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Independent Components Analysis through Product Density Estimation

Trevor Hastie, Robert Tibshirani
2002 Neural Information Processing Systems  
Given a candidate orthogonal frame, we model each of the coordinates using a semi-parametric density estimate based on cubic splines.  ...  We present a simple direct approach for solving the ICA problem, using density estimation and maximum likelihood.  ...  In this paper we fit the model (3) directly using semi-parametric maximum likelihood.  ... 
dblp:conf/nips/HastieR02 fatcat:cjgwpvcqjzayvfx5en7hvo5bh4

Gradient-Based Manipulation of Nonparametric Entropy Estimates

N.N. Schraudolph
2004 IEEE Transactions on Neural Networks  
We derive a family of differential learning rules that optimize the Shannon entropy at the output of an adaptive system via kernel density estimation.  ...  In contrast to parametric formulations of entropy, this nonparametric approach assumes no particular functional form of the output density.  ...  For large data samples, semi-parametric density estimation methods such as expectation-maximization (EM) [8, 11] or the self-organizing maps of van Hulle [39, 40] can be useful; for our purposes, however  ... 
doi:10.1109/tnn.2004.828766 pmid:15461076 fatcat:ccfcipibx5flfbibyv7yagrjva

Page 5569 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
Bunke, Bayesian in- ference in semiparametric problems (pp. 27-30); Nils Lid Hjort, Semi-parametric Bayes estimators (pp. 31-34); A.  ...  Dacunha-Castelle, Some uses of maximum-entropy methods for ill-posed problems in signal and crystallography theo- ries (pp. 55-58); K.  ... 

Projection pursuit based on Gaussian mixtures and evolutionary algorithms

Luca Scrucca, Alessio Serafini
2019 Journal of Computational And Graphical Statistics  
The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximised.  ...  We show that this semi-parametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly  ...  Semi-parametric density estimation via GMMs can be influenced by data sphering.  ... 
doi:10.1080/10618600.2019.1598871 fatcat:v7dzbktqlnbyvfh5v3qk2egnra

Markov chain importance sampling with applications to rare event probability estimation

Zdravko I. Botev, Pierre L'Ecuyer, Bruno Tuffin
2011 Statistics and computing  
We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation.  ...  Note that the estimator (25) requires that we estimate both the marginal densities of all d components of X via the semi-parametric estimator (17) , and the joint density of X via the nonparametric estimator  ...  Suppose for the moment that f (x) = d j=1 f j (x j ), that is, the components of the vector X are independent and we wish to estimate the rare-event probability Z = P f (S(X) γ) using Algorithm 21.  ... 
doi:10.1007/s11222-011-9308-2 fatcat:mtsxq2zicbf37mkvzgtvbeepbq

On a computationally-scalable sparse formulation of the multidimensional and non-stationary maximum entropy principle [article]

Horenko Illia and Marchenko Ganna and Gagliardini Patrick
2020 arXiv   pre-print
We derive a multivariate non-parametric and non-stationary formulation of the MaxEnt-principle and show that its solution can be approximated through a numerical maximisation of the sparse constrained  ...  This analysis also reveals a sparse network of statistically-significant temporal relations for the positive and negative latent variance changes among different markets.  ...  The TV-Entropy models were estimated with two regimes, six density regime parameters and [1 : 10] number of regime switches. We used 10 annealing steps for estimating both TV-Entropy and HMM models.  ... 
arXiv:2005.03253v1 fatcat:vsm4hzzqufetdaqlpfi6dlrsz4

Generative Models of Conformational Dynamics [chapter]

Christopher James Langmead
2013 Advances in Experimental Medicine and Biology  
We begin by discussing traditional methods, which produce multivariate Gaussian models.  ...  Atomistic simulations of the conformational dynamics of proteins can be performed using either Molecular Dynamics or Monte Carlo procedures.  ...  Acknowledgments This work is supported in part by US NSF grant IIS-0905193, US NIH RC2GM093307, and US NIH P41 GM103712.  ... 
doi:10.1007/978-3-319-02970-2_4 pmid:24446358 pmcid:PMC4090804 fatcat:codn6yvap5g2ziuxqycqmjrcum

Development of ICA and IVA Algorithms with Application to Medical Image Analysis [article]

Zois Boukouvalas
2018 arXiv   pre-print
properties due to improper estimation of the probability density function (PDF).  ...  Independent vector analysis (IVA) extends the applicability of ICA by jointly decomposing multiple datasets through the exploitation of the dependencies across datasets.  ...  Multidimensional Gaussian mixture model (MGMM) has been widely used for semi-parametric density estimation [17] .  ... 
arXiv:1801.08600v1 fatcat:nu2xlytexrcnnblws7zieo77be

Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis [article]

J. Emmanuel Johnson, Valero Laparra, Maria Piles, Gustau Camps-Valls
2020 arXiv   pre-print
In addition, this methodology allows us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual information.  ...  In this paper, we apply multivariate Gaussianization for probability density estimation which is robust to dimensionality, comes with statistical guarantees, and is easy to apply.  ...  by applying an orthogonal rotation matrix via independent components analysis (ICA) and then a mixture of Gaussians (MOGs) for the marginal Gaussian transformation.  ... 
arXiv:2010.06476v2 fatcat:nrwr3ad53jghhhwva7fmfuazti

Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas

N.J.-B. Brunel, J. Lapuyade-Lahorgue, W. Pieczynski
2010 IEEE Transactions on Automatic Control  
Moreover, the robustness can be increased for the estimation of the parameters of the copulas, by using a semi-parametric version of the IFM, called the omnibus estimator which estimates the copula without  ...  In the first one, we recall two classical multivariate parametric models and describe some associated estimation procedures in the case of independent observations.  ... 
doi:10.1109/tac.2009.2034929 fatcat:itcic5hfbjdudiflqs4obffene

On feature extraction by mutual information maximization

Kari Torkkola
2002 IEEE International Conference on Acoustics Speech and Signal Processing  
Instead of a commonly used mutual information measure based on Kullback-Leibler divergence, we use a quadratic divergence measure, which allows us to make an efficient non-parametric implementation and  ...  requires no prior assumptions about class densities.  ...  In terms of complexity and flexibility, semi-parametric density estimates lie between the fully nonparametric Parzen estimator and a fully parametric estimate, such as a Gaussian.  ... 
doi:10.1109/icassp.2002.5743865 dblp:conf/icassp/Torkkola02 fatcat:uzp6s7pznjbezkzyb2of2o7fvy

Robust estimation of group-wise cortical correspondence with an application to macaque and human neuroimaging studies

Ilwoo Lyu, Sun H. Kim, Joon-Kyung Seong, Sang W. Yoo, Alan Evans, Yundi Shi, Mar Sanchez, Marc Niethammer, Martin A. Styner
2015 Frontiers in Neuroscience  
We propose the use of an unbiased ensemble entropy minimization following the use of the pairwise registration as an initialization.  ...  The proposed method is based on our earlier template based registration that estimates a continuous, smooth deformation field via sulcal curve-constrained registration employing spherical harmonic decomposition  ...  For the density estimation, we assume a multivariate Gaussian distribution with covariance and therefore, the entropy is obtained by H[X] ≈ 1 2 ln | | = 1 2 ln λ , (15) where λ are the eigenvalues of .  ... 
doi:10.3389/fnins.2015.00210 pmid:26113807 pmcid:PMC4462677 fatcat:igx2moia2zfefobbqnjcsx3uve

Latent Class Analysis with Semi-parametric Proportional Hazards Submodel for Time-to-event Data [article]

Teng Fei, John Hanfelt, Limin Peng
2022 arXiv   pre-print
Latent class analysis (LCA) is a useful tool to investigate the heterogeneity of a disease population with time-to-event data.  ...  We propose a new method based on non-parametric maximum likelihood estimator (NPMLE), which facilitates theoretically validated inference procedure for covariate effects and cumulative hazard functions  ...  The authors wish to thank National Alzheimer's Coordinating Center for making the Uniform Data Set available for our analysis.  ... 
arXiv:2202.00775v1 fatcat:4yrbybe6n5bopdj3en3evxlgsu

Clustering via finite nonparametric ICA mixture models

Xiaotian Zhu, David R. Hunter
2018 Advances in Data Analysis and Classification  
We propose an extension of non-parametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure  ...  for optimizing this function and estimating the model parameters.  ...  The findings by Hunter & Young (2012) via modeling through a semi-parametric mixture of regressions conforms with the latter theory.  ... 
doi:10.1007/s11634-018-0338-x fatcat:glhnzn4hyzente6xiuige4rnke

Semi-supervised learning with an imperfect supervisor

Massih R. Amini, Patrick Gallinari
2005 Knowledge and Information Systems  
This algorithm optimizes the classification maximum likelihood of a set of labeled-unlabeled data, using a discriminant extension of the Classification Expectation Maximization algorithm.  ...  We further propose to extend this algorithm by modeling imperfections in the estimated class labels for unlabeled data.  ...  Discriminant semi-supervised CEM algorithm The generative approach to semi-supervised learning indirectly computes posteriors p( y = k | x, Θ) via conditional density estimation.  ... 
doi:10.1007/s10115-005-0219-4 fatcat:gh2ya53v2bhifgehbcmgizd2zm
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