Supervised Spectral Latent Variable Models

Liefeng Bo, Cristian Sminchisescu
; Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:33-40, 2009.

Abstract

We present a probabilistic structured prediction method for learning input-output dependencies where correlations between outputs are modeled as low-dimensional manifolds constrained by both geometric, distance preserving output relations,and predictive power of inputs. Technically this reduces to learning a probabilistic, input conditional model, over latent (manifold) and output variables using an alternation scheme. In one round, we optimize the parameters of an input-driven manifold predictor using latent targets given by preimages (conditional expectations) of the current manifold-to-output model. In the next round, we use the distribution given by the manifold predictor in order to maximize the probability of the outputs with an additional, implicit distance preserving constraint on the manifold. The resulting Supervised Spectral Latent Variable Model (SSLVM) combines the properties of probabilistic geometric manifold learning (accommodates geometric constraints corresponding to any spectral embedding method including PCA, ISOMAP or Laplacian Eigenmaps), with the additional supervisory information to further constrain it for predictive tasks. We demonstrate the superiority of the method over baseline PPCA + regression frameworks and show its potential in difficult realworld computer vision benchmarks designed for the reconstruction of three-dimensional human poses from monocular image sequences.

Cite this Paper


BibTeX
@InProceedings{pmlr-v5-bo09a, title = {Supervised Spectral Latent Variable Models}, author = {Liefeng Bo and Cristian Sminchisescu}, booktitle = {Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics}, pages = {33--40}, year = {2009}, editor = {David van Dyk and Max Welling}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/bo09a/bo09a.pdf}, url = {http://proceedings.mlr.press/v5/bo09a.html}, abstract = {We present a probabilistic structured prediction method for learning input-output dependencies where correlations between outputs are modeled as low-dimensional manifolds constrained by both geometric, distance preserving output relations,and predictive power of inputs. Technically this reduces to learning a probabilistic, input conditional model, over latent (manifold) and output variables using an alternation scheme. In one round, we optimize the parameters of an input-driven manifold predictor using latent targets given by preimages (conditional expectations) of the current manifold-to-output model. In the next round, we use the distribution given by the manifold predictor in order to maximize the probability of the outputs with an additional, implicit distance preserving constraint on the manifold. The resulting Supervised Spectral Latent Variable Model (SSLVM) combines the properties of probabilistic geometric manifold learning (accommodates geometric constraints corresponding to any spectral embedding method including PCA, ISOMAP or Laplacian Eigenmaps), with the additional supervisory information to further constrain it for predictive tasks. We demonstrate the superiority of the method over baseline PPCA + regression frameworks and show its potential in difficult realworld computer vision benchmarks designed for the reconstruction of three-dimensional human poses from monocular image sequences.} }
Endnote
%0 Conference Paper %T Supervised Spectral Latent Variable Models %A Liefeng Bo %A Cristian Sminchisescu %B Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-bo09a %I PMLR %J Proceedings of Machine Learning Research %P 33--40 %U http://proceedings.mlr.press %V 5 %W PMLR %X We present a probabilistic structured prediction method for learning input-output dependencies where correlations between outputs are modeled as low-dimensional manifolds constrained by both geometric, distance preserving output relations,and predictive power of inputs. Technically this reduces to learning a probabilistic, input conditional model, over latent (manifold) and output variables using an alternation scheme. In one round, we optimize the parameters of an input-driven manifold predictor using latent targets given by preimages (conditional expectations) of the current manifold-to-output model. In the next round, we use the distribution given by the manifold predictor in order to maximize the probability of the outputs with an additional, implicit distance preserving constraint on the manifold. The resulting Supervised Spectral Latent Variable Model (SSLVM) combines the properties of probabilistic geometric manifold learning (accommodates geometric constraints corresponding to any spectral embedding method including PCA, ISOMAP or Laplacian Eigenmaps), with the additional supervisory information to further constrain it for predictive tasks. We demonstrate the superiority of the method over baseline PPCA + regression frameworks and show its potential in difficult realworld computer vision benchmarks designed for the reconstruction of three-dimensional human poses from monocular image sequences.
RIS
TY - CPAPER TI - Supervised Spectral Latent Variable Models AU - Liefeng Bo AU - Cristian Sminchisescu BT - Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics PY - 2009/04/15 DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-bo09a PB - PMLR SP - 33 DP - PMLR EP - 40 L1 - http://proceedings.mlr.press/v5/bo09a/bo09a.pdf UR - http://proceedings.mlr.press/v5/bo09a.html AB - We present a probabilistic structured prediction method for learning input-output dependencies where correlations between outputs are modeled as low-dimensional manifolds constrained by both geometric, distance preserving output relations,and predictive power of inputs. Technically this reduces to learning a probabilistic, input conditional model, over latent (manifold) and output variables using an alternation scheme. In one round, we optimize the parameters of an input-driven manifold predictor using latent targets given by preimages (conditional expectations) of the current manifold-to-output model. In the next round, we use the distribution given by the manifold predictor in order to maximize the probability of the outputs with an additional, implicit distance preserving constraint on the manifold. The resulting Supervised Spectral Latent Variable Model (SSLVM) combines the properties of probabilistic geometric manifold learning (accommodates geometric constraints corresponding to any spectral embedding method including PCA, ISOMAP or Laplacian Eigenmaps), with the additional supervisory information to further constrain it for predictive tasks. We demonstrate the superiority of the method over baseline PPCA + regression frameworks and show its potential in difficult realworld computer vision benchmarks designed for the reconstruction of three-dimensional human poses from monocular image sequences. ER -
APA
Bo, L. & Sminchisescu, C.. (2009). Supervised Spectral Latent Variable Models. Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, in PMLR 5:33-40

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