Cooper Loughlin’s PhD Dissertation Defense

“Deep Generative Models for High Dimensional Spatial and Temporal Data Analysis”

Committee Members:
Prof. Vinay Ingle (Advisor)
Dr. Dimitris Manolakis
Prof. Purnima Ratilal-Makris

Abstract:
Data analysis and exploitation in practical applications is challenging when observations are the result of many interacting natural and man-made phenomena. We address two important problems for which traditional methods of analysis are insufficient. One problem of practical interest is the identification of particular materials from remotely sensed hyperspectral imagery. This is traditionally accomplished by comparing image pixel spectra to those from a known material library. Such techniques are limited by spectral variability, background interference, and imperfect compensation of atmospheric components. Established methods address these limitations with statistical techniques. Simple probability models result in tractable methods; however, analyses are limited by errors due, in particular, due to false alarms.

Analysis of complex time series is another challenging problem, particularly when data are high dimensional. This arises in air quality monitoring, where atmospheric concentration measurements of multiple pollutants are taken over time. Two analysis goals in this context are forecasting and anomaly detection. Both tasks are enabled by an accurate model for the temporal dynamics and interaction between pollutants. Air quality data are complex due to long term temporal dependencies, non-linear dependence between pollutants, and missing observations. Traditional multivariate time series analysis approaches, such as the vector autoregression and linear dynamical system models, fail to capture those characteristics necessary for a sufficient probabilistic model.

We use deep generative models to develop practical solutions that address these problems. This is made possible through the application of deep latent variable models. The modeling approach follows the philosophy that complex data can typically be explained by simpler underlying factors of variation. Variational autoencoders (VAEs) are deep latent variable models that emulate data generation by transforming simple, low dimensional, latent random vectors through a deep neural network. VAEs are trained to produce samples that resemble the training data, thus capturing a manifold on which complex data are distributed. This philosophy is extended to time series data, where we consider sequences of latent vectors.

We utilize VAEs develop a flexible generative model for hyperspectral imagery. Based on that model, we develop a novel material identification framework which localizes target material spectra along the manifold. Through experiments on real data, we show that the \ac{VAE} approach is better able to reject false alarms from materials with similar spectra when compared to established methods alone. We additionally develop a novel dynamical \ac{VAE} model for time series of air quality data. Using that model, we develop practical methods for computing forecast distributions using Monte Carlo integration. We evaluate forecast distributions against real air quality data and demonstrate the ability to predict temporal dynamics and forecast uncertainty. The primary contribution of this work is to develop practical solutions to challenging data analysis problems through the use of deep generative models.