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DNA methylation is an important epigenetic mark that has been studied extensively for its regulatory role in biological processes and diseases. WGBS allows for genome-wide measurements of DNA methylation up to single-base resolutions, yet…
Matrix variate beta (MVB) distributions are used in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. In this approach a unified methodology is proposed to…
Metagenomic binning aims to cluster DNA fragments from mixed microbial samples into their respective genomes, a critical step for downstream analyses of microbial communities. Existing methods rely on deterministic representations, such as…
Two-component mixture models are particularly useful for identifying differentially expressed genes, but their performance can deteriorate markedly when the alternative distribution departs from parametric assumptions or symmetry. We…
We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the…
The melting behavior of long, heterogeneous DNA chains is examined within the framework of the nonlinear lattice dynamics based Peyrard-Bishop-Dauxois (PBD) model. Data for the pBR322 plasmid and the complete T7 phage have been used to…
In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…
Learning a transport model that maps a source distribution to a target distribution is a canonical problem in machine learning, but scientific applications increasingly require models that can generalize to source and target distributions…
This paper proposes a novel signed $\beta$-model for directed signed network, which is frequently encountered in application domains but largely neglected in literature. The proposed signed $\beta$-model decomposes a directed signed network…
DNA methylation is an epigenetic mechanism whose important role in development has been widely recognized. This epigenetic modification results in heritable changes in gene expression not encoded by the DNA sequence. The underlying…
Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal…
Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…
Data augmentation is often used to enlarge datasets with synthetic samples generated in accordance with the underlying data distribution. To enable a wider range of augmentations, we explore negative data augmentation strategies (NDA)that…
Next-generation sequencing technologies provide a revolutionary tool for generating gene expression data. Starting with a fixed RNA sample, they construct a library of millions of differentially abundant short sequence tags or "reads",…
Recently, nonnegative matrix factorization (NMF) has been widely adopted for community detection, because of its better interpretability. However, the existing NMF-based methods have the following three problems: 1) they directly transform…
In search of robust and generalizable machine learning models, Domain Generalization (DG) has gained significant traction during the past few years. The goal in DG is to produce models which continue to perform well when presented with data…
The Diffusion Probabilistic Model (DPM) has emerged as a highly effective generative model in the field of computer vision. Its intermediate latent vectors offer rich semantic information, making it an attractive option for various…
Component network meta-analysis (CNMA) models are an extension of standard network meta-analysis (NMA) models which account for the use of multicomponent treatments in the network. This article contributes innovatively to several…
In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…
Let $\mathbf{B}_n=\mathbf {S}_n(\mathbf {S}_n+\alpha_n\mathbf {T}_N)^{-1}$, where $\mathbf {S}_n$ and $\mathbf {T}_N$ are two independent sample covariance matrices with dimension $p$ and sample sizes $n$ and $N$, respectively. This is the…