Divyat Mahajan

Kartik Ahuja, Divyat Mahajan, Yixin Wang et al.

Causal representation learning seeks to extract high-level latent factors from low-level sensory data. Most existing methods rely on observational 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 $do$ interventions. Moreover, we can achieve block affine identification, namely the estimated latent factors are only entangled with a few other latents if we have access to data from imperfect interventions. These results highlight the unique power of interventional data in causal representation learning; they can enable provable identification of latent factors without any assumptions about their distributions or dependency structure.

Sébastien Lachapelle, Tristan Deleu, Divyat Mahajan et al.

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding 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.

Sébastien Lachapelle, Divyat Mahajan, Ioannis Mitliagkas et al.

We tackle the problems of latent variables identification and ``out-of-support'' image generation in representation learning. We show that both 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.

Divyat Mahajan, Ioannis Mitliagkas, Brady Neal et al.

We study the problem of model selection in causal inference, specifically for conditional average treatment effect (CATE) estimation. Unlike machine learning, there is no perfect analogue of cross-validation for model selection as we do not observe the counterfactual potential outcomes. Towards this, a variety of surrogate metrics have been proposed for CATE model selection that use only observed data. However, we do not have a good understanding regarding their effectiveness due to limited comparisons in prior studies. We conduct an extensive empirical analysis to benchmark the surrogate model selection metrics introduced in the literature, as well as the novel ones introduced in this work. We ensure a fair comparison by tuning the hyperparameters associated with these metrics via AutoML, and provide more detailed trends by incorporating realistic datasets via generative modeling. Our analysis suggests novel model selection strategies based on careful hyperparameter selection of CATE estimators and causal ensembling.

Kartik Ahuja, Divyat Mahajan, Vasilis Syrgkanis et al.

Humans have a remarkable ability to disentangle complex sensory inputs (e.g., image, text) into simple factors of variation (e.g., shape, color) 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.

Divyat Mahajan, Chenhao Tan, Amit Sharma

To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work in counterfactual explanations by addressing the challenge of feasibility of such examples. For explanations of ML models in critical domains such as healthcare and finance, counterfactual examples are useful for an end-user only to the extent that perturbation of feature inputs is feasible in the real world. We formulate the problem of feasibility as preserving causal relationships among input features and present a method that uses (partial) structural causal models to generate actionable counterfactuals. When feasibility constraints cannot be easily expressed, we consider an alternative mechanism where people can label generated CF examples on feasibility: whether it is feasible to intervene and realize the candidate CF example from the original input. To learn from this labelled feasibility data, we propose a modified variational auto encoder loss for generating CF examples that optimizes for feasibility as people interact with its output. Our experiments on Bayesian networks and the widely used ''Adult-Income'' dataset show that our proposed methods can generate counterfactual explanations that better satisfy feasibility constraints than existing methods.. Code repository can be accessed here: \textit{https://github.com/divyat09/cf-feasibility}

Varun Khare, Divyat Mahajan, Homanga Bharadhwaj et al.

We present a domain adaptation based generative framework for zero-shot learning. Our framework addresses the problem of domain shift between the seen and unseen class distributions in zero-shot learning and minimizes the shift by developing a generative model trained via adversarial domain adaptation. Our approach is based on end-to-end learning of the class distributions of seen classes and unseen classes. To enable the model to learn the class distributions of unseen classes, we parameterize these class distributions in terms of the class attribute information (which is available for both seen and unseen classes). This provides a very simple way to learn the class distribution of any unseen class, given only its class attribute information, and no labeled training data. Training this model with adversarial domain adaptation further provides robustness against the distribution mismatch between the data from seen and unseen classes. Our approach also provides a novel way for training neural net based classifiers to overcome the hubness problem in zero-shot learning. Through a comprehensive set of experiments, we show that our model yields superior accuracies as compared to various state-of-the-art zero shot learning models, on a variety of benchmark datasets. Code for the experiments is available at github.com/vkkhare/ZSL-ADA

Tejas Kasetty, Divyat Mahajan, Gintare Karolina Dziugaite et al.

Numerous decision-making tasks require estimating causal effects under interventions on different parts of a system. As practitioners consider 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. We evaluate six LLMs on the benchmarks, finding that GPT models show promising accuracy at predicting the intervention effects.

