Benchmarking least squares support vector machine classifiers.

In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a ( convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LS-SVM classifier, the sparseness property of SVMs is lost due to the choice of the 2-norm. Sparseness can be imposed in a second stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LS-SVM classifiers with linear, polynomial and radial basis function (RBF) kernels. Both the SVM and LS-SVM classifier with RBF kernel in combination with standard cross-validation procedures for hyperparameter selection achieve comparable test set performances. These SVM and LS-SVM performances are consistently very good when compared to a variety of methods described in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LS-SVM sparse approximation procedure can be successfully applied.least squares support vector machines; multiclass support vector machines; sparse approximation; discriminant-analysis; sparse approximation; learning algorithms; classification; framework; kernels; time; SISTA;

GWAS meta-analysis of intrahepatic cholestasis of pregnancy implicates multiple hepatic genes and regulatory elements

Intrahepatic cholestasis of pregnancy (ICP) is a pregnancy-specific liver disorder affecting 0.5–2% of pregnancies. The majority of cases present in the third trimester with pruritus, elevated serum bile acids and abnormal serum liver tests. ICP is associated with an increased risk of adverse outcomes, including spontaneous preterm birth and stillbirth. Whilst rare mutations affecting hepatobiliary transporters contribute to the aetiology of ICP, the role of common genetic variation in ICP has not been systematically characterised to date. Here, we perform genome-wide association studies (GWAS) and meta-analyses for ICP across three studies including 1138 cases and 153,642 controls. Eleven loci achieve genome-wide significance and have been further investigated and fine-mapped using functional genomics approaches. Our results pinpoint common sequence variation in liver-enriched genes and liver-specific cis-regulatory elements as contributing mechanisms to ICP susceptibility

Identification of the Circulant Modulated Poisson Process: a Time Domain Approach

In this paper we will discuss a new time domain approach to the traffic identification problem for ATM networks. Our identification approach for the circulant modulated Poisson process (CMPP) consists of two steps: the identification of the first order parameters and the determination of the circulant stochastic matrix which matches the second order statistics of the data. The first step is composed of two parts. We first characterise the first order statistics of a given data sequence by the first order parameters of a Markov modulated Poisson process (MMPP). These parameters are computed by applying a nonnegative least squares algorithm. In addition, the MMPP parameters are translated into CMPP parameters in order to conform this MMPP description to the restrictions of the circulant modulated Poisson process. The identification of the circulant transition matrix is based on an unconstrained optimisation algorithm in which the circulant matrix structure is exploited. We compare our re..

Identification of the Circulant Modulated Poisson Process: a Time Domain Approach

In this paper we discuss a new time domain method for the traffic identification problem in ATM networks. Our identification approach for the circulant modulated Poisson process (CMPP) consists of two steps: the identification of the first order parameters and the determination of the circulant stochastic matrix which matches the second order statistics of the data

Imposing Stability in Subspace Identification by Regularization

In subspace methods for system identification, the system matrices are usually estimated by least squares, based on estimated Kalman filter state sequences and the observed inputs and outputs. For an infinite number of data points and a correct choice of the system order, this least squares estimate of the system matrices is unbiased. However, when using subspace identification on a finite number of data points, the estimated model can become unstable, for a given deterministic system which is known to be stable. In this paper, stability of the estimated model is imposed by adding a regularization term to the least squares cost function. The regular- ization term used here is the trace of a matrix which involves the dynamical system matrix and a positive (semi-)definite weighting matrix. The amount of regularization needed can be determined by solving a generalized eigenvalue problem. It is shown that the so-called data augmentation method proposed by Chui and Maciejowski corresponds to adding regularization terms with specific choices for the weighting matrix

Identification of Positive Real Models in Subspace Identification by Using Regularization

In time-domain subspace methods for identifying linear-time invariant dynamical systems, the model matrices are typically estimated from least squares, based on estimated Kalman filter state sequences and the observed outputs and/or inputs. It is well known that for an infinite amount of data, this least squares estimate of the system matrices is unbiased, when the system order is correctly estimated. However, for a finite amount of data, the obtained model may not be positive real, in which case the algorithm is not able to identify a valid stochastic model. In this note, positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm. The regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix