A Parametric Copula-Based Framework for Hypothesis Testing Using Heterogeneous Data

@article{Iyengar2011APC,
  title={A Parametric Copula-Based Framework for Hypothesis Testing Using Heterogeneous Data},
  author={Satish G. Iyengar and Pramod K. Varshney and Thyagaraju R. Damarla},
  journal={IEEE Transactions on Signal Processing},
  year={2011},
  volume={59},
  pages={2308-2319}
}
We present a parametric framework for the joint processing of heterogeneous data, specifically for a binary classification problem. Processing such a data set is not straightforward as heterogeneous data may not be commensurate. In addition, the signals may also exhibit statistical dependence due to overlapping fields of view. We propose a copula-based solution to incorporate statistical dependence between disparate sources of information. The important problem of identifying the best copula… 
Fusing heterogeneous data for detection under non-stationary dependence
TLDR
This paper designs a copula-based detector using the Neyman-Pearson framework, and involves a sample-wise copula selection scheme, which for a simple hypothesis test, is proved to perform better than previously used singleCopula selection schemes.
Unsupervised data classification using pairwise Markov chains with automatic copulas selection
Uncertainty characterization using copulas for classification
TLDR
This work addresses the problem of characterizing uncertainty for multisensor data fusion in a classification problem using copula functions while allowing the ability to incorporate any desired marginal distributions, i.e., any desired modalities.
A Copula Statistic for Measuring Nonlinear Multivariate Dependence
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties
Fusion for the detection of dependent signals using multivariate copulas
TLDR
This work considers the problem of fusion for the detection of dependent, heterogeneous signals and design a detector using a copula-based framework and addresses copula construction and model selection issues for the multivariate case.
Copula-based Multimodal Data Fusion for Inference with Dependent Observations
TLDR
This dissertation investigates inference problems with heterogeneous modalities by taking into account nonlinear cross-modal dependence, and proposes a novel parallel platform, C-Storm, by marrying copula-based dependence modeling for highly accurate inference and a highly-regarded parallel computing platform Storm for fast stream data processing.
Heterogeneous Sensor Signal Processing for Inference with Nonlinear Dependence
TLDR
This thesis considers not only inference in parallel frameworks but also the problem of collaborative inference where collaboration exists among local sensors, and proposes a copula-based joint characterization of multiple dependent time series from sensors and social media.
A Copula Statistic for Measuring Nonlinear Dependence with Application to Feature Selection in Machine Learning
TLDR
In this paper, a new index based on empirical copulas, termed the Copula Statistic (CoS), to assess the strength of statistical dependence and for testing statistical independence is introduced and it is shown that this test exhibits higher statistical power than other indices.
Bayesian Nonparametric Modeling of Categorical Data for Information Fusion and Causal Inference †
TLDR
A nonparametric regression model of categorical time series in the setting of conditional tensor factorization and Bayes network is presented, which can be used to improve the performance of prediction tasks and infer the causal relationship between key variables.
Hypothesis Testing With Dependent Observations
TLDR
The expectation maximization algorithm is developed and solved for the problem of detection in a network consisting of heterogeneous sensors collecting measurements which are dependent both among the samples collected by each sensor and among the data collected by different sensors.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 47 REFERENCES
Impact of feature correlations on separation between bivariate normal distributions
TLDR
It is shown that the impact of feature correlations on class separation between two bivariate normal distributions can be positive or negative, and that it can only be gauged in the context of the parameters of involved marginals.
Copulas in vectorial hidden Markov chains for multicomponent image segmentation
  • N. Brunel, W. Pieczynski, S. Derrode
  • Computer Science, Mathematics
    Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
  • 2005
TLDR
This work introduces an alternative solution based on a very general class of multivariate models called 'copulas', which are used in the frame of multidimensional mixture estimation arising in the segmentation of multicomponent images, when using a vectorial hidden Markov chain (HMC).
Copulas based multivariate gamma modeling for texture classification
TLDR
The d-variate Gaussian copula associated to univariate Gamma densities for modeling the texture is proposed and experiments were conducted aiming to compare the recognition rates of the proposed model with the univariate generalized Gaussian model, theUnivariate Gamma model, and the generalized Gaussian copula-based multivariate model.
Detecting Dependence With Kendall Plots
Earlier literature proposed a rank-based graphical tool called a chi-plot which, in conjunction with a traditional scatterplot of the raw data, can help detect the presence of association in a random
The Estimation Method of Inference Functions for Margins for Multivariate Models
An estimation approach is proposed for models for a multivariate (non–normal) response with covariates when each of the parameters (either a univariate or a dependence parameter) of the model can be
Statistical Inference Procedures for Bivariate Archimedean Copulas
Abstract A bivariate distribution function H(x, y) with marginals F(x) and G(y) is said to be generated by an Archimedean copula if it can be expressed in the form H(x, y) = ϕ–1[ϕ{F(x)} + ϕ{G(y)}]
Unsupervised Learning of Finite Mixture Models
TLDR
The novelty of the approach is that it does not use a model selection criterion to choose one among a set of preestimated candidate models; instead, it seamlessly integrate estimation and model selection in a single algorithm.
A Principled Approach to Score Level Fusion in Multimodal Biometric Systems
TLDR
An optimal framework for combining the matching scores from multiple modalities using the likelihood ratio statistic computed using the generalized densities estimated from the genuine and impostor matching scores is proposed.
What is the best index of detectability?
Various indices which have been proposed as measures of detectability (for unequal variance normal distributions of signal and nonsignal) are discussed. It is argued that the best measure is an
...
1
2
3
4
5
...