Construction and Analysis of Methods for Making Appropriate Use of Low Dimensional Structure in Data and Models When Apparent Dimension is Very High

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The investigator develops and analyzes asymptotically methods for inference and prediction for high dimensional data. His research with collaborators includes estimation of intrinsic dimension, estimation of high dimensional covariance matrices and prediction using low dimensional approximate representations of the data and/ or approximate low dimensional models.The goal of the investigators research is to improve prediction and inference in situations ranging from numerical weather prediction to computational biology when high dimensional data is the basis of action and understanding. In fact, such data nowadays arise everywhere. The underlying principle the investigator and collaborators are following is that the data is essentially low dimensional when properly represented and/or modeled and that appropriate representations can be found in computationally feasible ways.