Irregularly-sampled time series are characterized by non-uniform time intervals between successive measurements. Such time series naturally occur in various application areas including climate science, ecology, biology, and medicine. Irregular sampling posts a great challenge for modeling this type of data as there can be substantial uncertainty about the values of the underlying temporal processes. Moreover, different time series are not necessarily synchronized or of the same length that makes it difficult to deal with using standard machine learning methods that assume fixed-dimensional data spaces.
The goal of this thesis is to develop scalable probabilistic tools for modeling a large collection of irregularly-sampled time series over a common time interval. We first introduce an uncertainty-aware kernel framework based on a Gaussian process (GP) representation of the time series and then demonstrate how to scale up the model by linearizing the kernel with various acceleration techniques.
To further reduce the computational overhead of the GP representation and improve the expressiveness of the model, we then propose a generalized uncertainty-aware framework that integrates a posterior GP sampler with arbitrary black-box models including neural networks. We propose a linear time and linear space sampling algorithm and show how to efficiently train the entire framework end-to-end.
To better model the uncertainty by utilizing the information from the entire dataset collectively, we reframe our task as a missing data problem that aims at learning the distribution of the latent temporal process. We first study the missing data problem under a simplified setting where the data is defined on a finite-dimensional space and introduce a model based on generative adversarial networks for learning from incomplete data. To relax the finite-dimensional constraint, we propose a unified encoder-decoder framework that can be trained as a density model or an implicit model. We finally introduce a special architecture for this framework to efficiently featurize irregularly-sampled continuous time series.
Advisor: Ben Marlin
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Meeting ID: 332 043 306
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Meeting ID: 332 043 306