Theory and Methodology Research
The Department's research into high-dimensional statistics explores the rigorous analysis of data whose native dimension is larger than considered in classical multivariate analysis. These tools are crucial to take full advantage of modern collections of complex “Big Data.” Principled approaches to dimension reduction are of particular importance when faced with the curse of dimensionality.
Faculty Contact: Ann Lee
Topological Data Analysis
The CMU TopStat Group conducts research into the nascent and growing field of topological data analysis, focused on developing methods of inference that exploit the shape of data in a coordinate-free setting. Concepts such as statistical persistent homology have proved useful for finding meaningful low-dimensional structure in noisy, high-dimensional data, while making minimal assumptions.
Faculty Contact: Alessandro Rinaldo
Our Department has a long history of advancing Bayesian inference, well prior to when this approach was generally accepted. We continue this tradition by expanding the applicability of Bayesian techniques to the wide range of interdisciplinary research fields in which we collaborate. Each such application requires novel extensions of the classic Bayesian framework, often to improve computational feasibility.
Faculty Contact: Rob Kass
Network models represent the interrelationships between people, companies, genes, and so forth. Statistical procedures to analyze data in network form can discover communities, trends, and other relationships. For example, ongoing work in the Department focuses on building latent variable models for networks, applied to a study to better understand the benefits of interactions among teachers.
Faculty Contact: Brian Junker
Statistical Machine Learning
Our strong ties to machine learning are made clear when considering that six of our faculty are part of the core faculty for CMU's Machine Learning Department. Our StatML Theory Group focuses on the careful analysis of the statistical properties of machine learning procedures, serving to bring theoretical performance guarantees to these computationally-efficient algorithms for data analysis.
Faculty Contact: Larry Wasserman
Foundations of Inference
An active group of researchers in our Department studies the logical basis for statistical inference, i.e., foundational issues in the use of mathematics to draw conclusions in the presence of uncertainty in observable information. This generalizes deterministic reasoning, with the absence of uncertainty as a special case. The laws of valid statistical inference are best studied utilizing ideas found in the field of logic.
Faculty Contact: Jay Kadane
Using large quantities of data to address complex questions will naturally lead to nonparametric approaches, as these methods avoid unrealistic, restrictive assumptions. We pursue application-motivated nonparametric method development, e.g., recent work on nonparametric regression when the predictor is a noisy, high-dimensional emission spectrum of an astronomical object.
Faculty Contact: Christopher Genovese