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Comparing two samples of data, we observe a change in the distribution of an outcome variable. In the presence of multiple explanatory variables, how much of the change can be explained by each possible cause? We develop a new estimation strategy that, given a causal model, combines regression and re-weighting methods to quantify the contribution of each causal mechanism. Our proposed methodology is multiply robust, meaning that it still recovers the target parameter under partial misspecification. We prove that our estimator is consistent and asymptotically normal. Moreover, it can be incorporated into existing frameworks for causal attribution, such as Shapley values, which will inherit the consistency and large-sample distribution properties. Our method demonstrates excellent performance in Monte Carlo simulations, and we show its usefulness in an empirical application. Our method is implemented as part of the Python library ``DoWhy`` (Sharma & Kiciman, 2020; Blöbaum et al., 2022).

Causal dynamics learning has recently emerged as a promising approach to enhancing robustness in reinforcement learning (RL). Typically, the goal is to build a dynamics model that makes predictions based on the causal relationships among the entities. Despite the fact that causal connections often manifest only under certain contexts, existing approaches overlook such fine-grained relationships and lack a detailed understanding of the dynamics. In this work, we propose a novel dynamics model that infers fine-grained causal structures and employs them for prediction, leading to improved robustness in RL. The key idea is to jointly learn the dynamics model with a discrete latent variable that quantizes the state-action space into subgroups. This leads to recognizing meaningful context that displays sparse dependencies, where causal structures are learned for each subgroup throughout the training. Experimental results demonstrate the robustness of our method to unseen states and locally spurious correlations in downstream tasks where fine-grained causal reasoning is crucial. We further illustrate the effectiveness of our subgroup-based approach with quantization in discovering fine-grained causal relationships compared to prior methods.

We study inference on the long-term causal effect of a continual exposure to a novel intervention, which we term a long-term treatment, based on an experiment involving only short-term observations. Key examples include the long-term health effects of regularly-taken medicine or of environmental hazards and the long-term effects on users of changes to an online platform. This stands in contrast to short-term treatments or "shocks," whose long-term effect can reasonably be mediated by short-term observations, enabling the use of surrogate methods. Long-term treatments by definition have direct effects on long-term outcomes via continual exposure, so surrogacy conditions cannot reasonably hold. We connect the problem with offline reinforcement learning, leveraging doubly-robust estimators to estimate long-term causal effects for long-term treatments and construct confidence intervals.

The incredible success of transformers on sequence modeling tasks can be largely attributed to the self-attention mechanism, which allows information to be transferred between different parts of a sequence. Self-attention allows transformers to encode causal structure which makes them particularly suitable for sequence modeling. However, the process by which transformers learn such causal structure via gradient-based training algorithms remains poorly understood. To better understand this process, we introduce an in-context learning task that requires learning latent causal structure. We prove that gradient descent on a simplified two-layer transformer learns to solve this task by encoding the latent causal graph in the first attention layer. The key insight of our proof is that the gradient of the attention matrix encodes the mutual information between tokens. As a consequence of the data processing inequality, the largest entries of this gradient correspond to edges in the latent causal graph. As a special case, when the sequences are generated from in-context Markov chains, we prove that transformers learn an induction head (Olsson et al., 2022). We confirm our theoretical findings by showing that transformers trained on our in-context learning task are able to recover a wide variety of causal structures.

Partial identification (PI) presents a significant challenge in causal inference due to the incomplete measurement of confounders. Given that obtaining auxiliary variables of confounders is not always feasible and relies on untestable assumptions, researchers are encouraged to explore the internal information of latent confounders without external assistance. However, these prevailing PI results often lack precise mathematical measurement from observational data or assume that the information pertaining to confounders falls within extreme scenarios. In our paper, we reassess the significance of the marginal confounder distribution in PI. We refrain from imposing additional restrictions on the marginal confounder distribution, such as entropy or mutual information. Instead, we establish the closed-form tight PI for any possible P(U) in the discrete case. Furthermore, we establish the if and only if criterion for discerning whether the marginal confounder information leads to non-vanilla PI regions. This reveals a fundamental negative result wherein the marginal confounder information minimally contributes to PI as the confounder’s cardinality increases. Our theoretical findings are supported by experiments.

