Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery

We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tuning insensitiveness. Theoretically, we provide sufficient conditions under which CMR achieves the optimal rate of convergence in parameter estimation. Computationally, we propose an efficient smoothed proximal gradient algorithm with a worst-case numerical rate of convergence \cO(1/\epsilon), where $\epsilon$ is a pre-specified accuracy of the objective function value. We conduct thorough numerical simulations to illustrate that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR to solve a brain activity prediction problem and find that it is as competitive as a handcrafted model created by human experts. The R package \texttt{camel} implementing the proposed method is available on the Comprehensive R Archive Network \url{http://cran.r-project.org/web/packages/camel/}.Comment: Journal of Machine Learning Research, 201

The evaluation of protein folding rate constant is improved by predicting the folding kinetic order with a SVM-based method

Protein folding is a problem of large interest since it concerns the mechanism by which the genetic information is translated into proteins with well defined three-dimensional (3D) structures and functions. Recently theoretical models have been developed to predict the protein folding rate considering the relationships of the process with tolopological parameters derived from the native (atomic-solved) protein structures. Previous works classified proteins in two different groups exhibiting either a single-exponential or a multi-exponential folding kinetics. It is well known that these two classes of proteins are related to different protein structural features. The increasing number of available experimental kinetic data allows the application to the problem of a machine learning approach, in order to predict the kinetic order of the folding process starting from the experimental data so far collected. This information can be used to improve the prediction of the folding rate. In this work first we describe a support vector machine-based method (SVM-KO) to predict for a given protein the kinetic order of the folding process. Using this method we can classify correctly 78% of the folding mechanisms over a set of 63 experimental data. Secondly we focus on the prediction of the logarithm of the folding rate. This value can be obtained as a linear regression task with a SVM-based method. In this paper we show that linear correlation of the predicted with experimental data can improve when the regression task is computed over two different sets, instead of one, each of them composed by the proteins with a correctly predicted two state or multistate kinetic order.Comment: The paper will be published on WSEAS Transaction on Biology and Biomedicin