arXiv subjects

Yiming Ding

Publications and source records attributed to Yiming Ding.

27 records · Page 2Linked to original sources

arXiv2018

Equitability of Dependence Measure

Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two covariates, which requires the dependence measure to be equitable. That is, it gives similar scores to equally noisy relationship of different types. In fact, the dependence score is a continuous random variable taking values in $[0,1]$, thus it is theoretically impossible to give similar scores. In this paper, we introduce a new definition of equitability of a dependence measure, i.e, power-equitable (weak-equitable) and show by simulation that HHG and Copula Dependence Coefficient (CDC) are weak-equitable.

stat.ML↗

arXiv2018

Dependence Measure for non-additive model

We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These properties are important in many applications. Experimental results show that CDC can detect the dependence between variables in both additive and non-additive models.

stat.ML↗

arXiv2016

An entropic characterization of long memory stationary process

Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the second-order properties of the process. The excess entropy of a stationary process is the summation of redundancies which relates to the rate of convergence of the conditional entropy $H(X_n|X_{n-1},\cdots, X_1)$ to the entropy rate. It is proved that the excess entropy is identical to the mutual information between the past and the future when the entropy $H(X_1)$ is finite. We suggest the definition that a stationary process is long memory if the excess entropy is infinite. Since the definition of excess entropy of a stationary process requires very weak moment condition on the distribution of the process, it can be applied to processes whose distributions without bounded second moment. A significant property of excess entropy is that it is invariant under invertible transformation, which enables us to know the excess entropy of a stationary process from the excess entropy of other process. For stationary Guassian process, the excess entropy characterization of long memory relates to popular characterization well. It is proved that the excess entropy of fractional Gaussian noise is infinite if the Hurst parameter $H \in (1/2, 1)$.

math.PR↗

arXiv2015

Wavelet-based Estimator for the Hurst Parameters of Fractional Brownian Sheet

It is proposed a class of statistical estimators $\hat H =(\hat H_1, \ldots, \hat H_d)$ for the Hurst parameters $H=(H_1, \ldots, H_d)$ of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are asymptotically normal. These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals, which is important in texture classification and improvement of diffusion tensor imaging (DTI) of nuclear magnetic resonance (NMR). Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators. We find that when $H_i \geq 1/2$, the estimators are efficient, and when $H_i < 1/2$, there are some bias.

cs.IT↗

arXiv2014

Evaluation of node importance in complex networks

The assessment of node importance has been a fundamental issue in the research of complex networks. In this paper, we propose to use the Shannon-Parry measure (SPM) to evaluate the importance of a node quantitatively, because SPM is the stationary distribution of the most unprejudiced random walk on the network. We demonstrate the accuracy and robustness of SPM compared with several popular methods in the Zachary karate club network and three toy networks. We apply SPM to analyze the city importance of China Railways High-speed (CRH) network, and obtain reasonable results. Since SPM can be used effectively in weighted and directed network, we believe it is a relevant method to identify key nodes in networks.

cs.SI↗

arXiv2011

The rates of convergence for generalized entropy of the normalized sums of IID random variables

We consider the generalized differential entropy of normalized sums of independent and identically distributed (IID) continuous random variables. We prove that the Rényi entropy and Tsallis entropy of order $α (α>0)$ of the normalized sum of IID continuous random variables with bounded moments are convergent to the corresponding Rényi entropy and Tsallis entropy of the Gaussian limit, and obtain sharp rates of convergence.

cs.IT↗

arXiv2010

How to Measure Significance of Community Structure in Complex Networks

Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Recently, many approaches were proposed to community structure detection, but few works were focused on the significance of community structure. Since real networks obtained from complex systems always contain error links, and most of the community detection algorithms have random factors, evaluate the significance of community structure is important and urgent. In this paper, we use the eigenvectors' stability to characterize the significance of community structures. By employing the eigenvalues of Laplacian matrix of a given network, we can evaluate the significance of its community structure and obtain the optimal number of communities, which are always hard for community detection algorithms. We apply our method to many real networks. We find that significant community structures exist in many social networks and C.elegans neural network, and that less significant community structures appear in protein-interaction networks and metabolic networks. Our method can be applied to broad clustering problems in data mining due to its solid mathematical basis and efficiency.

physics.soc-ph↗

arXiv2009

Wandering intervals and absolutely continuous invariant probability measures of interval maps

For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove the nonexistence of wandering intervals, the existence of absolutely continuous invariant measures, and the bounded backward contraction property. The proofs are based on the method of proving the existence of absolutely continuous invariant measures of unimodal map, developed by Nowicki and van Strien.

math.DS↗

arXiv2009

Renormalization and alpha-limit set for expanding Lorenz maps

We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of periodic orbit of minimal period, the minimal completely invariant closed set is constructed. Topological characterizations of the renormalizations and $α$-limit sets are obtained via consecutive renormalizations. Some properties of periodic renormalizations are collected in Appendix.

math.DS↗