This study introduces an innovative method for analyzing the impact of various interventions on customer churn, using the potential outcomes framework. We present a new causal model, the tensorized latent factor block hazard model, which incorporates tensor completion methods for a principled causal analysis of customer churn. A crucial element of our approach is the formulation of a 1-bit tensor completion for the parameter tensor. This captures hidden customer characteristics and temporal elements from churn records, effectively addressing the binary nature of churn data and its time-monotonic trends. Our model also uniquely categorizes interventions by their similar impacts, enhancing the precision and practicality of implementing customer retention strategies. For computational efficiency, we apply a projected gradient descent algorithm combined with spectral clustering. We lay down the theoretical groundwork for our model, including its non-asymptotic properties. The efficacy and superiority of our model are further validated through comprehensive experiments on both simulated and real-world applications.

In recent years, Reinforcement Learning (RL) has shown great promise in session-based recommendation. Sequential models that use RL have reached state-of-the-art performance for the Next-item Prediction (NIP) task. This result is intriguing, as the NIP task only evaluates how well the system can correctly recommend the next item to the user, while the goal of RL is to find a policy that optimizes rewards in the long term -- sometimes at the expense of suboptimal short-term performance. Then, how can RL improve the system's performance on short-term metrics? This article investigates this question by exploring proxy learning objectives, which we identify as goals RL models might be following, and thus could explain the performance boost. We found that RL -- when used as an auxiliary loss -- promotes the learning of embeddings that capture information about the user's previously interacted items. Subsequently, we replaced the RL objective with a straightforward auxiliary loss designed to predict the number of items the user interacted with. This substitution results in performance gains comparable to RL. These findings pave the way to improve performance and understanding of RL methods for recommender systems.

Due to the high cost of Image Quality Assessment (IQA) datasets, achieving robust generalization remains challenging for prevalent deep learning-based IQA methods. To address this, this paper proposes a novel end-to-end blind IQA method: Causal-IQA. Specifically, we first analyze the causal mechanisms in IQA tasks and construct a causal graph to understand the interplay and confounding effects between distortion types, image contents, and subjective human ratings. Then, through shifting the focus from correlations to causality, Causal-IQA aims to improve the estimation accuracy of image quality scores by mitigating the confounding effects using a causality-based optimization strategy. This optimization strategy is implemented on the sample subsets constructed by a Counterfactual Division process based on the Backdoor Criterion. Extensive experiments illustrate the superiority of Causal-IQA.

The question-answering (QA) capabilities of foundation models are highly sensitive to prompt variations, rendering their performance susceptible to superficial, non-meaning-altering changes. This vulnerability often stems from the model's preference or bias towards specific input characteristics, such as option position or superficial image features in multi-modal settings. We propose to rectify this bias directly in the model's internal representation. Our approach, SteerFair, finds the bias direction in the model's representation space and steers activation values away from it during inference. Specifically, we exploit the observation that bias often adheres to simple association rules, such as the spurious association between the first option and correctness likelihood. Next, we construct demonstrations of these rules from unlabeled samples and use them to identify the bias directions. We empirically show that SteerFair significantly reduces instruction-tuned model performance variance across prompt modifications on three benchmark tasks. Remarkably, our approach surpasses a supervised baseline with 100 labels by an average of 10.86% accuracy points and 12.95 score points and matches the performance with 500 labels.

Causal models and methods have great promise, but their progress has been stalled. Proposals using causality get squeezed between two opposing worldviews. Scientific perfectionism--an insistence on only using ``correct'' models--slows the adoption of causal methods in knowledge generating applications. Pushing in the opposite direction, the academic discipline of computer science prefers algorithms with no or few assumptions, and technologies based on automation and scalability are often selected for economic and business applications. We argue that these system-centric inductive biases should be replaced with a human-centric philosophy we refer to as scientific pragmatism. The machine learning community must strike the right balance to make space for the causal revolution to prosper.

Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same causal model, while in practice, data is heterogeneous and can stem from different causal models. In this work, we relax this assumption and perform causal discovery from time series data originating from *a mixture of causal models*. We propose a general variational inference-based framework called MCD to infer the underlying causal models as well as the mixing probability of each sample. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood. We present two variants: MCD-Linear for linear relationships and independent noise, and MCD-Nonlinear for nonlinear causal relationships and history-dependent noise. We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks through extensive experimentation on synthetic and real-world datasets, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions. Implementation is available at [https://github.com/Rose-STL-Lab/MCD](https://github.com/Rose-STL-Lab/MCD).

