William Trouleau | EPFL Graph Search

After doing both a Bachelor and Master in Communication Systems at EPFL, I had the opportunity of working as an intern in the AI research lab of Technicolor in Los Altos, CA. The lab focuses on developing new analytics solutions in the areas of Human Behavior Modeling, Internet-Of-Things and wearable devices. I worked there for 9 months in 2014-2015 and developed a new generative mixture model to characterize the behavior of viewers on video-on-demand systems. Our approach enabled the predicting of future user actions (such as number of views and stopping time). This work lead to the publication "Just One More: Modeling Binge Watching Behavior" published in the 22nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) in August 2016.

Working in such a stimulating environment motivated me to continue my academic research. Therefore, I started my PhD at EPFL in September 2015. I received the EDIC Fellowship for my first year, and I am advised by Pr. Patrick Thiran and Pr. Matthias Grossglauser . My research revolves around the statistical and algorithmic aspects of learning causality structure from high-dimensional time series; with applications on epidemiology, public health, and information diffusion.

A Variational Inference Approach to Learning Multivariate Wold Processes

Seyed Jalal Etesami, Matthias Grossglauser, Negar Kiyavash, Patrick Thiran, William Trouleau

Temporal point-processes are often used for mathematical modeling of sequences of discrete events with asynchronous timestamps. We focus on a class of temporal point-process models called multivariate Wold processes (MWP). These processes are well suited to model real-world communication dynamics. Statistical inference on such processes often requires learning their corresponding parameters using a set of observed timestamps. In this work, we relax some of the restrictive modeling assumptions made in the state-of-the-art and introduce a Bayesian approach for inferring the parameters of MWP. We develop a computationally efficient variational inference algorithm that allows scaling up the approach to high-dimensional processes and long sequences of observations. Our experimental results on both synthetic and real-world datasets show that our proposed algorithm outperforms existing methods.

PMLR2021

Learning Self-Exciting Temporal Point Processes Under Noisy Observations

William Trouleau

Understanding the diffusion patterns of sequences of interdependent events is a central question for a variety of disciplines. Temporal point processes are a class of elegant and powerful models of such sequences; these processes have become popular across multiple fields of research due to the increasing availability of data that captures the occurrence of events over time. A notable example is the Hawkes process. It was originally introduced by Alan Hawkes in 1971 to model the diffusion of earthquakes and was subsequently applied across fields such as epidemiology, neuroscience, criminology, finance, genomic, and social-network analysis.A central question in these fields is the inverse problem of uncovering the diffusion patterns of the events from the observed data. The methods for solving this inverse problem assume that, in general, the data is noiseless. However, real-world observations are frequently tainted by noise in a number of ways. Most existing methods are not robust against noise and, in the presence of even a small amount of noise in the data, they might completely fail to recover the underlying dynamics. In this thesis, we remedy this shortcoming and address this problem for several types of observational noise.First, we study the effects of small event-streams that are known to make the learning task challenging by amplifying the risk of overfitting. Using recent advances in variational inference, we introduce a new algorithm that leads to better regularization schemes and provides a measure of uncertainty on the estimated parameters.Second, we consider events corrupted by unknown synchronized time delays. We show that the so-called synchronization noise introduces a bias in the existing estimation methods, which must be handled with care. We provide an algorithm to robustly learn the diffusion dynamics of the underlying process under this class of synchronized delays.Third, we introduce a wider class of random and unknown time shifts, referred to as random translations, of which synchronization noise is a special case. We derive the statistical properties of Hawkes processes subject to random translations. In particular, we prove that the cumulants of Hawkes processes are invariant to random translations and we show that cumulant-based algorithms can be used to learn their underlying causal structure even when unknown time shifts distort the observations.Finally, we consider another class of temporal point processes, the so-called Wold process that solves a computational limitation of the Bayesian treatment of Hawkes processes while retaining similar properties. We address the problem of learning the parameters of a Wold process by relaxing some of the restrictive assumptions made in the state of the art and by introducing a Bayesian approach for inferring its parameters.In summary, the results presented in this dissertation highlight the shortcomings of standard inference methods used to fit temporal point processes. Consequently, these results deepen our ability to extract reliable insights from networks of interdependent event streams.

EPFL2021

Quantifying the Effects of Contact Tracing, Testing, and Containment Measures in the Presence of Infection Hotspots

William Trouleau

Multiple lines of evidence at the individual and population level strongly suggest that infection hotspots, or superspreading events, where a single individual infects many others, play a key role in the transmission dynamics of COVID-19. However, most of the existing epidemiological models either assume or result in a Poisson distribution of the number of infections caused by a single infectious individual, often called secondary infections. As a result, these models overlook the observed overdispersion in the number of secondary infections and are unable to accurately characterize infection hotspots. In this work, we aim to fill this gap by introducing a temporal point process framework that explicitly represents sites where infection hotspots may occur. Under our model, overdispersion on the number of secondary infections emerges naturally. Moreover, using an efficient sampling algorithm, we demonstrate how to apply Bayesian optimization with longitudinal case data to estimate the transmission rate of infectious individuals at sites they visit and in their households, as well as the mobility reduction due to social distancing. Simulations using fine-grained demographic data and site locations from several cities and regions demonstrate that our framework faithfully characterizes the observed longitudinal trend of COVID-19 cases. In addition, the simulations show that our model can be used to estimate the effect of testing, contact tracing, and containment at an unprecedented spatiotemporal resolution, and reveal that these measures do not decrease overdispersion in the number of secondary infections.

2020

Learning Self-Exciting Temporal Point Processes Under Noisy Observations

William Trouleau

EPFL2021