scholarly journals Sampling conformations in high dimensions using low-dimensional distribution functions

2009 ◽  
Vol 130 (13) ◽  
pp. 134102 ◽  
Author(s):  
Sandeep Somani ◽  
Benjamin J. Killian ◽  
Michael K. Gilson
Keyword(s):  
Distribution Functions ◽  
High Dimensions ◽  
Dimensional Distribution ◽  
Low Dimensional

scholarly journals Bootstrapping spectral statistics in high dimensions

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 781-801 ◽  
Author(s):  
Miles E Lopes ◽  
Andrew Blandino ◽  
Alexander Aue
Keyword(s):  
Parametric Bootstrap ◽  
Covariance Matrices ◽  
Asymptotic Formulas ◽  
High Dimensional ◽  
High Dimensions ◽  
Full Data ◽  
Sample Covariance ◽  
Practical Standpoint ◽  
Spectral Statistics ◽  
Low Dimensional

Summary Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of spectral statistics in low-dimensional problems, such methods are relatively unexplored in the high-dimensional setting. The aim of this article is to focus on linear spectral statistics as a class of prototypes for developing a new bootstrap in high dimensions, a method we refer to as the spectral bootstrap. In essence, the proposed method originates from the parametric bootstrap and is motivated by the fact that in high dimensions it is difficult to obtain a nonparametric approximation to the full data-generating distribution. From a practical standpoint, the method is easy to use and allows the user to circumvent the difficulties of complex asymptotic formulas for linear spectral statistics. In addition to proving the consistency of the proposed method, we present encouraging empirical results in a variety of settings. Lastly, and perhaps most interestingly, we show through simulations that the method can be applied successfully to statistics outside the class of linear spectral statistics, such as the largest sample eigenvalue and others.

The dependence structure in credit risk between money and derivatives markets

2014 ◽  
Vol 40 (8) ◽  
pp. 758-769
Author(s):  
Weiou Wu ◽  
David G. McMillan
Keyword(s):  
Credit Risk ◽  
Sovereign Debt ◽  
Debt Crisis ◽  
Money Market ◽  
Distribution Functions ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Content Type ◽  
Dimensional Distribution ◽  
Derivatives Markets

Purpose – The purpose of this paper is to examine the dynamic dependence structure in credit risk between the money market and the derivatives market during 2004-2009. The authors use the TED spread to measure credit risk in the money market and CDS index spread for the derivatives market. Design/methodology/approach – The dependence structure is measured by a time-varying Gaussian copula. A copula is a function that joins one-dimensional distribution functions together to form multivariate distribution functions. The copula contains all the information on the dependence structure of the random variables while also removing the linear correlation restriction. Therefore, provides a straightforward way of modelling non-linear and non-normal joint distributions. Findings – The results show that the correlation between these two markets while fluctuating with a general upward trend prior to 2007 exhibited a noticeably higher correlation after 2007. This points to the evidence of credit contagion during the crisis. Three different phases are identified for the crisis period which sheds light on the nature of contagion mechanisms in financial markets. The correlation of the two spreads fell in early 2009, although remained higher than the pre-crisis level. This is partly due to policy intervention that lowered the TED spread while the CDS spread remained higher due to the Eurozone sovereign debt crisis. Originality/value – The paper examines the relationship between the TED and CDS spreads which measure credit risk in an economy. This paper contributes to the literature on dynamic co-movement, contagion effects and risk linkages.

scholarly journals Learning Markov Models Via Low-Rank Optimization

2021 ◽  
Author(s):  
Ziwei Zhu ◽  
Xudong Li ◽  
Mengdi Wang ◽  
Anru Zhang
Keyword(s):  
Markov Models ◽  
Supply And Demand ◽  
Likelihood Estimation ◽  
Low Rank ◽  
Programming Algorithm ◽  
High Dimensional ◽  
High Dimensions ◽  
Taxi Service ◽  
Low Dimensional ◽  
Nuclear Norm Regularization

Taming high-dimensional Markov models In “Learning Markov models via low-rank optimization”, Z. Zhu, X. Li, M. Wang, and A. Zhang focus on learning a high-dimensional Markov model with low-dimensional latent structure from a single trajectory of states. To overcome the curse of high dimensions, the authors propose to equip the standard MLE (maximum-likelihood estimation) with either nuclear norm regularization or rank constraint. They show that both approaches can estimate the full transition matrix accurately using a trajectory of length that is merely proportional to the number of states. To solve the rank-constrained MLE, which is a nonconvex problem, the authors develop a new DC (difference) programming algorithm. Finally, they apply the proposed methods to analyze taxi trips on the Manhattan island and partition the island based on the destination preference of customers; this partition can help balance supply and demand of taxi service and optimize the allocation of traffic resources.

