Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Matérn kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Matérn GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.
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Statistical Guarantees for Transformation Based Models with applications to Implicit Variational Inference
Transformation-based methods have been an
attractive approach in non-parametric inference for problems such as unconditional and
conditional density estimation due to their
unique hierarchical structure that models the
data as flexible transformation of a set of
common latent variables. More recently,
transformation-based models have been used
in variational inference (VI) to construct flexible implicit families of variational distributions. However, their use in both nonparametric inference and variational inference lacks theoretical justification. We provide theoretical justification for the use of
non-linear latent variable models (NL-LVMs)
in non-parametric inference by showing that
the support of the transformation induced
prior in the space of densities is sufficiently
large in the L1 sense. We also show that,
when a Gaussian process (GP) prior is placed
on the transformation function, the posterior concentrates at the optimal rate up to
a logarithmic factor. Adopting the flexibility demonstrated in the non-parametric setting, we use the NL-LVM to construct an
implicit family of variational distributions,
deemed GP-IVI. We delineate sufficient conditions under which GP-IVI achieves optimal
risk bounds and approximates the true posterior in the sense of the Kullback–Leibler
divergence. To the best of our knowledge,
this is the first work on providing theoretical
guarantees for implicit variational inference.
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- Award ID(s):
- 1916371
- NSF-PAR ID:
- 10281952
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 130
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 2449-2457
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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