An Information Geometry of Statistical Manifold Learning

Ke Sun, Stéphane Marchand-Maillet
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1-9, 2014.

Abstract

Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collectively. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions. There, manifold learning is interpreted as a trajectory of intermediate models. The volume of a continuous region reveals an amount of information. It can be measured to define model complexity and embedding quality. This provides deep unified perspectives of manifold learning theory.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-suna14, title = {An Information Geometry of Statistical Manifold Learning}, author = {Sun, Ke and Marchand-Maillet, Stéphane}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1--9}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/suna14.pdf}, url = {https://proceedings.mlr.press/v32/suna14.html}, abstract = {Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collectively. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions. There, manifold learning is interpreted as a trajectory of intermediate models. The volume of a continuous region reveals an amount of information. It can be measured to define model complexity and embedding quality. This provides deep unified perspectives of manifold learning theory.} }
Endnote
%0 Conference Paper %T An Information Geometry of Statistical Manifold Learning %A Ke Sun %A Stéphane Marchand-Maillet %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-suna14 %I PMLR %P 1--9 %U https://proceedings.mlr.press/v32/suna14.html %V 32 %N 2 %X Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collectively. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions. There, manifold learning is interpreted as a trajectory of intermediate models. The volume of a continuous region reveals an amount of information. It can be measured to define model complexity and embedding quality. This provides deep unified perspectives of manifold learning theory.
RIS
TY - CPAPER TI - An Information Geometry of Statistical Manifold Learning AU - Ke Sun AU - Stéphane Marchand-Maillet BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-suna14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1 EP - 9 L1 - http://proceedings.mlr.press/v32/suna14.pdf UR - https://proceedings.mlr.press/v32/suna14.html AB - Manifold learning seeks low-dimensional representations of high-dimensional data. The main tactics have been exploring the geometry in an input data space and an output embedding space. We develop a manifold learning theory in a hypothesis space consisting of models. A model means a specific instance of a collection of points, e.g., the input data collectively or the output embedding collectively. The semi-Riemannian metric of this hypothesis space is uniquely derived in closed form based on the information geometry of probability distributions. There, manifold learning is interpreted as a trajectory of intermediate models. The volume of a continuous region reveals an amount of information. It can be measured to define model complexity and embedding quality. This provides deep unified perspectives of manifold learning theory. ER -
APA
Sun, K. & Marchand-Maillet, S.. (2014). An Information Geometry of Statistical Manifold Learning. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1-9 Available from https://proceedings.mlr.press/v32/suna14.html.

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