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Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, reproduction numbers do not enable estimation and prediction in individual communities within networks, and they…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
The Recoil Growth algorithm, proposed in 1999 by Consta et al., is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding…
Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic…
Many recent successes of machine learning went hand in hand with advances in optimization. The exchange of ideas between these fields has worked both ways, with machine learning building on standard optimization procedures such as gradient…
Ordinary differential equation (ODE) models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital this is an extremely restrictive assumption as typically a hospital…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
Reproducibility is one of the core dimensions that concur to deliver Trustworthy Artificial Intelligence. Broadly speaking, reproducibility can be defined as the possibility to reproduce the same or a similar experiment or method, thereby…
A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of…
Network decomposition is a central tool in distributed graph algorithms. We present two improvements on the state of the art for network decomposition, which thus lead to improvements in the (deterministic and randomized) complexity of…
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of ``components.'' Typically, these components are linear combinations of the rows and columns of the matrix, and are thus…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
This paper tackles the reduction of redundant repeating generation that is often observed in RNN-based encoder-decoder models. Our basic idea is to jointly estimate the upper-bound frequency of each target vocabulary in the encoder and…
The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation…