Globally Sparse Probabilistic PCA

Pierre-Alexandre Mattei, Charles Bouveyron, Pierre Latouche
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:976-984, 2016.

Abstract

With the flourishing development of high-dimensional data, sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables may be difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure that allows to obtain several sparse components with the same sparsity pattern. To this end, using Roweis’ probabilistic interpretation of PCA and an isotropic Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. In order to avoid the drawbacks of discrete model selection, we propose a simple relaxation of our framework which allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood can eventually be maximized over this path, relying on Occam’s razor to select the relevant variables. Since the sparsity pattern is common to all components, we call this approach globally sparse probabilistic PCA (GSPPCA). Its usefulness is illustrated on synthetic data sets and on several real unsupervised feature selection problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-mattei16, title = {Globally Sparse Probabilistic PCA}, author = {Mattei, Pierre-Alexandre and Bouveyron, Charles and Latouche, Pierre}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {976--984}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/mattei16.pdf}, url = {https://proceedings.mlr.press/v51/mattei16.html}, abstract = {With the flourishing development of high-dimensional data, sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables may be difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure that allows to obtain several sparse components with the same sparsity pattern. To this end, using Roweis’ probabilistic interpretation of PCA and an isotropic Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. In order to avoid the drawbacks of discrete model selection, we propose a simple relaxation of our framework which allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood can eventually be maximized over this path, relying on Occam’s razor to select the relevant variables. Since the sparsity pattern is common to all components, we call this approach globally sparse probabilistic PCA (GSPPCA). Its usefulness is illustrated on synthetic data sets and on several real unsupervised feature selection problems.} }
Endnote
%0 Conference Paper %T Globally Sparse Probabilistic PCA %A Pierre-Alexandre Mattei %A Charles Bouveyron %A Pierre Latouche %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-mattei16 %I PMLR %P 976--984 %U https://proceedings.mlr.press/v51/mattei16.html %V 51 %X With the flourishing development of high-dimensional data, sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables may be difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure that allows to obtain several sparse components with the same sparsity pattern. To this end, using Roweis’ probabilistic interpretation of PCA and an isotropic Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. In order to avoid the drawbacks of discrete model selection, we propose a simple relaxation of our framework which allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood can eventually be maximized over this path, relying on Occam’s razor to select the relevant variables. Since the sparsity pattern is common to all components, we call this approach globally sparse probabilistic PCA (GSPPCA). Its usefulness is illustrated on synthetic data sets and on several real unsupervised feature selection problems.
RIS
TY - CPAPER TI - Globally Sparse Probabilistic PCA AU - Pierre-Alexandre Mattei AU - Charles Bouveyron AU - Pierre Latouche BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-mattei16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 976 EP - 984 L1 - http://proceedings.mlr.press/v51/mattei16.pdf UR - https://proceedings.mlr.press/v51/mattei16.html AB - With the flourishing development of high-dimensional data, sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables may be difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure that allows to obtain several sparse components with the same sparsity pattern. To this end, using Roweis’ probabilistic interpretation of PCA and an isotropic Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. In order to avoid the drawbacks of discrete model selection, we propose a simple relaxation of our framework which allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood can eventually be maximized over this path, relying on Occam’s razor to select the relevant variables. Since the sparsity pattern is common to all components, we call this approach globally sparse probabilistic PCA (GSPPCA). Its usefulness is illustrated on synthetic data sets and on several real unsupervised feature selection problems. ER -
APA
Mattei, P., Bouveyron, C. & Latouche, P.. (2016). Globally Sparse Probabilistic PCA. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:976-984 Available from https://proceedings.mlr.press/v51/mattei16.html.

Related Material