Annual Report 2 November 8 th , 2012

We propose an upper confidence bound for the threshold at which a regression function takes off from its baseline value in a white noise model. The confidence bound is based on multi-scale test statistics which involve combining one-sided kernel estimates with varying bandwidths in a specific manner. The bound is adaptive and near-optimal in the sense that it does require knowing the smoothness of the underlying regression function in the vicinity of the threshold and attains the minimax convergence rate up to a factor of log(n), n being the scale parameter or the ‘sample size’. Further, we extend our approach to Gaussian regression framework with a uniform fixed design. Shawn Mankad Title: Matrix Factorization Models for Dynamic Network and Three-Way Data Abstract: Collections of data matrices (data arrays) are becoming increasingly available due to advances in acquisition technologies. Various matrix factorization techniques have been applied to such data for integrating them and extraction of common patterns. However, a direct application of such techniques to such structured data can be adversely affected by transient patterns, and thus fail to extract parsimonious ones. In this talk, we introduce a model for non-negative matrix factorization that captures how structure evolves through the data. The model decomposes the data into two factors: a basis common to all data matrices, and a coefficient matrix that varies for each data matrix. A regularization is utilized within the framework of non-negative matrix factorization to encourage local smoothness of the coefficient matrix. This improves interpretability and highlights the structural patterns underlying the data, while mitigating noise effects. The proposed methodology is illustrated on paper citation data. Collections of data matrices (data arrays) are becoming increasingly available due to advances in acquisition technologies. Various matrix factorization techniques have been applied to such data for integrating them and extraction of common patterns. However, a direct application of such techniques to such structured data can be adversely affected by transient patterns, and thus fail to extract parsimonious ones. In this talk, we introduce a model for non-negative matrix factorization that captures how structure evolves through the data. The model decomposes the data into two factors: a basis common to all data matrices, and a coefficient matrix that varies for each data matrix. A regularization is utilized within the framework of non-negative matrix factorization to encourage local smoothness of the coefficient matrix. This improves interpretability and highlights the structural patterns underlying the data, while mitigating noise effects. The proposed methodology is illustrated on paper citation data.