Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFast Variational Learning in State-Space Gaussian Process Models
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods which can make the implementation difficult, e.g., expectation propagation can be numerically unstable and variational inference can be computationally inefficient. In this paper, we propose a new method that removes such difficulties. Building upon an existing method called conjugate-computation variational inference, our approach enables linear-time inference via Kalman recursions while avoiding numerical instabilities and convergence issues. We provide an efficient JAX implementation which exploits just-in-time compilation and allows for fast automatic differentiation through large for-loops. Overall, our approach leads to fast and stable variational inference in state-space GP models that can be scaled to time series with millions of data points.
rate research
Read More
We investigate active learning in Gaussian Process state-space models (GPSSM). Our problem is to actively steer the system through latent states by determining its inputs such that the underlying dynamics can be optimally learned by a GPSSM. In order that the most informative inputs are selected, we employ mutual information as our active learning criterion. In particular, we present two approaches for the approximation of mutual information for the GPSSM given latent states. The proposed approaches are evaluated in several physical systems where we actively learn the underlying non-linear dynamics represented by the state-space model.
Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed. However, for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks. In this work, we introduce a new model, the Gaussian Process (GP) Prior Variational Autoencoder (GPPVAE), to specifically address this issue. The GPPVAE aims to combine the power of VAEs with the ability to model correlations afforded by GP priors. To achieve efficient inference in this new class of models, we leverage structure in the covariance matrix, and introduce a new stochastic backpropagation strategy that allows for computing stochastic gradients in a distributed and low-memory fashion. We show that our method outperforms conditional VAEs (CVAEs) and an adaptation of standard VAEs in two image data applications.
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system states and the transition function. We exploit Markov structure in the true posterior, as well as an inducing point approximation to achieve linear time complexity in the length of the time series. Contrary to previous approaches, no Monte Carlo sampling is required: inference is cast as a deterministic optimisation problem. In a number of experiments, we demonstrate the ability to model non-linear dynamics in the presence of both process and observation noise as well as to impute missing information (e.g. velocities from raw positions through time), to de-noise, and to estimate the underlying dimensionality of the system. Finally, we also introduce a closed-form method for multi-step prediction, and a novel criterion for assessing the quality of our approximate posterior.
Learning a model of dynamics from high-dimensional images can be a core ingredient for success in many applications across different domains, especially in sequential decision making. However, currently prevailing methods based on latent-variable models are limited to working with low resolution images only. In this work, we show that some of the issues with using high-dimensional observations arise from the discrepancy between the dimensionality of the latent and observable space, and propose solutions to overcome them.
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This strategy, however, is ineffective when there are outlier data samples whose latent representations are meaningless, yet contaminating the estimation of key major clusters in the latent space. This exact problem arises in the context of resting-state fMRI (rs-fMRI) analysis, where clustering major functional connectivity patterns is often hindered by heavy noise of rs-fMRI and many minor clusters (rare connectivity patterns) of no interest to analysis. In this paper we propose a novel generative process, in which we use a Gaussian-mixture to model a few major clusters in the data, and use a non-informative uniform distribution to capture the remaining data. We embed this truncated Gaussian-Mixture model in a Variational AutoEncoder framework to obtain a general joint clustering and outlier detection approach, called tGM-VAE. We demonstrated the applicability of tGM-VAE on the MNIST dataset and further validated it in the context of rs-fMRI connectivity analysis.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
