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Although supervised deep-learning has achieved promising performance in medical image segmentation, many methods cannot generalize well on unseen data, limiting their real-world applicability. To address this problem, we propose a deep…

Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…

Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in…

De novo genome assembly is challenging in highly repetitive regions; however, reference-guided assemblers often suffer from bias. We propose a framework for pangenome-guided sequence assembly, which can resolve short-read data in complex…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…

With the recent advances in machine learning for quantum chemistry, it is now possible to predict the chemical properties of compounds and to generate novel molecules. Existing generative models mostly use a string- or graph-based…

Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…

Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…

Over the past two decades, a series of works have aimed at studying the problem of genome assembly: the process of reconstructing a genome from sequence reads. An early formulation of the genome assembly problem showed that genome…

In this paper we study structural properties of LV-degrees of the algebra of collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. We construct atoms…

We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…

The MLE (Maximum Likelihood Estimate) for a multinomial model is proportional to the data. We call such estimate an eigenestimate and the relationship of it to the data as the eigenstructure. When the multinomial model is generalized to…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…

In this article, we revisit the problem of fitting a mixture model under the assumption that the mixture components are symmetric and log-concave. To this end, we first study the nonparametric maximum likelihood estimation (NPMLE) of a…

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…

We propose a new compression scheme for genomic data given as sequence fragments called reads. The scheme uses a reference genome at the decoder side only, freeing the encoder from the burdens of storing references and performing…