High-Dimensional Data Analysis
High-dimensional statistics focuses on problem settings in which the number of features is of comparable size, or larger than the number of observations. Problems of this type present a variety of new challenges, since classical theory and methodology can break down in surprising and unexpected ways.
Berkeley researchers study both the statistical and computational challenges that arise in the high-dimensional setting. On the theoretical side, they bring to bear a range of techniques from statistics, probability, and information theory, including empirical process theory, concentration inequalities, as well as random matrix theory and free probability. Methodological innovations include new estimators in high-dimensional regression, classification, and multivariate analysis, as well as randomized algorithms for optimization, and techniques for prediction, inference, and decision-making in sequential settings. The work is motivated and applied to various scientific and engineering disciplines, including computational biology, astronomy, financial time series, epidemic forecasting, and climate forecasting.
Researchers
statistics, machine learning, semiparametric models, asymptotic theory, hidden Markov models, applications to molecular biology
phase transitions, networks, graphs, graphons, algorithmic game theory, machine learning, applications in cancer immunotherapy, ethical decision-making, climate change, materials science
high-dimensional statistical learning, statistical computing, computational biology and genomics, precision medicine and health
selective inference, multiple testing, multivariate analysis, risks of artificial intelligence, ecological statistics
integrable probability, 2d statistical mechanics, random matrices, interacting particle systems, asymptotic representation theory, high-dimensional statistics
nonparametric estimation, shape-constrained estimation, high-dimensional statistics, Bayesian and empirical Bayes methods
high-dimensional and integrative genomic data analysis, network modeling, hierarchical classification, translational bioinformatics
scientific/engineering machine learning, randomized numerical linear algebra, random matrix theory, stochastic optimization, spectral graph theory, time series forecasting, fluid solid subsurface and chemistry/physics applications, internet and social media analysis
language models and diffusion models, deep learning theory, reinforcement learning theory, high-dimensional statistics, quantum algorithms, and uncertainty quantification
AI and machine learning, applied probability, computational biology, computational genomics, evolutionary biology, human genetics
uncertainty quantification and inference, inverse problems, nonparametrics, risk assessment, elections, geophysics, astrophysics, cosmology, litigation, health
Bayesian inference, inverse problems, stochastic processes, biological systems, empirical game theory, nonequilibrium thermodynamics, optimization, and computational topology
high-dimensional statistics, nonparametric estimation, distribution-free inference, machine learning, optimization, numerical methods, probabilistic forecasting, computational epidemiology
nonparametric estimation, hypothesis testing, applied probability, statistical learning theory, online learning