Related papers: Hadamard Conjugation for the Kimura 3ST Model: Com…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
We show that the Hadamard and Unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set $A = {{| {\Psi_i} > ,| {\bar {\Psi}_i} >}}({i = 1,2})$ if and only if $| {\Psi_1} >…
Statistical models for families of evolutionary related proteins have recently gained interest: in particular pairwise Potts models, as those inferred by the Direct-Coupling Analysis, have been able to extract information about the…
Motivation: Standard algorithms for pairwise protein sequence alignment make the simplifying assumption that amino acid substitutions at neighboring sites are uncorrelated. This assumption allows implementation of fast algorithms for…
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…
We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is…
While convolution and self-attention mechanisms have dominated architectural design in deep learning, this survey examines a fundamental yet understudied primitive: the Hadamard product. Despite its widespread implementation across various…
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
In recent works on the theory of machine learning, it has been observed that heavy tail properties of Stochastic Gradient Descent (SGD) can be studied in the probabilistic framework of stochastic recursions. In particular,…
While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
Pathogen genome data offers valuable structure for spatial models, but its utility is limited by incomplete sequencing coverage. We propose a probabilistic framework for inferring genetic distances between unsequenced cases and known…
The goal of this paper is to describe an elementary combinatorial heuristic that predicts Hardy and Littlewood's extended Goldbach's conjecture. We examine common features of other heuristics in additive prime number theory, such as…
Krawtchouk's polynomials occur classically as orthogonal polynomials with respect to the binomial distribution. They may be also expressed in the form of matrices, that emerge as arrays of the values that the polynomials take. The algebraic…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup defined in Quantum Probability via quantum stochastic differential equations. Given a homogeneous Markov chain in continuous time in a finite…
Recent years have seen substantial advances in the development of biofunctional materials using synthetic polymers. The growing problem of elusive sequence-functionality relations for most biomaterials has driven researchers to seek more…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been recentlyintroduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain…
Motivated by a problem in population genetics, we examine the combinatorics of dissimilarity for pairs of random unordered draws of multiple objects, with replacement, from a collection of distinct objects. Consider two draws of size $K$…