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Coupled Compound Poisson Factorization [article]

Mehmet E. Basbug, Barbara E. Engelhardt
2017 arXiv   pre-print
and factor analysis---to robustly model non-random missing data in the context of clustering, prediction, and matrix factorization.  ...  In all three cases, we test our framework against models that ignore the missing-data mechanism on large scale studies with non-random missing data, and we show that explicitly modeling the missing-data  ...  Probabilistic models for low-rank approximation of extremely sparse matrices are abundant, and include probabilistic matrix factorization (PMF) (Salakhutdinov & Mnih, 2011) , non-negative matrix factorization  ... 
arXiv:1701.02058v1 fatcat:3h27rc2pejhmjh6mzl6rvhq2be

Collaborative prediction and ranking with non-random missing data

Benjamin M. Marlin, Richard S. Zemel
2009 Proceedings of the third ACM conference on Recommender systems - RecSys '09  
In this paper we present the first study of the effect of non-random missing data on collaborative ranking, and extend our previous results regarding the impact of non-random missing data on collaborative  ...  The statistical theory of missing data shows that incorrect assumptions about missing data can lead to biased parameter estimation and prediction.  ...  Matrix factorization We consider a probabilistic matrix factorization model with global mean offset as seen in Equations 21 to 23 [10] .  ... 
doi:10.1145/1639714.1639717 dblp:conf/recsys/MarlinZ09 fatcat:drndmqvloja7fhb6vpt6fdgwmm

Slides | Bayesian temporal factorization for multidimensional time series prediction

Xinyu Chen
2021 Zenodo  
By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies  ...  missing data imputation and multi-step rolling prediction tasks.  ...  Missing data generation: • Random missing (RM) (Data are missing at random.) T 2T 3T 4T 5T 6T 7T • Non-random missing (NM) (Data are missing continuously during a few time periods.)  ... 
doi:10.5281/zenodo.4693405 fatcat:tkogabg4kvex3mowjx7ypnykm4

Probabilistic Non-Negative Tensor Factorization Using Markov Chain Monte Carlo

Shakir Mohamed, Mikkel Schmidt
2009 Zenodo  
CONCLUSIONS We have presented a model for probabilistic non-negative matrix factorization.  ...  elements in the likelihood term, which corresponds to dealing with the "missing at random" data assumption.  ... 
doi:10.5281/zenodo.41712 fatcat:ophf4getkrbfhksok2teyftvee

Fast nonparametric matrix factorization for large-scale collaborative filtering

Kai Yu, Shenghuo Zhu, John Lafferty, Yihong Gong
2009 Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval - SIGIR '09  
In this paper we develop nonparametric matrix factorization methods by allowing the latent factors of two low-rank matrix factorization methods, the singular value decomposition (SVD) and probabilistic  ...  principal component analysis (pPCA), to be data-driven, with the dimensionality increasing with data size.  ...  However (11) is not a probabilistic way to deal with uncertainties and missing data.  ... 
doi:10.1145/1571941.1571979 dblp:conf/sigir/YuZLG09 fatcat:wvjkf54or5fcznyhc4nidt7cxm

Autoencoders and Probabilistic Inference with Missing Data: An Exact Solution for The Factor Analysis Case [article]

Christopher K. I. Williams, Charlie Nash, Alfredo Nazábal
2019 arXiv   pre-print
Latent variable models can be used to probabilistically "fill-in" missing data entries.  ...  We show how to calculate exactly the latent posterior distribution for the factor analysis (FA) model in the presence of missing data, and note that this solution implies that a different encoder network  ...  CN is supported by a PhD studentship from the EPSRC CDT in Data Science EP/L016427/1. CW thanks Kevin Murphy for a useful email discussion.  ... 
arXiv:1801.03851v3 fatcat:snapaakk4nblddmpxhtcmvvuja

Optimal Recovery of Missing Values for Non-negative Matrix Factorization

Rebecca Chen Dean, Lav Varshney
2021 IEEE Open Journal of Signal Processing  
We describe a straightforward unsupervised imputation algorithm, a minimax approach based on optimal recovery, and derive probabilistic error bounds on downstream non-negative matrix factorization (NMF  ...  Missing values imputation is often evaluated on some similarity measure between actual and imputed data.  ...  Non-negative matrix factorization (NMF) Matrix factorization is commonly used for clustering and dimensionality reduction in computational biology, imaging, and other fields.  ... 
doi:10.1109/ojsp.2021.3069373 fatcat:xzb5cz3j5rc45gb4lfbc3c4kdm

Non-linear matrix factorization with Gaussian processes

Neil D. Lawrence, Raquel Urtasun
2009 Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09  
A popular approach to collaborative filtering is matrix factorization. In this paper we develop a non-linear probabilistic matrix factorization using Gaussian process latent variable models.  ...  SGD allows us to apply Gaussian processes to data sets with millions of observations without approximate methods. We apply our approach to benchmark movie recommender data sets.  ...  We then extend this model in a non-linear way to give a probabilistic non-linear matrix factorization.  ... 
doi:10.1145/1553374.1553452 dblp:conf/icml/LawrenceU09 fatcat:rkl3ehvatveohojdicxlhkw2vq

