Related papers: Probabilistic Approach to Pattern Selection
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
Probabilistic programming makes it easy to represent a probabilistic model as a program. Building an individual model, however, is only one step of probabilistic modeling. The broader challenge of probabilistic modeling is in understanding…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…
The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be…
The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the…
A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This…
Similarly to the derivation of the Gibbs-Boltzmann distribution for structureless indistinguishable particles, we consider multi-particle systems some of which are contained (or delimited) inside others (Problem 1), as well as systems of…
We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…
The way that people make choices or exhibit preferences can be strongly affected by the set of available alternatives, often called the choice set. Furthermore, there are usually heterogeneous preferences, either at an individual level…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally,…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…