Sébastien Lachapelle

2024-01-10

ArXiv (prépublication)

doi.org

Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation

Sébastien Lachapelle

Divyat Mahajan

Ioannis Mitliagkas

We tackle the problems of latent variables identification and "out-of-support'' image generation in representation learning. We show that bo… (voir plus)th are possible for a class of decoders that we call additive, which are reminiscent of decoders used for object-centric representation learning (OCRL) and well suited for images that can be decomposed as a sum of object-specific images. We provide conditions under which exactly solving the reconstruction problem using an additive decoder is guaranteed to identify the blocks of latent variables up to permutation and block-wise invertible transformations. This guarantee relies only on very weak assumptions about the distribution of the latent factors, which might present statistical dependencies and have an almost arbitrarily shaped support. Our result provides a new setting where nonlinear independent component analysis (ICA) is possible and adds to our theoretical understanding of OCRL methods. We also show theoretically that additive decoders can generate novel images by recombining observed factors of variations in novel ways, an ability we refer to as Cartesian-product extrapolation. We show empirically that additivity is crucial for both identifiability and extrapolation on simulated data.

Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning

Sébastien Lachapelle

Tristan Deleu

Divyat Mahajan

Ioannis Mitliagkas

Yoshua Bengio

Quentin Bertrand

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding … (voir plus)is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.

2023-01-01

ICML (publié)

Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning

Sébastien Lachapelle

Tristan Deleu

Divyat Mahajan

Ioannis Mitliagkas

Yoshua Bengio

Quentin Bertrand

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding … (voir plus)is limited. In this work, we provide evidence that disentangled representations coupled with sparse task-specific predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.

2023-01-01

ICML (publié)

proceedings.mlr.press

Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA

Sébastien Lachapelle

Pau Rodriguez

Yash Sharma

Katie E Everett

Rémi LE PRIOL

Alexandre Lacoste

This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, which can be applied when the latent f… (voir plus)actors of interest depend sparsely on past latent factors and/or observed auxiliary variables. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that relates them. We develop a rigorous identifiability theory, building on recent nonlinear independent component analysis (ICA) results, that formalizes this principle and shows how the latent variables can be recovered up to permutation if one regularizes the latent mechanisms to be sparse and if some graph connectivity criterion is satisfied by the data generating process. As a special case of our framework, we show how one can leverage unknown-target interventions on the latent factors to disentangle them, thereby drawing further connections between ICA and causality. We propose a VAE-based method in which the latent mechanisms are learned and regularized via binary masks, and validate our theory by showing it learns disentangled representations in simulations.

2022-01-01

CLeaR (publié)

proceedings.mlr.press

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

Eric Larsen

Sébastien Lachapelle

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a method… (voir plus)ology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming, where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second-stage problem, conditionally on the first-stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second-stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training data set consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

2022-01-01

INFORMS Journal on Computing (publié)

doi.org

Differentiable Causal Discovery from Interventional Data

Philippe Brouillard

Sébastien Lachapelle

Alexandre Lacoste

Alexandre Drouin

Discovering causal relationships in data is a challenging task that involves solving a combinatorial problem for which the solution is not a… (voir plus)lways identifiable. A new line of work reformulates the combinatorial problem as a continuous constrained optimization one, enabling the use of different powerful optimization techniques. However, methods based on this idea do not yet make use of interventional data, which can significantly alleviate identifiability issues. In this work, we propose a neural network-based method for this task that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.

G RADIENT -B ASED N EURAL DAG L EARNING WITH I NTERVENTIONS

Philippe Brouillard

Alexandre Drouin

Sébastien Lachapelle

Alexandre Lacoste

Decision making based on statistical association alone can be a dangerous endeavor due to non-causal associations. Ideally, one would rely o… (voir plus)n causal relationships that enable reasoning about the effect of interventions. Several methods have been proposed to discover such relationships from observational and inter-ventional data. Among them, GraN-DAG, a method that relies on the constrained optimization of neural networks, was shown to produce state-of-the-art results among algorithms relying purely on observational data. However, it is limited to observational data and cannot make use of interventions. In this work, we extend GraN-DAG to support interventional data and show that this improves its ability to infer causal structures

2020-01-01

(publié)

www.semanticscholar.org

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

Eric P. Larsen

Sébastien Lachapelle

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a method… (voir plus)ology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming, where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second-stage problem, conditionally on the first-stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second-stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training data set consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

2018-07-31

ArXiv (preprint)

doi.org