scholarly journals scSemiAE: A Deep Model with Semi-Supervised Learning for Single-Cell Transcriptomics

2021 ◽  
Author(s):  
Jiayi Dong ◽  
Yin Zhang ◽  
Fei Wang
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Cell Subpopulation ◽  
High Dimensions ◽  
Deep Model ◽  
Unsupervised Approach ◽  
Cell Subpopulations ◽  
Downstream Analysis ◽  
Low Dimensional ◽  
Public Datasets

Abstract Background: With the development of modern sequencing technology, hundreds of thousands of single-cell RNA-sequencing(scRNA-seq) profiles allow to explore the heterogeneity in the cell level, but it faces the challenges of high dimensions and high sparsity. Dimensionality reduction is essential for downstream analysis, such as clustering to identify cell subpopulations. Usually, dimensionality reduction follows unsupervised approach. Results: In this paper, we introduce a semi-supervised dimensionality reduction method named scSemiAE, which is based on an autoencoder model. It transfers the information contained in available datasets with cell subpopulation labels to guide the search of better low-dimensional representations, which can ease further analysis. Conclusions: Experiments on five public datasets show that, scSemiAE outperforms both unsupervised and semi-supervised baselines whether the transferred information embodied in the number of labeled cells and labeled cell subpopulations is much or less.

Numerical Analysis of Conservative Maps: A Possible Foundation of Nonextensive Phenomena

2004 ◽  
Author(s):  
Fulvio Baldovin
Keyword(s):  
Statistical Mechanics ◽  
High Energy Physics ◽  
Financial Analysis ◽  
Initial Conditions ◽  
Research Area ◽  
Distribution Functions ◽  
Point Of View ◽  
Dissipative Systems ◽  
Definition Of ◽  
Low Dimensional

We discuss the sensitivity to initial conditions and the entropy production of low-dimensional conservative maps, focusing on situations where the phase space presents complex (fractal-like) structures. We analyze numerically the standard map as a specific example and we observe a scenario that presents appealing analogies with anomalies detected in long-range Hamiltonian systems. We see how the Tsallis nonextensive formalism handles this situation both from a dynamical and from a statistical mechanics point of view…. In recent years, the Tsallis extension of the Boltzmann-Gibbs (BG) statistical mechanics [9, 26], usually referred to as nonextensive (NE) statistical mechanics, has become an intense and exciting research area (see, e.g., Tsallis [25]). The q-exponential distribution functions that emerge as a consequence of the NE formalism have been applied to an impressive variety of problems, ranging from turbulence, to high-energy physics, epilepsy, protein folding, and financial analysis. Yet, the foundation of this formalism, as well as the definition of its area of applicability, is still not completely understood, and it stands as a present challenge in the affirmation of the whole proposal. An intensive effort is currently being made to investigate this point, precisely in trying to understand: (1) which mechanisms lead to a crisis of the BG formalism; and (2) in these cases, does the NE formalism provide a "way out" to some of the problems? A possible approach to these questions comes from the study of the underlying dynamics that gives the basis for a statistical mechanic treatment of the system. This idea is not new. Einstein, in his critical remark about the validity of the Boltzmann principle [10], was one of the first to call attention to the relevance of a dynamical foundation of statistical mechanics. Another fundamental contribution is Krylov's seminal work [14] on the mixing properties of dynamical systems. In one-dimensional (dissipative) systems, intensive effort has been made to analyze the properties of the systems at the edge of chaos, i.e., at the critical poin that marks the transition between chaoticity and regularity [6, 8, 16, 19, 18, 23, 27].

The optical determination of preferred orientation in clays and its application to the study of microstructure in consolidated kaolin. І

1967 ◽  
Vol 300 (1461) ◽  
pp. 218-234 ◽  
Keyword(s):  
Three Dimensional ◽  
Optical Microscope ◽  
Preferred Orientation ◽  
Distribution Functions ◽  
Thin Sections ◽  
Clay Particles ◽  
Degree Of Orientation ◽  
Dimensional Distribution ◽  
Optical Determination

Although single clay particles can seldom be seen with an optical microscope the preferred orientation of an aggregate of clay particles may be investigated by studying in thin section the birefringence of the aggregate. The techniques of preparing thin sections of clay with a minimum of disturbance of the structure and for measuring the birefringence under crossed nicols are described. It is shown that the birefringence of the aggregate arises solely from the birefringence of the constituent particles at least for the porosities of the clay used in this study. If a model distribution function for the spatial orientation of the particles be adopted the birefringent behaviour of the aggregate may be predicted and birefringence observations may be used to interpret the degree of orientation of an aggregate in terms of a model parameter. Two- and three-dimensional distribution functions are considered and the two-dimensional theory is judged to be preferable.

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