Regularization is a solution to solve the problem of unstable estimation of covariance matrix with a small sample set in Gaussian classifier. And multi-regularization parameters estimation is more difficult than single parameter estimation. In this paper, KLIM_L covariance matrix estimation is derived theoretically based on MDL (minimum description length) principle for the small sample problem...

The inference of population divergence times and branching patterns is of fundamental importance in many population genetic analyses. Many methods have been developed for estimating population divergence times, and recently, there has been particular attention towards genome-wide single-nucleotide polymorphisms (SNP) data. However, most SNP data have been affected by an ascertainment bias cause...

Phylogenetic reconstruction of the evolutionary history of closely related organisms may be difficult because of the presence of unsorted lineages and of a relatively high proportion of heterozygous sites that are usually not handled well by phylogenetic programs. Genomic data may provide enough fixed polymorphisms to resolve phylogenetic trees, but the diploid nature of sequence data remains a...

In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show c...

Background: The aim of the present study is to compare time perception among drug addicts and controls. Methods: 30 drug addicts were selected, and 30 non-addict individuals were selected as the control group. The two groups performed three tests of time reproduction, time estimation, and time discrimination. Findings: There was a significant difference between the addicts group and the control...

Rates of molecular evolution can vary over time. Diverse statistical techniques for divergence time estimation have been developed to accommodate this variation. These typically require that all sequence (or codon) positions at a locus change independently of one another. They also generally assume that the rates of different types of nucleotide substitutions vary across a phylogeny in the same...

The contrastive divergence(CD) method proposed by Hinton finds an approximate solution of the maximum likelihood of complex probability models. It is known empirically that the CD method gives a high-quality estimation in a small computation time. In this paper, we give an intuitive explanation about the reason why the CD method can approximate well by using the information geometry. We further...

Time to contact can be approximated from the divergence of the ow eld. Direct diierentiation of a measured ow eld is not feasible in practice because of the ill-posedness of diierentiation. We propose a group theoretical framework for direct determination of higher order ow elds. The basis is the invariance of the power spectrum of the Fourier transform to translations. By change of coordinate-...