Weighted k-Nearest-Neighbor Techniques and Ordinal Classification

In the field of statistical discrimination k-nearest neighbor classification is a well-known, easy and successful method. In this paper we present an extended version of this technique, where the distances of the nearest neighbors can be taken into account. In this sense there is a close connection to LOESS, a local regression technique. In addition we show possibilities to use nearest neighbor for classification in the case of an ordinal class structure. Empirical studies show the advantages of the new techniques

Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection

A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been demonstrated to have attractive theoretical properties, but model fitting is not a straightforward task, and the resulting solutions may be unstable. Here, we demonstrate the potential of coordinate descent algorithms for fitting these models, establishing theoretical convergence properties and demonstrating that they are significantly faster than competing approaches. In addition, we demonstrate the utility of convexity diagnostics to determine regions of the parameter space in which the objective function is locally convex, even though the penalty is not. Our simulation study and data examples indicate that nonconvex penalties like MCP and SCAD are worthwhile alternatives to the lasso in many applications. In particular, our numerical results suggest that MCP is the preferred approach among the three methods.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS388 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

PLS dimension reduction for classification of microarray data

PLS dimension reduction is known to give good prediction accuracy in the context of classification with high-dimensional microarray data. In this paper, PLS is compared with some of the best state-of-the-art classification methods. In addition, a simple procedure to choose the number of components is suggested. The connection between PLS dimension reduction and gene selection is examined and a property of the first PLS component for binary classification is proven. PLS can also be used as a visualization tool for high-dimensional data in the classification framework. The whole study is based on 9 real microarray cancer data sets

Sparse regulatory networks

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses $L_1$ penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS350 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org