Zoom Link - Available on 5/19 at 4:00 pm

 

ROBERTA DE VITO

Assistant Professor of Data Science and Biostatistics

 

MULTI-STUDY FACTOR ANALYSIS IN GENOMIC AND EPIDEMIOLOGICAL DATA

Biostatistics and computational biology are increasingly facing the urgent challenge of efficiently dealing with a large amount of experimental data. In particular, high-throughput assays are transforming the study of biology, as they generate a rich, complex, and diverse collection of high-dimensional data sets. Through compelling statistical analysis, these large data sets lead to discoveries, advances, and knowledge that were never accessible before, via compelling statistical analysis. Building such systematic knowledge is a cumulative process which requires analyses that integrate multiple sources, studies, and technologies. The increased availability of ensembles of studies on related clinical populations, technologies, and genomic features poses four categories of important multi-study statistical questions: 1) To what extent is biological signal reproducibly shared across different studies? 2) How can this global signal be extracted? 3) How can we detect and quantify local signals that may be masked by strong global signals? 4) How do these global and local signals manifest differently in different data types?

We will answer these four questions by introducing a novel class of methodologies for the joint analysis of different studies. The goal is to separately identify and estimate 1) common factors reproduced across multiple studies, and 2) study-specific factors. We present different medical and biological applications. In all the cases, we clarify the benefits of a joint analysis compared to the standard methods.

Our method could accelerate the pace at which we can combine unsupervised analysis across different studies, and understand the cross-study reproducibility of signal in multivariate data.

 

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Rough path theory emerged as a branch of stochastic analysis to give an improved approach to dealing with the interactions of complex random systems. In that context, it continues to resolve important questions, but its broader theoretical footprint has been substantial. Most notable is its contribution to Hairer’s Fields-Medal-winning work on regularity structures. At the core of rough path theory is the so-called signature transform which, while being simple to define, has rich mathematical properties bringing in aspects of analysis, geometry, and algebra. Hambly and Lyons (Annals of Math, 2010) built upon earlier work of Chen, showing how the signature represents the path uniquely up to generalized reparameterizations. This turns out to have practical implications allowing one to summarise the space of functions on unparameterized paths and data streams in a very economical way.

Over the past five years, a significant strand of applied work has been undertaken to exploit the mathematical richness of this object in diverse data science challenges from healthcare, to computer vision to gesture recognition. The log signature is becoming a powerful way to summarise the fine structure of a data stream in a neural net. The emergence of neural differential equations as an important tool in data science further deepens the connections with rough paths.

This four-day workshop will bring together key expertise across disciplines to advance understanding on some of the most pressing and exciting challenges. The week will begin with five structured, tutorial-style lectures on the foundational aspects of signatures their use in data science and topics of broad appeal such as Neural Rough Differential Equations. During the rest of the week, the morning activities will be broadly based with the afternoons focusing on more technical talks with additional opportunities for small group/breakout sessions

A challenge for mathematical modeling, from toy dynamical system models to full weather and climate models, is applying data assimilation and dynamical systems techniques to models that exhibit chaos and stochastic variability in the presence of coupled slow and fast modes of variability. Recent collaborations between universities and government agencies in India and the United States have resulted in detailed observations of oceanic and atmospheric processes in the Bay of Bengal, the Arabian Sea, and the Indian Ocean, collectively observing many coupled modes of variability. One key target identified by these groups was the improvement of forecasts of variability of the summer monsoon, which significantly affects agriculture and water management practices throughout South Asia. The Monsoon Intraseasonal Oscillation is a northward propagating mode of precipitation variability and is one of the most conspicuous examples of coupled atmosphere-ocean processes during the summer monsoon. Simulating coupled atmosphere-ocean processes present mathematical challenges spanning numerical methods, data assimilation, stochastic modeling, dynamical systems and chaos, and uncertainty quantification. Predicting monsoon variability is one of the hardest, most important forecasting problems on earth due to its impact on billions of people, a key aspect of the desire to push weather forecasts into the management-actionable “medium-range” horizon of weeks to seasons. Addressing this challenge requires an interdisciplinary effort to combine observations, computation, and theory. A better understanding of these processes and how they can be represented in a variety of coupled ocean-atmosphere simulations and models (including statistical and dynamical approaches) and forecast systems (including data assimilation techniques and uncertainty quantification) is the primary topic of this workshop. While the set of observations to be discussed will emphasize this region, the mathematical and computational aspects of the program will be significantly broader, covering: coupled ocean-atmosphere modeling for weather models, climate models and idealized models; theory of the atmospheric and oceanic boundary layers, and waves on the interface; data assimilation in coupled modeling systems; and numerical methods for coupled systems.