Oscar Clivio, Divyat Mahajan, Perouz Taslakian et al.

Integrating expert knowledge, e.g. from large language models, into causal discovery algorithms can be challenging when the knowledge is not guaranteed to be correct. Expert recommendations may contradict data-driven results, and their reliability can vary significantly depending on the domain or specific query. Existing methods based on soft constraints or inconsistencies in predicted causal relationships fail to account for these variations in expertise. To remedy this, we propose L2D-CD, a method for gauging the correctness of expert recommendations and optimally combining them with data-driven causal discovery results. By adapting learning-to-defer (L2D) algorithms for pairwise causal discovery (CD), we learn a deferral function that selects whether to rely on classical causal discovery methods using numerical data or expert recommendations based on textual meta-data. We evaluate L2D-CD on the canonical Tübingen pairs dataset and demonstrate its superior performance compared to both the causal discovery method and the expert used in isolation. Moreover, our approach identifies domains where the expert's performance is strong or weak. Finally, we outline a strategy for generalizing this approach to causal discovery on graphs with more than two variables, paving the way for further research in this area.

Divyat Mahajan, Shruti Tople, Amit Sharma

With the goal of generalizing to out-of-distribution (OOD) data, recent domain generalization methods aim to learn "stable" feature representations whose effect on the output remains invariant across domains. Given the theoretical connection between generalization and privacy, we ask whether better OOD generalization leads to better privacy for machine learning models, where privacy is measured through robustness to membership inference (MI) attacks. In general, we find that the relationship does not hold. Through extensive evaluation on a synthetic dataset and image datasets like MNIST, Fashion-MNIST, and Chest X-rays, we show that a lower OOD generalization gap does not imply better robustness to MI attacks. Instead, privacy benefits are based on the extent to which a model captures the stable features. A model that captures stable features is more robust to MI attacks than models that exhibit better OOD generalization but do not learn stable features. Further, for the same provable differential privacy guarantees, a model that learns stable features provides higher utility as compared to others. Our results offer the first extensive empirical study connecting stable features and privacy, and also have a takeaway for the domain generalization community; MI attack can be used as a complementary metric to measure model quality.

Yanbo Xu, Divyat Mahajan, Liz Manrao et al.

For many kinds of interventions, such as a new advertisement, marketing intervention, or feature recommendation, it is important to target a specific subset of people for maximizing its benefits at minimum cost or potential harm. However, a key challenge is that no data is available about the effect of such a prospective intervention since it has not been deployed yet. In this work, we propose a split-treatment analysis that ranks the individuals most likely to be positively affected by a prospective intervention using past observational data. Unlike standard causal inference methods, the split-treatment method does not need any observations of the target treatments themselves. Instead it relies on observations of a proxy treatment that is caused by the target treatment. Under reasonable assumptions, we show that the ranking of heterogeneous causal effect based on the proxy treatment is the same as the ranking based on the target treatment's effect. In the absence of any interventional data for cross-validation, Split-Treatment uses sensitivity analyses for unobserved confounding to select model parameters. We apply Split-Treatment to both a simulated data and a large-scale, real-world targeting task and validate our discovered rankings via a randomized experiment for the latter.

Divyat Mahajan, Shruti Tople, Amit Sharma

In the domain generalization literature, a common objective is to learn representations independent of the domain after conditioning on the class label. We show that this objective is not sufficient: there exist counter-examples where a model fails to generalize to unseen domains even after satisfying class-conditional domain invariance. We formalize this observation through a structural causal model and show the importance of modeling within-class variations for generalization. Specifically, classes contain objects that characterize specific causal features, and domains can be interpreted as interventions on these objects that change non-causal features. We highlight an alternative condition: inputs across domains should have the same representation if they are derived from the same object. Based on this objective, we propose matching-based algorithms when base objects are observed (e.g., through data augmentation) and approximate the objective when objects are not observed (MatchDG). Our simple matching-based algorithms are competitive to prior work on out-of-domain accuracy for rotated MNIST, Fashion-MNIST, PACS, and Chest-Xray datasets. Our method MatchDG also recovers ground-truth object matches: on MNIST and Fashion-MNIST, top-10 matches from MatchDG have over 50% overlap with ground-truth matches.