representing a large vocabulary requires significant memory, which can cause problems, particularly on resource-constrained platforms.…
We consider three bivariate polynomial invariants $P$, $A$, and $S$ for rooted trees, as well as a trivariate polynomial invariant $M$. These invariants are motivated by random destruction processes such as the random cutting model or site…
We report on work towards flexible algorithms for solving decision problems represented as influence diagrams. An algorithm is given to construct a tree structure for each decision node in an influence diagram. Each tree represents a…
Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees…
We reduce the calculation of the simplest Hodge integrals to some sums over decorated trees. Since Hodge integrals are already calculated, this gives a proof of a rather interesting combinatorial theorem and a new representation of…
This paper presents a model-based, unsupervised algorithm for recovering word boundaries in a natural-language text from which they have been deleted. The algorithm is derived from a probability model of the source that generated the text.…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
We consider a pruning of the inhomogeneous continuum random trees, as well as the cut trees that encode the genealogies of the fragmentations that come with the pruning. We propose a new approach to the reconstruction problem, which has…