Bayesian Learning for Low-Rank matrix reconstruction

نویسندگان

  • Martin Sundin
  • Cristian R. Rojas
  • Magnus Jansson
  • Saikat Chatterjee
چکیده

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Low-rank matrix reconstruction and clustering via approximate message passing

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for...

متن کامل

Spatial Design for Knot Selection in Knot-Based Low-Rank Models

‎Analysis of large geostatistical data sets‎, ‎usually‎, ‎entail the expensive matrix computations‎. ‎This problem creates challenges in implementing statistical inferences of traditional Bayesian models‎. ‎In addition,researchers often face with multiple spatial data sets with complex spatial dependence structures that their analysis is difficult‎. ‎This is a problem for MCMC sampling algorith...

متن کامل

Joint Feature Selection with Low-rank Dictionary Learning

Feature selection is one of the well known dimensionality reduction methods that efficiently describes the input data by removing irrelevant variables and reduces the effects of noise to provide good prediction results. In this paper, we propose a feature selection method by integrating dictionary learning and low-rank matrix approximation and apply it to image classification. The objective fun...

متن کامل

Sparse Bayesian Multi-Task Learning

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can...

متن کامل

An ECG Compressed Sensing Method of Low Power Body Area Network

Aimed at low power problem in body area network, an ECG compressed sensing method of low power body area network based on the compressed sensing theory was proposed. Random binary matrices were used as the sensing matrix to measure ECG signals on the sensor nodes. After measured value is transmitted to remote monitoring center, ECG signal sparse representation under the discrete cosine transfor...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1501.05740  شماره 

صفحات  -

تاریخ انتشار 2015