Continuous-time Latent-variable Models for Time Series

Time series data play a crucial role in many applications, such as biology, medicine, economics, engineering and others. One of the most powerful approaches for time series is latent-variable models, thanks to their ability to handle multi-dimensional data with complex interactions. Typically, these models represent a timeline as a sequence of discrete states and therefore assume that observations occur at regular intervals. However, this assumption does not always hold. An illustrative example is medical records, where a patient is screened only when the need arises, resulting in the irregularly-spaced and possibly sparse time series. In this type of time series, the time intervals between the observations can provide valuable information about the time series, such as patient's health condition. To bridge the gap between the data and the available models, a common approach is to convert a continuous timeline into a discrete one by aggregating observations into a sequence of discrete clusters. However, this transformation erases a lot of the temporal structure of the data and prevents us from utilizing the data to its full potential. In this thesis, I present latent-variable models for continuous-time data across several application domains. First, I present a method for ordering cancer mutations on a linear timeline and use a mixture model to summarize them into a set of trajectories over time. Thanks to this ordering, I perform a more fine-grained discretization of the cancer timeline in comparison to the previous methods and can more accurately detect the changes in cancer dynamics. Next, I introduce Latent Ordinary Differential Equations (Latent ODE) -- a framework that allows to model time series as a solution of a differential equation, in other words, as a continuous function over time. Unlike the previous models, this approach does not require any discretization of the data and can naturally handle irregularly-spaced time points. I showcase the potential of the model on the interpretable dataset. I demonstrate that the Latent ODE model has better extrapolation properties and is more robust to noise compared to existing sequential models. Finally, I improve the Latent ODE model by proposing an ODE-based recognition model. I demonstrate that, by preserving the observations on a real-values timeline and modelling them as a continuous function, we can get improvement in a variety of tasks, such as forecasting, imputation and classification.

Department dc:contributor.department

Computer Science

Year dc:date.issued

2020

Author dc:creator

• Rubanova, Yulia

Advisor dc:contributor.advisor

• Morris, Quaid

• Cancer evolution
• Latent-variable models
• Neural ODE
• Time series

Statement dc:rights

• Attribution 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/4.0/

Handle dc:identifier.uri

http://hdl.handle.net/1807/103759

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/103759