RgCop-A regularized copula based method for gene selection in single cell rna-seq data

Gene selection in unannotated large single cell RNA sequencing (scRNA-seq) data is important and crucial step in the preliminary step of downstream analysis. The existing approaches are primarily based on high variation (highly variable genes) or significant high expression (highly expressed genes) failed to provide stable and predictive feature set due to technical noise present in the data. Here, we propose RgCop, a novel regularized copula based method for gene selection from large single cell RNA-seq data. RgCop utilizes copula correlation (Ccor), a robust equitable dependence measure that captures multivariate dependency among a set of genes in single cell expression data. We raise an objective function by adding a l1 regularization term with Ccor to penalizes the redundant co-efficient of features/genes, resulting non-redundant effective features/genes set. Results show a significant improvement in the clustering/classification performance of real life scRNA-seq data over the other state-of-the-art. RgCop performs extremely well in capturing dependence among the features of noisy data due to the scale invariant property of copula, thereby improving the stability of the method. Moreover, the differentially expressed (DE) genes identified from the clusters of scRNA-seq data are found to provide an accurate annotation of cells. Finally, the features/genes obtained from RgCop can able to annotate the unknown cells with high accuracy.

Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk

These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.

Alternative Measures of Dependence for Cyclic Behaviour Identification in the Signal with Impulsive Noise—Application to the Local Damage Detection

The local damage detection procedures in rotating machinery are based on the analysis of the impulsiveness and/or the periodicity of disturbances corresponding to the failure. Recent findings related to non-Gaussian vibration signals showed some drawbacks of the classical methods. If the signal is noisy and it is strongly non-Gaussian (heavy-tailed), searching for impulsive behvaior is pointless as both informative and non-informative components are transients. The classical dependence measure (autocorrelation) is not suitable for non-Gaussian signals. Thus, there is a need for new methods for hidden periodicity detection. In this paper, an attempt will be made to use alternative measures of dependence used in time series analysis that are less known in the condition monitoring (CM) community. They are proposed as alternatives for the classical autocovariance function used in the cyclostationary analysis. The methodology of the auto-similarity map calculation is presented as well as a procedure for a “quality” or “informativeness” assessment of the map is proposed. In the most complex case, the most resistant to heavy-tailed noise turned out the proposed techniques based on Kendall, Spearman and Quadrant autocorrelations. Whereas in the case of the local fault disturbed by the Gaussian noise, the most efficient proved to be a commonly-known approach based on Pearson autocorrelation. The ideas proposed in the paper are supported by simulation signals and real vibrations from heavy-duty machines.

Ordinal Pattern Dependence in the Context of Long-Range Dependence

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for a long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so, we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings.

ITERATIONS OF DEPENDENT RANDOM MAPS AND EXOGENEITY IN NONLINEAR DYNAMICS

We discuss the existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated into the dynamic. To this end, we consider the convergence of the backward iterations of dependent random maps. In particular, we give a new result when the classical condition of contraction on average is replaced with a contraction in conditional expectation. Under some conditions, we also discuss the dependence properties of these processes using the functional dependence measure of Wu (2005, Proceedings of the National Academy of Sciences 102, 14150–14154) that delivers a central limit theorem giving a wide range of applications. Our results are illustrated with conditional heteroscedastic autoregressive nonlinear models, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) processes, count time series, binary choice models, and categorical time series for which we provide many extensions of existing results.