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Bayesian Manifold Learning: The Locally Linear Latent Variable Model (LL-LVM)
Mijung Park · Wittawat Jitkrittum · Ahmad Qamar · Zoltan Szabo · Lars Buesing · Maneesh Sahani

Thu Dec 10 08:00 AM -- 12:00 PM (PST) @ 210 C #29 #None

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold model with additional probabilistic models that capture the structure of coordinates within the manifold.

Author Information

Mijung Park (UCL)
Wittawat Jitkrittum (Gatsby Unit, UCL)

Wittawat Jitkrittum is a postdoctoral researcher at Max Planck Institute for Intelligent Systems, Germany. He earned his PhD from Gatsby Unit, University College London with a thesis on informative features for comparing distributions. He received a best paper award at NeurIPS 2017 and the ELLIS PhD award 2019 for outstanding dissertation. Wittawat has broad research interests covering kernel methods, deep generative models, and approximate Bayesian inference. He served as a publication chair for AISTATS 2016, a program committee for NeurIPS, ICML, AISTATS, among others, and is a co-organizer of the first Southeast Asia Machine Learning School (SEAMLS 2019) in Indonesia and a co-organizer of the first Machine Learning Research School (MLRS 2019) in Thailand.

Ahmad Qamar
Zoltan Szabo (Gatsby Unit, UCL)
Lars Buesing (DeepMind)
Maneesh Sahani (Gatsby Unit, UCL)

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