Related papers: Optimal sequencing depth for single-cell RNA-seque…
The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Sequencing by tunneling is a next-generation approach to read single-base information using electronic tunneling transverse to the single-stranded DNA (ssDNA) backbone while the latter is translocated through a narrow channel. The original…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
The analysis of single-cell RNA sequencing (scRNA-seq) data often involves fitting a latent variable model to learn a low-dimensional representation for the cells. Validating such a model poses a major challenge. If we could sequence the…
RNA-seq has become a de facto standard for measuring gene expression. Traditionally, RNA-seq experiments are mathematically averaged -- they sequence the mRNA of individuals from different treatment groups, hoping to correlate phenotype…
RNA-Seq is rapidly becoming the standard technology for transcriptome analysis. Fundamental to many of the applications of RNA-Seq is the quantification problem, which is the accurate measurement of relative transcript abundances from the…
We present a novel inference approach that we call Sample Out-of-Sample (or SOS) inference. The approach can be used widely, ranging from semi-supervised learning to stress testing, and it is fundamental in the application of data-driven…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
We initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close…
Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample…
We develop statistically based methods to detect single nucleotide DNA mutations in next generation sequencing data. Sequencing generates counts of the number of times each base was observed at hundreds of thousands to billions of genome…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…