Warped Diffusion for Latent Differentiation Inference

Masahiro Nakano, Hiroki Sakuma, Ryo Nishikimi, Ryohei Shibue, Takashi Sato, Tomoharu Iwata, Kunio Kashino
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4789-4797, 2024.

Abstract

This paper proposes a Bayesian nonparametric diffusion model with a black-box warping function represented by a Gaussian process to infer potential diffusion structures latent in observed data, such as differentiation mechanisms of living cells and phylogenetic evolution processes of media information. In general, the task of inferring latent differentiation structures is very difficult to handle due to two interrelated settings. One is that the conversion mechanism between hidden structure and often higher dimensional observations is unknown (and is a complex mechanism). The other is that the topology of the hidden diffuse structure itself is unknown. Therefore, in this paper, we propose a BNP-based strategy as a natural way to deal with these two challenging settings simultaneously. Specifically, as an extension of the Gaussian process latent variable model, we propose a model in which the black box transformation from latent variable space to observed data space is represented by a Gaussian process, and introduce a BNP diffusion model for the latent variable space. We show its application to the visualization of the diffusion structure of media information and to the task of inferring cell differentiation structure from single-cell gene expression levels.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-nakano24a, title = {Warped Diffusion for Latent Differentiation Inference}, author = {Nakano, Masahiro and Sakuma, Hiroki and Nishikimi, Ryo and Shibue, Ryohei and Sato, Takashi and Iwata, Tomoharu and Kashino, Kunio}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {4789--4797}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/nakano24a/nakano24a.pdf}, url = {https://proceedings.mlr.press/v238/nakano24a.html}, abstract = {This paper proposes a Bayesian nonparametric diffusion model with a black-box warping function represented by a Gaussian process to infer potential diffusion structures latent in observed data, such as differentiation mechanisms of living cells and phylogenetic evolution processes of media information. In general, the task of inferring latent differentiation structures is very difficult to handle due to two interrelated settings. One is that the conversion mechanism between hidden structure and often higher dimensional observations is unknown (and is a complex mechanism). The other is that the topology of the hidden diffuse structure itself is unknown. Therefore, in this paper, we propose a BNP-based strategy as a natural way to deal with these two challenging settings simultaneously. Specifically, as an extension of the Gaussian process latent variable model, we propose a model in which the black box transformation from latent variable space to observed data space is represented by a Gaussian process, and introduce a BNP diffusion model for the latent variable space. We show its application to the visualization of the diffusion structure of media information and to the task of inferring cell differentiation structure from single-cell gene expression levels.} }
Endnote
%0 Conference Paper %T Warped Diffusion for Latent Differentiation Inference %A Masahiro Nakano %A Hiroki Sakuma %A Ryo Nishikimi %A Ryohei Shibue %A Takashi Sato %A Tomoharu Iwata %A Kunio Kashino %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-nakano24a %I PMLR %P 4789--4797 %U https://proceedings.mlr.press/v238/nakano24a.html %V 238 %X This paper proposes a Bayesian nonparametric diffusion model with a black-box warping function represented by a Gaussian process to infer potential diffusion structures latent in observed data, such as differentiation mechanisms of living cells and phylogenetic evolution processes of media information. In general, the task of inferring latent differentiation structures is very difficult to handle due to two interrelated settings. One is that the conversion mechanism between hidden structure and often higher dimensional observations is unknown (and is a complex mechanism). The other is that the topology of the hidden diffuse structure itself is unknown. Therefore, in this paper, we propose a BNP-based strategy as a natural way to deal with these two challenging settings simultaneously. Specifically, as an extension of the Gaussian process latent variable model, we propose a model in which the black box transformation from latent variable space to observed data space is represented by a Gaussian process, and introduce a BNP diffusion model for the latent variable space. We show its application to the visualization of the diffusion structure of media information and to the task of inferring cell differentiation structure from single-cell gene expression levels.
APA
Nakano, M., Sakuma, H., Nishikimi, R., Shibue, R., Sato, T., Iwata, T. & Kashino, K.. (2024). Warped Diffusion for Latent Differentiation Inference. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:4789-4797 Available from https://proceedings.mlr.press/v238/nakano24a.html.

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