We discuss the behavior of penalized robust regression estimators in high-dimension and compare our theoretical predictions to simulations. Our results show the importance of the geometry of the dataset and shed light on the theoretical behavior of LASSO and much more involved methods.

We develop a novel method, based on the statistical concept of the Vapnik-Chervonenkis dimension, to evaluate the selectivity (output cardinality) of SQL queries – a crucial step in optimizing the execution of large scale database and data-mining operations. The major theoretical contribution of this work, which is of independent interest, is an explicit bound to the VC-dimension of a range spa...

A b s t r a c t J u s t a s a b u s y k i t c h e n c a n b e m o r e e c i e n t t h a n

Many data-mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous possibilities of such selections. How can we know statistically our discoveries better than those by chance? In this paper, we define a measure of goodness ...

Linear Discriminant (LD) techniques are typically used in pattern recognition tasks when there are many (n >> 10) datapoints in low-dimensional (d < 10) space. In this paper we argue on theoretical grounds that LD is in fact more appropriate when training data is sparse, and the dimension of the space is extremely high. To support this conclusion we present experimental results on a medical tex...

With advancing of modern technologies, high-dimensional data have prevailed in computational biology. The number of variables p is very large, and in many applications, p is larger than the number of observational units n. Such high dimensionality and the unconventional small-n-large-p setting have posed new challenges to statistical analysis methods. Dimension reduction, which aims to reduce t...

In this note, we study the n×n random Euclidean matrix whose entry (i, j) is equal to f(‖Xi−Xj‖) for some function f and the Xi’s are i.i.d. isotropic vectors inR. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.