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Bayesian Variable Selection for Globally Sparse Probabilistic PCA [article]

Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei
2016 arXiv   pre-print
To overcome this drawback, we propose a Bayesian procedure called globally sparse probabilistic PCA (GSPPCA) that allows to obtain several sparse components with the same sparsity pattern.  ...  To this end, using Roweis' probabilistic interpretation of PCA and a Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model.  ...  A general framework for globally sparse PPCA In a classical (locally) sparse PCA context, the loading matrix W would be expected to contain few nonzero coefficients.  ... 
arXiv:1605.05918v2 fatcat:sckpgvdblnbpviisplroaxgmma

Bayesian variable selection for globally sparse probabilistic PCA

Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei
2018 Electronic Journal of Statistics  
A general framework for globally sparse PPCA In a classical (locally) sparse PCA context, the loading matrix W would be expected to contain few nonzero coefficients.  ...  Using a formula in Abramowitz and Stegun (1965, p. 486) , we eventually find that ϕ y 1 W (u) = 1 1 + α||u|| 2 2 , which leads to ϕ Wy (u) = 1 (1 + α||u|| 2 2 ) d/2 . 22 Globally Sparse Probabilistic  ... 
doi:10.1214/18-ejs1450 fatcat:imv2bdsolbfpba3vh2h3yj4oty

A Deflation Method for Structured Probabilistic PCA [chapter]

Rajiv Khanna, Joydeep Ghosh, Russell Poldrack, Oluwasanmi Koyejo
2017 Proceedings of the 2017 SIAM International Conference on Data Mining  
The components estimated using the proposed deflation regain some of the interpretability of classic PCA such as straightforward estimates of variance explained, while retaining the ability to incorporate  ...  This work introduces a novel, robust and efficient deflation method for Probabilistic Principal Component Analysis using tools recently developed for constrained probabilistic estimation via information  ...  We term the overall procedure sparse orthogonal probabilistic PCA (soPPCA).  ... 
doi:10.1137/1.9781611974973.60 dblp:conf/sdm/KhannaGPK17 fatcat:vz6utipauzcslgasgdcpzea6pq

Principal Component Analysis (PCA) and Hough Transform as Tool for Simultaneous Localization and Mapping (SLAM) with Sparse and Noisy Sensors

Stephanie Kamarry Sousa, Elyson Adan Carvalho, Raimundo Carlos Freire, Lucas Molina, Eduardo Oliveira Freire
2020 Journal of Integrated Circuits and Systems  
This work proposes a method of handling the difficulties generated by sparse and noisy sensorial output from a small quantity of ultrasonic sensors in order to develop a low cost SLAM system.  ...  A pre-processing step of detecting faulty sensors was implemented by applying PCA on the available data in order to extract more reliable baseline features through the Hough Transform.  ...  The sensor measurements acquired from each time step were processed by the PCA so that data could be used to construct the global map.  ... 
doi:10.29292/jics.v15i3.162 fatcat:xmyeio5g5ba2fmxdp42wjlkr4m

Probabilistic 3D surface reconstruction from sparse MRI information [article]

Katarína Tóthová, Sarah Parisot, Matthew Lee, Esther Puyol-Antón, Andrew King, Marc Pollefeys, Ender Konukoglu
2020 arXiv   pre-print
In this paper, we present a novel probabilistic deep learning approach for concurrent 3D surface reconstruction from sparse 2D MR image data and aleatoric uncertainty prediction.  ...  Prior shape information is encoded using a built-in linear principal component analysis (PCA) model.  ...  Based on principles of probabilistic PCA [6] , our framework addresses the inherent challenges linked with the sparse and heterogeneous input data via the use of a spatially aware deep CNN computing distributions  ... 
arXiv:2010.02041v1 fatcat:rkyfsqzkjzekrd6kql37vmeohq

Expectation-maximization for sparse and non-negative PCA

Christian D. Sigg, Joachim M. Buhmann
2008 Proceedings of the 25th international conference on Machine learning - ICML '08  
Finally, we show the usefulness of non-negative sparse PCA for unsupervised feature selection in a gene clustering task.  ...  Based on expectation-maximization for probabilistic PCA, we present an algorithm for any combination of these constraints. Its complexity is at most quadratic in the number of dimensions of the data.  ...  The first simplification reduces probabilistic PCA to standard PCA.  ... 
doi:10.1145/1390156.1390277 dblp:conf/icml/SiggB08 fatcat:2hepxelr5fg7lj2rfinypmg6tu

A Literature Survey on High-Dimensional Sparse Principal Component Analysis

Shen Ning-min, Li Jing
2015 International Journal of Database Theory and Application  
Firstly we give the overview for PCA and sparse PCA.  ...  Sparse principal component analysis (sparse PCA) is proposed mainly for the challenges of PCA above.  ...  The object of the sparse probabilistic PCA is to estimate the parameters.  ... 
doi:10.14257/ijdta.2015.8.6.06 fatcat:6nt3kqwtjzhiznqj2ylzmbjnbi

Trace your sources in large-scale data: one ring to find them all [article]

