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Modeliranje multivariatnih diskretnih podatkov z latentnimi Gaussovimi procesi
ID DIMITRIEV, ALEKSANDAR (Author), ID Štrumbelj, Erik (Mentor) More about this mentor... This link opens in a new window

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Abstract
Multivariatni števni podatki so pogosti na področjih kot so šport, nevroznanost in besedilno rudarjenje. Modeli, ki lahko natančno opravljajo faktorsko analizo, so potrebni zlasti za strukturirane podatke kot na primer števne matrike s časovnimi vrstami. Predstavljamo Poissonovo faktorsko analizo z latentnimi Gaussovimi procesi, ki je nova metoda za analizo multivariatnih števnih podatkov. Naš pristop omogoča analizo odvisnih podatkov, ki so povezani v latentnem prostoru s pomočjo Gaussovega procesa. Zaradi eksponentne nelinearnosti v modelu ne obstaja zaprta rešitev. Zato smo razvili postopek maksimizacije pričakovane vrednosti z Laplacovim približkom za lažjo uporabo. Predstavljamo rezultate na različnih podatkovnih naborih, tako sintetičnih kot realnih, v primerjavi z drugimi metodami faktorske analize. Naša metoda je kvalitativno in kvantitativno boljša za strukturirane podatke, saj so predpostavke, ki jih naredi, primerne za podatke.

Language:English
Keywords:faktorska analiza, Gaussovi procesi, latentni prostor, Poisson, števni podatki
Work type:Master's thesis/paper (mb22)
Organization:FRI - Faculty of computer and information science
Year:2017
Publication date in RUL:28.03.2017
Views:906
Downloads:337
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Secondary language

Language:Slovenian
Title:Modelling multivariate discrete data with latent Gaussian processes
Abstract:
Multivariate count data are common in some fields, such as sports, neuroscience, and text mining. Models that can accurately perform factor analysis are required, especially for structured data, such as time-series count matrices. We present Poisson Factor Analysis using Latent Gaussian Processes, a novel method for analyzing multivariate count data. Our approach allows for non-i.i.d observations, which are linked in the latent space using a Gaussian Process. Due to an exponential non-linearity in the model, there is no closed form solution. Thus, we resort to an expectation maximization approach with a Laplace approximation for tractable inference. We present results on several data sets, both synthetic and real, of a comparison with other factor analysis methods. Our method is both qualitatively and quantitatively superior for non-i.i.d Poisson data, because the assumptions it makes are well suited for the data.

Keywords:factor analysis, Gaussian process, latent space, Poisson, count data

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