Deep learning · causal inference

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) $G^*$ while minimizing the number of interventions made. In our setting, we are additionally given side information about $G^*$ as advice, e.g. a DAG $G$ purported to be $G^*$. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on _algorithms with predictions_. When the advice is a DAG $G$, we design an adaptive search algorithm to recover $G^*$ whose intervention cost is at most $\mathcal{O}(\max\{1, \log \psi\})$ times the cost for verifying $G^*$; here, $\psi$ is a distance measure between $G$ and $G^*$ that is upper bounded by the number of variables $n$, and is exactly 0 when $G=G^*$. Our approximation factor matches the state-of-the-art for the advice-less setting.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. We ensure invariance in the next-step prediction across such inputs, by employing a self-supervised objective derived by our observation, formalised in a causal graph. We prove that the resulting method, which we call Hint-ReLIC, improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3x improvements on the OOD test data.

Estimating heterogeneous treatment effects from observational data is a crucial task across many fields, helping policy and decision-makers take better actions. There has been recent progress on robust and efficient methods for estimating the conditional average treatment effect (CATE) function, but these methods often do not take into account the risk of hidden confounding, which could arbitrarily and unknowingly bias any causal estimate based on observational data. We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on the level of hidden confounding. We derive the B-Learner by adapting recent results for sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into the framework given by Kallus & Oprescu (2023) for robust and model-agnostic learning of conditional distributional treatment effects. The B-Learner can use any function estimator such as random forests and deep neural networks, and we prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods. Semi-synthetic experimental comparisons validate the theoretical findings, and we use real-world data demonstrate how the method might be used in practice.

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding'" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.

With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet, existing association-based approaches on rationalization cannot identify true rationales when two or more snippets are highly inter-correlated and thus provide a similar contribution to prediction accuracy, so-called spuriousness. To address this limitation, we novelly leverage two causal desiderata, non-spuriousness and efficiency, into rationalization from the causal inference perspective. We formally define a series of probabilities of causation based on a newly proposed structural causal model of rationalization, with its theoretical identification established as the main component of learning necessary and sufficient rationales. The superior performance of the proposed causal rationalization is demonstrated on real-world review and medical datasets with extensive experiments compared to state-of-the-art methods.

We consider the problem of computing bounds for causal queries on quasi-Markovian graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use multilinear programming (MP) formulations that are often intractable for existing solvers when the degree of the polynomial objective is greater than two. Hence, one often has to resort to either fast approximate heuristics which are not guaranteed to contain the true query value, or more accurate but computationally intensive procedures. We show how to construct an equivalent MP with a polynomial objective of lower degree. In particular, the degree of the objective in the new MP is equal to only the number of C-components that are intervened upon, instead of the total number of C-components. As a result, we can compute exact bounds for significantly larger causal inference problems as compared to what is possible using existing techniques. We also propose a very efficient Frank-Wolfe heuristic that produces very high quality bounds, and scales to large multilinear problems of higher degree.

Collaborative causal inference (CCI) aims to improve the estimation of the causal effect of treatment variables by utilizing data aggregated from multiple self-interested parties. Since their source data are valuable proprietary assets that can be costly or tedious to obtain, every party has to be incentivized to be willing to contribute to the collaboration, such as with a guaranteed fair and sufficiently valuable reward (than performing causal inference on its own). This paper presents a reward scheme designed using the unique statistical properties that are required by causal inference to guarantee certain desirable incentive criteria (e.g., fairness, benefit) for the parties based on their contributions. To achieve this, we propose a data valuation function to value parties' data for CCI based on the distributional closeness of its resulting treatment effect estimate to that utilizing the aggregated data from all parties. Then, we show how to value the parties' rewards fairly based on a modified variant of the Shapley value arising from our proposed data valuation for CCI. Finally, the Shapley fair rewards to the parties are realized in the form of improved, stochastically perturbed treatment effect estimates. We empirically demonstrate the effectiveness of our reward scheme using simulated and real-world datasets.

