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In any knowledge discovery process the value of extracted knowledge is directly related to the quality of the data used. Big Data problems, generated by massive growth in the scale of data observed in recent years, also follow the same…
Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model…
How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…
There is an extensive set of methods to determine sparse sources from mixtures where the mixing coefficients are unknown. Each method involves plotting N sets of mixed data against each other in N-dimensional space. In the approach adopted…
Motivation: The rapid growth of diverse biological data allows us to consider interactions between a variety of objects, such as genes, chemicals, molecular signatures, diseases, pathways and environmental exposures. Often, any pair of…
We consider learning from data of variable quality that may be obtained from different heterogeneous sources. Addressing learning from heterogeneous data in its full generality is a challenging problem. In this paper, we adopt instead a…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
High-dimensional data often exhibit variation that can be captured by lower dimensional factors. For high-dimensional data from multiple studies or environments, one goal is to understand which underlying factors are common to all studies,…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…
Usage data of a group of users distributed across a number of categories, such as songs, movies, webpages, links, regular household products, mobile apps, games, etc. can be ultra-high dimensional and massive in size. More often this kind…
Ongoing advances in microbiome profiling have allowed unprecedented insights into the molecular activities of microbial communities. This has fueled a strong scientific interest in understanding the critical role the microbiome plays in…
The measurement of data over time and/or space is of utmost importance in a wide range of domains from engineering to physics. Devices that perform these measurements therefore need to be extremely precise to obtain correct system…
Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…
A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…
Individual neurons often produce highly variable responses over nominally identical trials, reflecting a mixture of intrinsic "noise" and systematic changes in the animal's cognitive and behavioral state. Disentangling these sources of…
Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
Temporal data, obtained in the setting where it is only possible to observe one time point per experiment, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often…