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Divyat Mahajan

Doctorat - Université de Montréal
Superviseur⋅e principal⋅e

Publications

Evaluating Interventional Reasoning Capabilities of Large Language Models
Numerous decision-making tasks require estimating causal effects under interventions on different parts of a system. As practitioners consid… (voir plus)er using large language models (LLMs) to automate decisions, studying their causal reasoning capabilities becomes crucial. A recent line of work evaluates LLMs ability to retrieve commonsense causal facts, but these evaluations do not sufficiently assess how LLMs reason about interventions. Motivated by the role that interventions play in causal inference, in this paper, we conduct empirical analyses to evaluate whether LLMs can accurately update their knowledge of a data-generating process in response to an intervention. We create benchmarks that span diverse causal graphs (e.g., confounding, mediation) and variable types, and enable a study of intervention-based reasoning. These benchmarks allow us to isolate the ability of LLMs to accurately predict changes resulting from their ability to memorize facts or find other shortcuts. Our analysis on four LLMs highlights that while GPT- 4 models show promising accuracy at predicting the intervention effects, they remain sensitive to distracting factors in the prompts.
Empirical Analysis of Model Selection for Heterogeneous Causal Effect Estimation
Divyat Mahajan
Brady Neal
Vasilis Syrgkanis
Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation
Sébastien Lachapelle
Divyat Mahajan
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.
Interventional Causal Representation Learning
Kartik Ahuja
Divyat Mahajan
Yixin Wang
Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observa… (voir plus)tional data and structural assumptions (e.g., conditional independence) to identify the latent factors. However, interventional data is prevalent across applications. Can interventional data facilitate causal representation learning? We explore this question in this paper. The key observation is that interventional data often carries geometric signatures of the latent factors' support (i.e. what values each latent can possibly take). For example, when the latent factors are causally connected, interventions can break the dependency between the intervened latents' support and their ancestors'. Leveraging this fact, we prove that the latent causal factors can be identified up to permutation and scaling given data from perfect
Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning
Sébastien Lachapelle
Tristan Deleu
Divyat Mahajan
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.
Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning
Sébastien Lachapelle
Tristan Deleu
Divyat Mahajan
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.
Towards efficient representation identification in supervised learning
Kartik Ahuja
Divyat Mahajan
Vasilis Syrgkanis
Humans have a remarkable ability to disentangle complex sensory inputs (e.g., image, text) into simple factors of variation (e.g., shape, co… (voir plus)lor) without much supervision. This ability has inspired many works that attempt to solve the following question: how do we invert the data generation process to extract those factors with minimal or no supervision? Several works in the literature on non-linear independent component analysis have established this negative result; without some knowledge of the data generation process or appropriate inductive biases, it is impossible to perform this inversion. In recent years, a lot of progress has been made on disentanglement under structural assumptions, e.g., when we have access to auxiliary information that makes the factors of variation conditionally independent. However, existing work requires a lot of auxiliary information, e.g., in supervised classification, it prescribes that the number of label classes should be at least equal to the total dimension of all factors of variation. In this work, we depart from these assumptions and ask: a) How can we get disentanglement when the auxiliary information does not provide conditional independence over the factors of variation? b) Can we reduce the amount of auxiliary information required for disentanglement? For a class of models where auxiliary information does not ensure conditional independence, we show theoretically and experimentally that disentanglement (to a large extent) is possible even when the auxiliary information dimension is much less than the dimension of the true latent representation.
Empirical Analysis of Model Selection for Heterogenous Causal Effect Estimation
Divyat Mahajan
Brady Neal
Vasilis Syrgkanis
We study the problem of model selection in causal inference, specifically for the case of conditional average treatment effect (CATE) estima… (voir plus)tion under binary treatments. Unlike model selection in machine learning, there is no perfect analogue of cross-validation as we do not observe the counterfactual potential outcome for any data point. Towards this, there have been a variety of proxy metrics proposed in the literature, that depend on auxiliary nuisance models estimated from the observed data (propensity score model, outcome regression model). However, the effectiveness of these metrics has only been studied on synthetic datasets as we can access the counterfactual data for them. We conduct an extensive empirical analysis to judge the performance of these metrics introduced in the literature, and novel ones introduced in this work, where we utilize the latest advances in generative modeling to incorporate multiple realistic datasets. Our analysis suggests novel model selection strategies based on careful hyperparameter tuning of CATE estimators and causal ensembling.