The geometric structure of data is an important inductive bias in machine learning. In this work, we characterize the data manifolds entailed by structural causal models. The strengths of the proposed framework are twofold: firstly, the geometric structure of the data manifolds is causally informed, and secondly, it enables causal reasoning about the data manifolds in an interventional and a counterfactual sense. We showcase the versatility of the proposed framework by applying it to the generation of causally-grounded counterfactual explanations for machine learning classifiers, measuring distances along the data manifold in a differential geometric-principled manner.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot do. How do upstream factors such as data, model prediction, hyperparameters, and random initialization influence downstream explanations? While previous work raised concerns that explanations (E) may have little relationship with the prediction (Y), there is a lack of conclusive study to quantify this relationship. Our work borrows tools from causal inference to systematically assay this relationship. More specifically, we study the relationship between E and Y by measuring the treatment effect when intervening on their causal ancestors, i.e., on hyperparameters and inputs used to generate saliency-based Es or Ys. Our results suggest that the relationships between E and Y is far from ideal. In fact, the gap between 'ideal' case only increase in higher-performing models --- models that are likely to be deployed. Our work is a promising first step towards providing a quantitative measure of the relationship between E and Y, which could also inform the future development of methods for E with a quantitative metric.

In meta reinforcement learning (meta RL), an agent seeks a Bayes-optimal policy -- the optimal policy when facing an unknown task that is sampled from some known task distribution. Previous approaches tackled this problem by inferring a $\textit{belief}$ over task parameters, using variational inference methods. Motivated by recent successes of contrastive learning approaches in RL, such as contrastive predictive coding (CPC), we investigate whether contrastive methods can be used for learning Bayes-optimal behavior. We begin by proving that representations learned by CPC are indeed sufficient for Bayes optimality. Based on this observation, we propose a simple meta RL algorithm that uses CPC in lieu of variational belief inference. Our method, $\textit{ContraBAR}$, achieves comparable performance to state-of-the-art in domains with state-based observation and circumvents the computational toll of future observation reconstruction, enabling learning in domains with image-based observations. It can also be combined with image augmentations for domain randomization and used seamlessly in both online and offline meta RL settings.

Causal effect identification is a fundamental task in artificial intelligence. A most ideal scenario for causal effect identification is that there is a directed acyclic graph as a prior causal graph encoding the causal relations of all relevant variables. In real tasks, however, the prior causal graph is usually not available, and some relevant variables may be latent as well. With observational data, we can only learn a partial ancestral graph (PAG), which contains some indeterminate causal relations. Since many causal graphs can correspond to one PAG, they are possibly associated with different causal effects. The aim of this paper is to estimate these possible causal effects via covariate adjustment given a PAG. This task is challenging because the number of causal graphs corresponding to a PAG grows super-exponentially with the number of variables. We propose a new graphical characterization for possible adjustment sets, and based on this, we develop the first method to determine the set of possible causal effects that are consistent with the given PAG without enumerating any causal graphs. Our method can output the same set as the enumeration method with super-exponentially less complexity. Experiments validate the effectiveness and tremendous efficiency improvement of the proposed method.

Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the Kullback-Leibler (KL) divergence to $\pi$ over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when $\pi$ is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when $\pi$ is only log-smooth.

Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate predictions, but they generally still lack precise statistical guarantees unless they are further calibrated using independent hold-out data. This paper addresses the above limitation with conformalized early stopping: a novel method that combines early stopping with conformal calibration while efficiently recycling the same hold-out data. This leads to models that are both accurate and able to provide exact predictive inferences without multiple data splits nor overly conservative adjustments. Practical implementations are developed for different learning tasks---outlier detection, multi-class classification, regression---and their competitive performance is demonstrated on real data.

In this paper, we propose a novel framework, Active Learning based Structural Inference (ALaSI), to infer the existence of directed connections from observed agents' states over a time period in a dynamical system. With the help of deep active learning, ALaSI is competent in learning the representation of connections with a relatively small pool of prior knowledge. Moreover, based on information theory, the proposed inter- and out-of-scope message learning pipelines are remarkably beneficial to structural inference for large dynamical systems. We evaluate ALaSI on various large datasets including simulated systems and real-world networks, to demonstrate that ALaSI is able to outperform previous methods in precisely inferring the existence of connections in large systems under either supervised learning or unsupervised learning.