The probabilistic tensor decomposition toolbox

Jesper Løve Hinrich, Morten Mørup, Kristoffer Hougaard Madsen
2020 Machine Learning: Science and Technology  
Acknowledgments The Probabilistic Tensor Toolbox was developed as part of the PhD thesis of the first author and supervised by both co-authors.  ...  Figure 4 . 4 Tensor Completion: Data entries are missing at random (top row) or fibers are missing at random (bottom row).  ...  factor matrix A (n) .  ... 
doi:10.1088/2632-2153/ab8241 fatcat:e3jyr3iahvgfdkmr6jlmqx3ixu

Survey on Probabilistic Models of Low-Rank Matrix Factorizations

Jiarong Shi, Xiuyun Zheng, Wei Yang
2017 Entropy  
approximation of a given data matrix.  ...  The most significant difference between low-rank matrix factorizations and their corresponding probabilistic models is that the latter treat the low-rank components as random variables.  ...  Probabilistic Models of Non-Negative Matrix Factorization Non-negative matrix factorization (NMF) decomposes a non-negative data matrix into the product of two non-negative low-rank matrices.  ... 
doi:10.3390/e19080424 fatcat:5joohnutojgidny6o3frsiezki

Missing Data in Kernel PCA [chapter]

Guido Sanguinetti, Neil D. Lawrence
2006 Lecture Notes in Computer Science  
Despite its success and flexibility, the lack of a probabilistic interpretation means that some problems, such as handling missing or corrupted data, are very hard to deal with.  ...  This in turn allows a principled approach to the missing data problem. Furthermore, this new approach can be extended to reconstruct corrupted test data using fixed kernel feature extractors.  ...  G.S. gratefully acknowledges support from a BBSRC award "Improved processing of microarray data using probabilistic models".  ... 
doi:10.1007/11871842_76 fatcat:gyjkd2d4rjfe3ltldr7hxmbcgu

RECOVERY OF MISSING DATA USING ENHANCED PROBABILISTIC MATRIX FACTORIZATION

U. Priyanka, Dr. K. Kumar
2020 International Journal of Engineering Applied Sciences and Technology  
One of the most common ways to build a recommendation system is with matrix factorization, which finds ways to predict a user's rating for a specific product based on previous ratings and other users'  ...  Motivated by the observation that incorporating user network information is not as effective as constraining the user feature vector with latent constraint similarity matrix, we developed Constrained Kernelized  ...  ., (2017) proposed recovery of missing data through probabilistic matrix factoristion. k-means algorithm is used to cluster the sensor data and through factorization, missing data has been recovered.  ... 
doi:10.33564/ijeast.2020.v05i02.045 fatcat:vyzjpio2sfdgnhtoyj5eibdiwu

A Survey of Tensor Factorization Frameworks on Audio Modelling

Unsal Gokdag
2014 International Journal of Applied Mathematics Electronics and Computers  
This survey is about Tensor Factorization methods for audio modeling, which focuses on probabilistic latent tensor factorization and generalized coupled tensor factorization by expectation maximization  ...  The matrix factorization had major impact on clustering, non-negative matrix factorization, latent semantic indexing, collaborative indexing and many other methods when considered as matrix factorization  ...  One improvement over the NMF model is capturing temporal variations by deconvolution which is introduced by Smaragadis [9] with the name of Non-negative Matrix Factor Deconvolution(NMFD). { } { } { } {  ... 
doi:10.18100/ijamec.70262 fatcat:5ooutd6x3rbzvn6adtwupx76zy

Probabilistic matrix factorization from quantized measurements

Giulio Bottegal, Johan A. K. Suykens
2017 2017 International Joint Conference on Neural Networks (IJCNN)  
We consider the problem of factorizing a matrix with discrete-valued entries as a product of two low-rank matrices.  ...  Extension to the case of missing values is also discussed. The proposed methods are evaluated on simulated data, and on a real data set for recommender systems.  ...  However, the optimization problem associated with matrix factorization is in general non-convex, so specific optimization techniques have to be devised to solve it.  ... 
doi:10.1109/ijcnn.2017.7965865 dblp:conf/ijcnn/BottegalS17 fatcat:fm4jd57gtfbepnnvbd2wncnmye

Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation [article]

Thomas Brouwer, Jes Frellsen, Pietro Lio'
2016 arXiv   pre-print
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation.  ...  We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional samples to estimate the  ...  The non-probabilistic method starts overfitting from 20% missing values, leading to very high prediction errors.  ... 
arXiv:1610.08127v1 fatcat:iscci3gogngw5ewq3qjlvswzma
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