Prem S. Puri Memorial Lecture

Sparse Learning and Distributed PCA with Control of Statistical Errors and Computing Resources

Jianqing Fan
Professor of Statistics and Frederick L. Moore '18 Professor of Finance
Department of Operations Research and Financial Engineering, Princeton University

Start Date and Time: Fri, 21 Apr 2017, 10:30 AM

End Date and Time: Fri, 21 Apr 2017, 11:20 AM

Venue: Stanley Coulter 239


High-dimensional sparse learning and analysis of Big Data pose significant challenges on computation and communication. Scalable statistical procedures need to take into account both statistical errors and computing resource constraints. This talk illustrates this idea by using two important examples in statistical machine learning. The first one is to solve sparse learning via a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional sparse models via a family of folded concave penalized quasi-likelihood. The algorithmic complexity and statistical errors are explicitly given and we show that the algorithm achieves the optimal statistical error rate under the weakest signal strength assumptions. The second problem is to study distributed PCA with communication constraints:  each node machine computes the top eigenvectors and communicates to the central server; the central server then aggregates the information transmitted from the node machines and conducts another PCA based on the aggregated information. We investigate the bias and variance for such a distributed PCA. We derive the rate of convergence for distributed PCA, which depends explicitly on effective rank, eigen-gap, and the number of machines, and show that the distributed PCA performs as well as the whole sample PCA, even without full access of whole data.

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