Alexander Böttcher, Wieland Brendel, Bernhard Englitz, Matthias Bethge
2018 arXiv   pre-print
DECOMPOSE encompasses and generalises many traditional BSS algorithms such as PCA, ICA and NMF and we demonstrate substantial improvements in accuracy and robustness on artificial and real data.  ...  In contrast, their rarely used probabilistic counterparts can get away with little cross-validation and are more accurate and reliable but no simple and scalable implementations are available.  ...  Most commonly used BSS algorithm like PCA, ICA, NMF, sparse NMF or sparse PCA are part of our framework.  ... 
arXiv:1803.08882v1 fatcat:hbfo3p3ohve4plrypwz3ghcyqm

Probabilistic-Interval Energy Flow Analysis of Regional Integrated Electricity and Gas System Considering Multiple Uncertainties and Correlations

Xiaoyun Hu, Xia Zhao, Xinxin Feng
2019 IEEE Access  
The polynomial chaos expansion (PCE) method is introduced to IEGS analysis and an improved PCE-based method combining the technique of dimensionreduction and the sparse-PCE is proposed to address the numerous  ...  A methodological framework considering probabilistic/interval uncertainties, linear/rank correlations among probabilistic variables, and dependency between interval variables is then developed for both  ...  This is because power loss is a global variable while pipeline flow is a local variable.  ... 
doi:10.1109/access.2019.2958704 fatcat:hqrarfwygzhbloksgwxfp6ybxm

Survey on Probabilistic Models of Low-Rank Matrix Factorizations

Jiarong Shi, Xiuyun Zheng, Wei Yang
2017 Entropy  
The categories are performed via different matrix factorizations formulations, which mainly include PCA, matrix factorizations, robust PCA, NMF and tensor factorizations.  ...  This paper makes a survey of the probabilistic models of low-rank matrix factorizations.  ...  VB Probabilistic Models of Robust PCA Compared with traditional PCA, robust PCA is more robust to outliers or large sparse noise.  ... 
doi:10.3390/e19080424 fatcat:5joohnutojgidny6o3frsiezki

Multimode Process Monitoring Based on Sparse Principal Component Selection and Bayesian Inference-Based Probability

Xiaodong Jiang, Haitao Zhao, Bo Jin
2015 Mathematical Problems in Engineering  
BIP is utilized to compute the posterior probabilities of each monitored sample belonging to the multiple components and derive an integrated global probabilistic index for fault detection of multimode  ...  In this paper, a novel algorithm based on sparse principal component selection (SPCS) and Bayesian inference-based probability (BIP) is proposed for multimode process monitoring.  ...  BIP can compute the posterior probabilities of each monitored sample belonging to the multiple components and derive an integrated global probabilistic index for fault detection of multimode processes.  ... 
doi:10.1155/2015/465372 fatcat:4xfytkbqg5harho3smpqioyyvm

Improved Two-Step Human Face Hallucination with Coupled Residue Compensation

Haju Muhamed Muhamed Naleer, Yao Lu, Zubair Ahmed Memon
2012 Mehran University Research Journal of Engineering and Technology  
Considering the coupled PCA compensation algorithm, this capably exploits the local distribution structure in the training samples.  ...  The first and second steps were generate global features the main characteristics of the real image and produces residual image to compensate the outcome of the first step respectively.  ...  The first step generates global structure of real image by means of probabilistic method in MAP (Maximum a Posteriori) frame or manifold learning method such as LLE (Locally Linear Embedding), the second  ... 
doaj:ff11e70e138c4c97a65451cc4e201d28 fatcat:ntmppn77nnd7tipt3od3cft75a

Spectral Latent Variable Models for Perceptual Inference

Atul Kanaujia, Cristian Sminchisescu, Dimitris Metaxas
2007 2007 IEEE 11th International Conference on Computer Vision  
: (1) provide stable latent spaces that preserve global or local geometric properties of the modeled data; (2) offer low-dimensional generative models with probabilistic, bi-directional mappings between  ...  We propose non-linear generative models referred to as Sparse Spectral Latent Variable Models (SLVM), that combine the advantages of spectral embeddings with the ones of parametric latent variable models  ...  On the other hand, a variety of probabilistic, non-linear latent variable models are available (mixture of PCA, Factor Analyzers, etc.), but they lack a global perceptual coordinate system and are not  ... 
doi:10.1109/iccv.2007.4408845 dblp:conf/iccv/KanaujiaSM07 fatcat:alca33lpzfegrdzgaz52hln5bm

Closed-form EM for Sparse Coding and its Application to Source Separation

Jörg Lücke, Abdul-Saboor Sheikh
2012 arXiv   pre-print
Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic PCA. The resulting EM algorithm can take all modes of a potentially multi-modal posterior into account.  ...  In numerical experiments on artificial data we verify likelihood maximization and show that the derived algorithm recovers the sparse directions of standard sparse coding distributions.  ...  In this work we study a generative model that combines the Gaussian prior of probabilistic PCA (p-PCA) with a binary prior distribution.  ... 
arXiv:1105.2493v6 fatcat:efdkf53yjfbi7pyxi5hzoco4lq

Probabilistic Approach to Neural Networks Computation Based on Quantum Probability Model Probabilistic Principal Subspace Analysis Example [article]

Marko V. Jankovic
2010 arXiv   pre-print
In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework.  ...  As an example, we will show that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for PSA, which are preferably realized by a parallel hardware based on very  ...  Probabilistic PCA In this section, we are going to give a definition of the probabilistic PCA that can be used for creation of symmetric PCA algorithms.  ... 
arXiv:1001.4301v1 fatcat:uhxwhf34h5eylobmnazspkqtru
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