# Ambiguity Modeling in Latent Spaces

Carl Henrik Ek, University of Bristol
Jon Rihan
Philip H. S. Torr, University of Oxford
Gregory Rogez
Neil D. Lawrence, University of Sheffield

in Machine Learning for Multimodal Interaction (MLMI 2008), pp 62-73

#### Abstract

We are interested in the situation where we have two or more representations of an underlying phenomenon. In particular we are interested in the scenario where the representation are complementary. This implies that a single individual representation is not sufficient to fully discriminate a specific instance of the underlying phenomenon, it also means that each representation is an ambiguous representation of the other complementary spaces. In this paper we present a latent variable model capable of consolidating multiple complementary representations. Our method extends canonical correlation analysis by introducing additional latent spaces that are specific to the different representations, thereby explaining the full variance of the observations. These additional spaces, explaining representation specific variance, separately model the variance in a representation ambiguous to the other. We develop a spectral algorithm for fast computation of the embeddings and a probabilistic model (based on Gaussian processes) for validation and inference. The proposed model has several potential application areas, we demonstrate its use for multi-modal regression on a benchmark human pose estimation data set.

  @InProceedings{ek-ambiguity08, title = {Ambiguity Modeling in Latent Spaces}, author = {Carl Henrik Ek and Jon Rihan and Philip H. S. Torr and Gregory Rogez and Neil D. Lawrence}, booktitle = {Machine Learning for Multimodal Interaction (MLMI 2008)}, pages = {62}, year = {2008}, editor = {Andrei Popescu-Belis and Rainer Stiefelhagen}, series = {LNCS}, month = {00}, publisher = {Springer-Verlag}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2008-01-01-ek-ambiguity08.md}, url = {http://inverseprobability.com/publications/ek-ambiguity08.html}, abstract = {We are interested in the situation where we have two or more representations of an underlying phenomenon. In particular we are interested in the scenario where the representation are complementary. This implies that a single individual representation is not sufficient to fully discriminate a specific instance of the underlying phenomenon, it also means that each representation is an ambiguous representation of the other complementary spaces. In this paper we present a latent variable model capable of consolidating multiple complementary representations. Our method extends canonical correlation analysis by introducing additional latent spaces that are specific to the different representations, thereby explaining the full variance of the observations. These additional spaces, explaining representation specific variance, separately model the variance in a representation ambiguous to the other. We develop a spectral algorithm for fast computation of the embeddings and a probabilistic model (based on Gaussian processes) for validation and inference. The proposed model has several potential application areas, we demonstrate its use for multi-modal regression on a benchmark human pose estimation data set.}, key = {Ek:ambiguity08}, linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/mlmi2008.pdf}, linksoftware = {https://github.com/SheffieldML/SGPLVM/}, OPTgroup = {} }
 %T Ambiguity Modeling in Latent Spaces %A Carl Henrik Ek and Jon Rihan and Philip H. S. Torr and Gregory Rogez and Neil D. Lawrence %B %C Machine Learning for Multimodal Interaction (MLMI 2008) %D %E Andrei Popescu-Belis and Rainer Stiefelhagen %F ek-ambiguity08 %I Springer-Verlag %P 62--73 %R %U http://inverseprobability.com/publications/ek-ambiguity08.html %X We are interested in the situation where we have two or more representations of an underlying phenomenon. In particular we are interested in the scenario where the representation are complementary. This implies that a single individual representation is not sufficient to fully discriminate a specific instance of the underlying phenomenon, it also means that each representation is an ambiguous representation of the other complementary spaces. In this paper we present a latent variable model capable of consolidating multiple complementary representations. Our method extends canonical correlation analysis by introducing additional latent spaces that are specific to the different representations, thereby explaining the full variance of the observations. These additional spaces, explaining representation specific variance, separately model the variance in a representation ambiguous to the other. We develop a spectral algorithm for fast computation of the embeddings and a probabilistic model (based on Gaussian processes) for validation and inference. The proposed model has several potential application areas, we demonstrate its use for multi-modal regression on a benchmark human pose estimation data set. 
 TY - CPAPER TI - Ambiguity Modeling in Latent Spaces AU - Carl Henrik Ek AU - Jon Rihan AU - Philip H. S. Torr AU - Gregory Rogez AU - Neil D. Lawrence BT - Machine Learning for Multimodal Interaction (MLMI 2008) PY - 2008/01/01 DA - 2008/01/01 ED - Andrei Popescu-Belis ED - Rainer Stiefelhagen ID - ek-ambiguity08 PB - Springer-Verlag SP - 62 EP - 73 L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/mlmi2008.pdf UR - http://inverseprobability.com/publications/ek-ambiguity08.html AB - We are interested in the situation where we have two or more representations of an underlying phenomenon. In particular we are interested in the scenario where the representation are complementary. This implies that a single individual representation is not sufficient to fully discriminate a specific instance of the underlying phenomenon, it also means that each representation is an ambiguous representation of the other complementary spaces. In this paper we present a latent variable model capable of consolidating multiple complementary representations. Our method extends canonical correlation analysis by introducing additional latent spaces that are specific to the different representations, thereby explaining the full variance of the observations. These additional spaces, explaining representation specific variance, separately model the variance in a representation ambiguous to the other. We develop a spectral algorithm for fast computation of the embeddings and a probabilistic model (based on Gaussian processes) for validation and inference. The proposed model has several potential application areas, we demonstrate its use for multi-modal regression on a benchmark human pose estimation data set. ER - 
 Ek, C.H., Rihan, J., Torr, P.H.S., Rogez, G. & Lawrence, N.D.. (2008). Ambiguity Modeling in Latent Spaces. Machine Learning for Multimodal Interaction (MLMI 2008) :62-73