Dear all / Bonjour à tous,

We are happy to invite you to Tristan Deleu's PhD defense on December 18th, at 1 pm (hybrid).

Vous êtes cordialement invité.e.s à la soutenance de thèse de Tristan Deleu, le 18 décembre à 1 pm (hybrid).

Jury

Abstract

Discovering the structure of a causal model purely from data is plagued
with problems of identifiability. In general, without any assumptions about
data generation, multiple equivalent models may explain observations
equally well even if they could entail widely different causal conclusions.
As a consequence, choosing an arbitrary element among them could result in
unsafe decisions if it is not aligned with how the world truly works. It is
therefore imperative to maintain a notion of epistemic uncertainty about
our possible candidates to mitigate the risks posed by these misaligned
models, especially when the data is limited.
Taking a Bayesian perspective, this uncertainty can be captured through the
posterior distribution over models given data. As is the case with many
problems in Bayesian inference though, the posterior is typically
intractable due to the vast number of possible structures, represented as
directed acyclic graphs (DAGs). Hence, approximations are necessary.
Although there have been significant advances in generative modeling over
the past decade, spearheaded by the powerful combination of amortized
variational inference and deep learning, most of these models focus on
continuous spaces, making them unsuitable for problems involving discrete
objects like directed graphs, with highly complex acyclicity constraints.
In the first part of this thesis, we introduce generative flow networks
(GFlowNet), a novel class of probabilistic models specifically designed for
distributions over discrete and compositional objects such as graphs.
GFlowNets treat generation as a sequential decision making problem,
constructing samples piece by piece. These models describe distributions
defined up to a normalization constant by enforcing the conservation of
certain flows through a network. We will highlight how they are rooted in
various domains of machine learning and statistics, including variational
inference and reinforcement learning, and discuss extensions to general
spaces.
Then in the second part of this thesis, we demonstrate how GFlowNets can
approximate the posterior distribution over the DAG structures of Bayesian
networks given data. Beyond structure alone, we show that the parameters of
the conditional distributions can also be integrated in the posterior
approximated by the GFlowNet, allowing for flexible representations of
Bayesian networks.
*Keywords*: Generative flow networks, Bayesian inference, Structure
learning, Bayesian networks, Reinforcement learning, Variational inference.