**Zhishen Huang**

**Department of Applied Mathematics, University of Colorado Boulder**

*Finding local minimizers in nonconvex and non-smooth optimization *

We consider the problem of finding local minimizers in nonconvex and non-smooth optimization. The objective function we consider is in the form of the sum of a nonconvex function and a l1-penalty. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm.

**Antony Pearson **

**Department of Applied Mathematics, University of Colorado Boulder**

*Extracting structure from contaminated independent models*

We describe a new quantity, the latent weight, which measures the average fraction of data from a multivariate probabilistic source which can be attributed to an independent model. We give mathematical properties on this weight and contrast its interpretation with that of p-values resulting from hypothesis tests of independence. We report an efficient algorithm to compute this weight from a given source and apply the methodology to real transcription factor binding data to demonstrate its usefulness in exploratory data analysis.