Tristan Deleu

Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes

Jithendaraa Subramanian

Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that defin… (voir plus)e the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.

2022-11-04

ArXiv (prépublication)

doi.org

arxiv.org

Learning Latent Structural Causal Models

Jithendaraa Subramanian

Yashas Annadani

Ivaxi Sheth

Nan Rosemary Ke

Tristan Deleu

Stefan Bauer

Derek Nowrouzezahrai

Samira Ebrahimi Kahou

Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better e… (voir plus)xplanations of out-of-distribution data. Prior works on causal learning assume that the high-level causal variables are given. However, in machine learning tasks, one often operates on low-level data like image pixels or high-dimensional vectors. In such settings, the entire Structural Causal Model (SCM) -- structure, parameters, \textit{and} high-level causal variables -- is unobserved and needs to be learnt from low-level data. We treat this problem as Bayesian inference of the latent SCM, given low-level data. For linear Gaussian additive noise SCMs, we present a tractable approximate inference method which performs joint inference over the causal variables, structure and parameters of the latent SCM from random, known interventions. Experiments are performed on synthetic datasets and a causally generated image dataset to demonstrate the efficacy of our approach. We also perform image generation from unseen interventions, thereby verifying out of distribution generalization for the proposed causal model.

2022-10-24

ArXiv (prépublication)

doi.org

openreview.net

Bayesian Structure Learning with Generative Flow Networks

In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian ne… (voir plus)tworks, from data. Defining such a distribution is very challenging, due to the combinatorially large sample space, and approximations based on MCMC are often required. Recently, a novel class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling of discrete and composite objects, such as graphs. In this work, we propose to use a GFlowNet as an alternative to MCMC for approximating the posterior distribution over the structure of Bayesian networks, given a dataset of observations. Generating a sample DAG from this approximate distribution is viewed as a sequential decision problem, where the graph is constructed one edge at a time, based on learned transition probabilities. Through evaluation on both simulated and real data, we show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs, and it compares favorably against other methods based on MCMC or variational inference.

2022-05-20

auai.org/UAI/2022/Conference (poster)

proceedings.mlr.press

openreview.net

Continuous-Time Meta-Learning with Forward Mode Differentiation

David Kanaa

Giancarlo Kerg

Drawing inspiration from gradient-based meta-learning methods with infinitely small gradient steps, we introduce Continuous-Time Meta-Learni… (voir plus)ng (COMLN), a meta-learning algorithm where adaptation follows the dynamics of a gradient vector field. Specifically, representations of the inputs are meta-learned such that a task-specific linear classifier is obtained as a solution of an ordinary differential equation (ODE). Treating the learning process as an ODE offers the notable advantage that the length of the trajectory is now continuous, as opposed to a fixed and discrete number of gradient steps. As a consequence, we can optimize the amount of adaptation necessary to solve a new task using stochastic gradient descent, in addition to learning the initial conditions as is standard practice in gradient-based meta-learning. Importantly, in order to compute the exact meta-gradients required for the outer-loop updates, we devise an efficient algorithm based on forward mode differentiation, whose memory requirements do not scale with the length of the learning trajectory, thus allowing longer adaptation in constant memory. We provide analytical guarantees for the stability of COMLN, we show empirically its efficiency in terms of runtime and memory usage, and we illustrate its effectiveness on a range of few-shot image classification problems.

2022-01-28

ICLR.cc/2022/Conference (spotlight)

doi.org

openreview.net

Boosting Exploration in Multi-Task Reinforcement Learning using Adversarial Networks

Ramnath Kumar

Tristan Deleu

Yoshua Bengio

2022-01-27

ArXiv (prépublication)

arxiv.org

Effect of diversity in Meta-Learning

Ramnath Kumar

Tristan Deleu

Yoshua Bengio

Few-shot learning aims to learn representations that can tackle novel tasks given a small number of examples. Recent studies show that task … (voir plus)distribution plays a vital role in the performance of the model. Conventional wisdom is that task diversity should improve the performance of meta-learning. In this work, we find evidence to the contrary; we study different task distributions on a myriad of models and datasets to evaluate the effect of task diversity on meta-learning algorithms. For this experiment, we train on two datasets - Omniglot and miniImageNet and with three broad classes of meta-learning models - Metric-based (i.e., Protonet, Matching Networks), Optimization-based (i.e., MAML, Reptile, and MetaOptNet), and Bayesian meta-learning models (i.e., CNAPs). Our experiments demonstrate that the effect of task diversity on all these algorithms follows a similar trend, and task diversity does not seem to offer any benefits to the learning of the model. Furthermore, we also demonstrate that even a handful of tasks, repeated over multiple batches, would be sufficient to achieve a performance similar to uniform sampling and draws into question the need for additional tasks to create better models.

2021-12-10

NeurIPS.cc/2021/Workshop/MetaLearn (poster)

GFlowNet Foundations

Edward J Hu

Mo Tiwari

2021-11-17

ArXiv (prépublication)

GFlowNet Foundations

Edward J Hu

Mo Tiwari

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, w… (voir plus)ith a training objective that makes them approximately sample in proportion to a given reward function. In this paper, we show a number of additional theoretical properties of GFlowNets. They can be used to estimate joint probability distributions and the corresponding marginal distributions where some variables are unspecified and, of particular interest, can represent distributions over composite objects like sets and graphs. GFlowNets amortize the work typically done by computationally expensive MCMC methods in a single but trained generative pass. They could also be used to estimate partition functions and free energies, conditional probabilities of supersets (supergraphs) given a subset (subgraph), as well as marginal distributions over all supersets (supergraphs) of a given set (graph). We introduce variations enabling the estimation of entropy and mutual information, sampling from a Pareto frontier, connections to reward-maximizing policies, and extensions to stochastic environments, continuous actions and modular energy functions.

2021-11-17

ArXiv (prépublication)

GFlowNet Foundations

Edward J Hu

Mo Tiwari

2021-11-17

ArXiv (prépublication)

GFlowNet Foundations

Edward J Hu

Mo Tiwari

2021-11-17

ArXiv (prépublication)

GFlowNet Foundations

Edward J Hu

Mo Tiwari

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, w… (voir plus)ith a training objective that makes them approximately sample in proportion to a given reward function. In this paper, we show a number of additional theoretical properties of GFlowNets. They can be used to estimate joint probability distributions and the corresponding marginal distributions where some variables are unspecified and, of particular interest, can represent distributions over composite objects like sets and graphs. GFlowNets amortize the work typically done by computationally expensive MCMC methods in a single but trained generative pass. They could also be used to estimate partition functions and free energies, conditional probabilities of supersets (supergraphs) given a subset (subgraph), as well as marginal distributions over all supersets (supergraphs) of a given set (graph). We introduce variations enabling the estimation of entropy and mutual information, sampling from a Pareto frontier, connections to reward-maximizing policies, and extensions to stochastic environments, continuous actions and modular energy functions.

2021-11-17

ArXiv (prépublication)

arxiv.org