William Trouleau

Related publications (8)

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

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Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization. Our approach is able to optimize over an extended set of hyper-parameters. It is also able to take into account the uncertainty in the model parameters by learning a posterior distribution over them. Experimental results on both synthetic and real datasets show that our approach significantly outperforms state-of-the-art methods under short observation sequences.

2019

Learning Hawkes Processes Under Synchronization Noise

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

Multivariate Hawkes processes (MHP) are widely used in a variety of fields to model the occurrence of discrete events. Prior work on learning MHPs has only focused on inference in the presence of perfect traces without noise. We address the problem of learning the causal structure of MHPs when observations are subject to an unknown delay. In particular, we introduce the so-called synchronization noise, where the stream of events generated by each dimension is subject to a random and unknown time shift. We characterize the robustness of the classic maximum likelihood estimator to synchronization noise, and we introduce a new approach for learning the causal structure in the presence of noise. Our experimental results show that our approach accurately recovers the causal structure of MHPs for a wide range of noise levels, and significantly outperforms classic estimation methods.

PMLR2019

Stochastic Optimal Control of Epidemic Processes in Networks

William Trouleau, Utkarsh Upadhyay

We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential equations (SDEs) with jumps. In contrast to previous work, this novel perspective is particularly well-suited to make use of fine-grained data about disease outbreaks and lets us overcome the shortcomings of current control strategies. Our control strategy resorts to treatment intensities to determine who to treat and when to do so to minimize the amount of infected individuals over time. Preliminary experiments with synthetic data show that our control strategy consistently outperforms several alternatives. Looking into the future, we believe our methodology provides a promising step towards the development of practical data-driven control strategies of epidemic processes.

2018

Easy accessibility can often lead to over-consumption, as seen in food and alcohol habits. On video on-demand (VOD) services, this has recently been referred to as binge watching, where potentially entire seasons of TV shows are consumed in a single viewing session. While a user viewership model may reveal this binging behavior, creating an accurate model has several challenges, including censored data, deviations in the population, and the need to consider external influences on consumption habits. In this paper, we introduce a novel statistical mixture model that incorporates these factors and presents a first of its kind characterization of viewer consumption behavior using a real-world dataset that includes playback data from a VOD service. From our modeling, we tackle various predictive tasks to infer the consumption decisions of a user in a viewing session, including estimating the number of episodes they watch and classifying if they continue watching another episode. Using these insights, we then identify binge watching sessions based on deviation from normal viewing behavior. We observe different types of binging behavior, that binge watchers often view certain content out-of-order, and that binge watching is not a consistent behavior among our users. These insights and our findings have application in VOD revenue generation, consumer health applications, and customer retention analysis.

ACM Press2016

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MLR Press