Related papers: Algorithmic approach for an unique definition of t…
This paper studies the problem of expected loss minimization given a data distribution that is dependent on the decision-maker's action and evolves dynamically in time according to a geometric decay process. Novel algorithms for both the…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally…
We consider the problem of computing a grevlex Gr\"obner basis for the set $F_r(M)$ of minors of size $r$ of an $n\times n$ matrix $M$ of generic linear forms over a field of characteristic zero or large enough. Such sets are not regular…
A zero-one matrix is a matrix with entries from $\{0, 1\}$. We study monoids containing only such matrices. A finite set of zero-one matrices generating such a monoid can be seen as the matrix representation of an unambiguous finite…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
Chord generation is an inherently constrained creative task that requires balancing stylistic diversity with music-theoretic feasibility. Existing approaches typically entangle candidate generation and constraint enforcement within a single…
A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries. Reconstruction of X from the singular values and singular vectors of the contaminated matrix Y is a key problem in…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
We study the decomposition of zero-dimensional persistence modules, viewed as functors valued in the category of vector spaces factorizing through sets. Instead of working directly at the level of vector spaces, we take a step back and…
Reproducibility is a confused terminology. In this paper, I take a fundamental view on reproducibility rooted in the scientific method. The scientific method is analysed and characterised in order to develop the terminology required to…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain sub-class of compartmental models whose classes may be divided into three "(x, y, z)" groups, which we will call…
Finding a globally optimal Bayesian Network using exhaustive search is a problem with super-exponential complexity, which severely restricts the number of variables that it can work for. We implement a dynamic programming based algorithm…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…