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In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Ising models are a simple generative approach to describing interacting binary variables. They have proven useful in a number of biological settings because they enable one to represent observed many-body correlations as the separable…
The aim of this paper is to propose a novel estimation method of using genetic-predicted observations to estimate trans-ancestry genetic correlations, which describes how genetic architecture of complex traits varies among populations, in…
The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is…
Inferring a graphical model or network from observational data from a large number of variables is a well studied problem in machine learning and computational statistics. In this paper we consider a version of this problem that is relevant…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
Genome-wide association study (GWAS) tests single nucleotide polymorphism (SNP) markers across the genome to localize the underlying causal variant of a trait. Because causal variants are seldom observed directly, a surrogate model based on…
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this…
Genome-wide association studies, in which as many as a million single nucleotide polymorphisms (SNP) are measured on several thousand samples, are quickly becoming a common type of study for identifying genetic factors associated with many…
Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…
Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…
In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine,…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
We study the challenges of applying deep learning to gene expression data. We find experimentally that there exists non-linear signal in the data, however is it not discovered automatically given the noise and low numbers of samples used in…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the…
Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the…