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We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…

In this paper, we consider the problem of generating a set of counterfactual explanations for a group of instances, with the one-for-many allocation rule, where one explanation is allocated to a subgroup of the instances. For the first…

Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal number of previous terms…

Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…

A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…

A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…

Let G be a simple connected graph with vertex set V(G) and edge set E(G. Each vertex of V(G) is colored by a color from the set of colors {c_1, c_2,\dots, c_{\alpha}}. We take a subset S of V(G), such that for every vertex v in V(G)\S, at…

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

Scientific practice typically involves repeatedly studying a system, each time trying to unravel a different perspective. In each study, the scientist may take measurements under different experimental conditions (interventions,…

Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values.…

As a step towards improving the abstract reasoning capability of machines, we aim to solve Raven's Progressive Matrices (RPM) with neural networks, since solving RPM puzzles is highly correlated with human intelligence. Unlike previous…

We systematically study the computational complexity of a broad class of computational problems in phylogenetic reconstruction. The class contains for example the rooted triple consistency problem, forbidden subtree problems, the quartet…

The well-known Deficiency One Theorem gives structural conditions on a chemical reaction network under which, for any set of parameter values, the steady states of the corresponding mass action system may be easily characterized. It is also…

Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…

In this paper, we study contention resolution schemes for matchings. Given a fractional matching $x$ and a random set $R(x)$ where each edge $e$ appears independently with probability $x_e$, we want to select a matching $M \subseteq R(x)$…

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…

We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has…

The perfect phylogeny is one of the most used models in different areas of computational biology. In this paper we consider the problem of the Persistent Perfect Phylogeny (referred as P-PP) recently introduced to extend the perfect…