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Author: | Noeva, Polina |
Title: | Sampling Methods for Missing Value Reconstruction |
Publication type: | Master's thesis |
Publication year: | 2012 |
Pages: | [8] + 60 s. + liitt. 10 Language: eng |
Department/School: | Tietotekniikan laitos |
Main subject: | Informaatiotekniikka (T-61) |
Supervisor: | Oja, Erkki |
Instructor: | Ilin, Alexander |
OEVS: | Electronic archive copy is available via Aalto Thesis Database.
Instructions Reading digital theses in the closed network of the Aalto University Harald Herlin Learning CentreIn the closed network of Learning Centre you can read digital and digitized theses not available in the open network. The Learning Centre contact details and opening hours: https://learningcentre.aalto.fi/en/harald-herlin-learning-centre/ You can read theses on the Learning Centre customer computers, which are available on all floors.
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Location: | P1 Ark Aalto | Archive |
Keywords: | sampling methods Markov chain Monte Carlo Gibbs sampling Langevin dynamics variational inference natural gradient stochastic gradient sparse dataset |
Abstract (eng): | The main theme of this thesis is reconstruction of missing value in sparse datasets with algorithms based on sampling methods. A probabilistic principal component analysis model is used to model the data. In contrast to the standard principal component analysis, this model allows to avoid over fitting and to use Bayesian inference methods by adding the noise term into the model and introducing prior distributions over the model parameters. The parameters of the model are estimated by approximate inference methods. Particularly, variational Bayesian principal component analysis is used as a baseline method in the experiments part where the parameters of the model are estimated with a maximum likelihood estimate by using expectation maximization algorithm. The other approach to approximate inference is sampling from posterior distribution. Particularly, Metropolis-Hastings sampling, Gibbs sampling, Langevin dynamics MCMC and Langevin dynamics MCMC with stochastic gradient, are considered. Gradient-based algorithms allow to use the geometry information of the posterior distribution and to move in the direction of the higher probability density at each step. Langevin dynamics sampling method is also generalized by using natural gradient instead of the standard gradient in the update rules. Presented gradient-based sampling methods are tested on a simple example involving only two parameters. Also, all sampling methods are applied to the problem of missing value reconstruction in the Movielens dataset. The results are promising and show that the proposed sampling methods outperform variational Bayesian inference approach and suggest that sampling methods can be efficiently applied for large-scale problems. |
ED: | 2012-06-27 |
INSSI record number: 44737
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