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Alexandre Belloni works across optimization, econometrics and high-dimensional statistics. His Chicago Booth profile describes research connecting statistical inference with decisions under limited information.^[ref]

With Victor Chernozhukov and Lie Wang, he formulated the Square-root Lasso as a convex conic optimization problem. This connects a statistically pivotal tuning rule with algorithms for convex optimization, giving a computable sparse regression estimator without a preliminary estimate of noise scale.^[ref]

Arthur P. Dempster contributed to multivariate analysis, incomplete-data inference and the representation of uncertain evidence. With Nan Laird and Donald Rubin, he developed the general expectation-maximization algorithm formulation published in 1977. Its expectation step averages a complete-data log likelihood using the current Conditional distribution of latent or missing variables; its maximization step updates parameters using that average. This makes a difficult incomplete-data likelihood accessible through a sequence of simpler calculations.

Harvard's institutional tribute also traces his work on Dempster-Shafer theory, in which evidence can leave an explicit component of uncertainty about an assertion. His dissertation concerned multivariate settings with more variables than observations, anticipating a central difficulty of high-dimensional statistics.^[ref]

Identity and life dates: Harvard Department of Statistics obituary and tribute.

Eugene Katsevich works on high-dimensional statistics, variable selection and multiple testing, motivated in part by genetics and genomics. These problems require distinguishing reproducible signals from the many associations that can arise when thousands of features are examined.^[ref]

His joint work on the conditional randomization test uses a known feature conditional distribution to calibrate tests of conditional independence. Distillation makes flexible prediction methods more practical as test statistics.^[ref]

High-dimensional statistics studies inference when the number of variables or parameters is large relative to the number of observations, often allowing both to grow. The difficulty is structural rather than merely computational: with an $n\times p$ design matrix and $p>n$, the null space is nontrivial, so $X\beta =X(\beta +v)$ for every $v$ in that null space.

The data alone then cannot identify an arbitrary coefficient vector. Assuming a sparse vector of regression coefficients can make restricted recovery possible when the design matrix is injective on the allowed differences. Regularization encodes or exploits such structural assumptions. A fitted model with many parameters is therefore not automatically informative about every parameter; identifiability and uncertainty depend on the model's structure and sampling design.

Lucas Janson studies high-dimensional statistics and statistical machine learning, with scientific collaborations in genetics, climatology and political science. His current Stanford homepage describes this combination of methodological research and applications.^[ref]

He coauthored distillation for the conditional randomization test. Its computational motivation is that a powerful test statistic may involve expensive machine learning; distillation avoids repeating the most costly fitting step for every conditional resample.^[ref]

Purnamrita Sarkar works at the intersection of high-dimensional statistics, machine-learning theory, differential privacy and large-scale optimization. Her University of Texas at Austin profile describes this combination of statistical and computational research.^[ref]

Her lecture on the Efron–Stein inequality presents a general way to control the variance of a function of independent inputs: compare the function with versions in which one input is independently replaced. For a sum, the resulting bound recovers the familiar sum of variances; for a complicated estimator, it gives a route to uncertainty control without expanding every covariance term.^[ref]

Sara van de Geer develops the mathematical theory of high-dimensional statistics. Her Statistical Theory for High-Dimensional Models by Sara van de Geer studies prediction bounds for the Lasso and Square-root Lasso, and inference after correcting shrinkage bias.^[ref]

The distinction is useful: an estimator that predicts well may still bias an individual coefficient toward zero. A de-sparsified estimator adds a correction whose leading error can have an approximately normal distribution. Bounds on the remaining error, together with sparsity and design assumptions, then justify confidence intervals. The same notes connect generic chaining and concentration inequalities with control of random-process suprema.^[ref]

Tony Cai develops methods and theory for high-dimensional statistics, statistical decision theory and statistical machine learning. His research includes functional data analysis and applications to genomics.^[ref]

With Weidong Liu and Xi Luo, he introduced CLIME, estimating a sparse precision matrix through linear programming. Their results bound estimation error under sparsity and tail assumptions. The method makes a useful distinction between an optimization constraint and a theorem: positive definiteness of the final estimate is established under conditions, rather than imposed as a constraint in the columnwise programs.^[ref]

Weidong Liu works on high-dimensional statistics. Shanghai Jiao Tong University's institutional profile identifies this researcher and his focus on high-dimensional statistical inference.^[ref]

His CLIME paper with Tony Cai and Xi Luo estimates a sparse precision matrix even when direct inversion of the sample covariance matrix is unsuitable. It controls $\Vert \hat{\Sigma }\Omega -I{\Vert }_{\max }$ while minimizing an entrywise absolute-value objective, then uses a symmetrization rule. Statistical accuracy requires assumptions on sparsity and the distribution's tails.^[ref]