We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method.

This document presents the extended abstract for "Recommender Systems and Their Effect on Consumers" and a link to the full paper on SSRN.

How do we know if what we see is really there? When visualizing data, how do we avoid falling into the trap of apophenia where we see patterns in random noise? Traditionally, infovis has been concerned with discovering new relationships, and statistics with preventing spurious relationships from being reported. We pull these opposing poles closer with two new techniques for rigorous statistical inference of visual discoveries. The "Rorschach" helps the analyst calibrate their understanding of uncertainty and "line-up" provides a protocol for assessing the significance of visual discoveries, protecting against the discovery of spurious structure.

We present a study of separability of acoustic waveforms of speech at phoneme level. The analyzed data consist of 64ms segments of acoustic waveforms of individual phonemes from TIMIT data base, sampled at 16kHz. For each phoneme, by means of principal component analysis, we identify subspaces which contain a given proportion of the total energy of the available waveforms in time-domain, and also in spectral-magnitude domain. In order to assess separation between phonemes in the two domains, we perform pairwise classification of phonemes on clean data and on data immersed in white additive Gaussian noise up to 0dB signal to noise ratio. While the classification based on spectral magnitudes exhibits high sensitivity to additive noise, the time-domain classification proves to be very robust.

This paper is concerned with the construction of regression and classification trees that are more adapted to data mining applications than conventional trees. To this end, we propose new splitting criteria for growing trees. Conventional splitting criteria attempt to perform well on both sides of a split by attempting a compromise in the quality of fit between the left and the right side. By contrast, we adopt a data mining point of view by proposing criteria that search for interesting subsets of the data, as opposed to modeling all of the data equally well. The new criteria do not split based on a compromise between the left and the right bucket; they effectively pick the more interesting bucket and ignore the other.As expected, the result is often a simpler characterization of interesting subsets of the data. Less expected is that the new criteria often yield whole trees that provide more interpretable data descriptions. Surprisingly, it is a "flaw" that works to their advantage: The new criteria have an increased tendency to accept splits near the boundaries of the predictor ranges. This so-called "end-cut problem" leads to the repeated peeling of small layers of data and results in very unbalanced but highly expressive and interpretable trees.

Two basic principles for interactive visualization of high-dimensional data-focusing and linking-are discussed. Focusing techniques may involve selecting subsets, dimension reduction, or some more general manipulation of the layout information on the page or screen. A consequent of focusing is that each view only conveys partial information about the data and needs to be linked so that the information contained in individual views can be integrated into a coherent image of the data as a whole. Examples are given of how graphical data analysis methods based on focusing and linking are used in applications including linguistics, geographic information systems, time series analysis, and the analysis of multi-channel images arising in radiology and remote sensing.>