Foundation models have brought changes to the landscape of machine learning, demonstrating sparks of human-level intelligence across a diverse array of tasks. However, a gap persists in complex tasks such as causal inference, primarily due to challenges associated with intricate reasoning steps and high numerical precision requirements. In this work, we take a first step towards building causally-aware foundation models for treatment effect estimations. We propose a novel, theoretically justified method called Causal Inference with Attention (CInA), which utilizes multiple unlabeled datasets to perform self-supervised causal learning, and subsequently enables zero-shot causal inference on unseen tasks with new data. This is based on our theoretical results that demonstrate the primal-dual connection between optimal covariate balancing and self-attention, facilitating zero-shot causal inference through the final layer of a trained transformer-type architecture. We demonstrate empirically that CInA effectively generalizes to out-of-distribution datasets and various real-world datasets, matching or even surpassing traditional per-dataset methodologies. These results provide compelling evidence that our method has the potential to serve as a stepping stone for the development of causal foundation models.

We consider the effect of temporal aggregation on instantaneous (non-temporal) causal discovery in general setting. This is motivated by the observation that the true causal time lag is often considerably shorter than the observational interval. This discrepancy leads to high aggregation, causing time-delay causality to vanish and instantaneous dependence to manifest. Although we expect such instantaneous dependence has consistency with the true causal relation in certain sense to make the discovery results meaningful, it remains unclear what type of consistency we need and when will such consistency be satisfied. We proposed functional consistency and conditional independence consistency in formal way correspond functional causal model-based methods and conditional independence-based methods respectively and provide the conditions under which these consistencies will hold. We show theoretically and experimentally that causal discovery results may be seriously distorted by aggregation especially in complete nonlinear case and we also find causal relationship still recoverable from aggregated data if we have partial linearity or appropriate prior. Our findings suggest community should take a cautious and meticulous approach when interpreting causal discovery results from such data and show why and when aggregation will distort the performance of causal discovery methods.

Sound and complete algorithms have been proposed to compute identifiable causal queries using the causal structure and data. However, most of these algorithms assume accurate estimation of the data distribution, which is impractical for high-dimensional variables such as images. On the other hand, modern deep generative architectures can be trained to sample from high-dimensional distributions. However, training these networks are typically very costly. Thus, it is desirable to leverage pre-trained models to answer causal queries using such high-dimensional data. To address this, we propose modular training of deep causal generative models that not only makes learning more efficient, but also allows us to utilize large, pre-trained conditional generative models. To the best of our knowledge, our algorithm, Modular-DCM is the first algorithm that, given the causal structure, uses adversarial training to learn the network weights, and can make use of pre-trained models to provably sample from any identifiable causal query in the presence of latent confounders. With extensive experiments on the Colored-MNIST dataset, we demonstrate that our algorithm outperforms the baselines. We also show our algorithm's convergence on the COVIDx dataset and its utility with a causal invariant prediction problem on CelebA-HQ.

Recent advances in foundation models have led to a promising trend of developing large recommendation models to leverage vast amounts of available data. Still, mainstream models remain embarrassingly small in size and naive enlarging does not lead to sufficient performance gain, suggesting a deficiency in the model scalability. In this paper, we identify the embedding collapse phenomenon as the inhibition of scalability, wherein the embedding matrix tends to occupy a low-dimensional subspace. Through empirical and theoretical analysis, we demonstrate a two-sided effect of feature interaction specific to recommendation models. On the one hand, interacting with collapsed embeddings restricts embedding learning and exacerbates the collapse issue. On the other hand, interaction is crucial in mitigating the fitting of spurious features as a scalability guarantee. Based on our analysis, we propose a simple yet effective multi-embedding design incorporating embedding-set-specific interaction modules to learn embedding sets with large diversity and thus reduce collapse. Extensive experiments demonstrate that this proposed design provides consistent scalability and effective collapse mitigation for various recommendation models. Code is available at this repository: https://github.com/thuml/Multi-Embedding.

Latent confounding bias and collider bias are two key challenges of causal inference in observational studies. Latent confounding bias occurs when failing to control the unmeasured covariates that are common causes of treatments and outcomes, which can be addressed by using the Instrumental Variable (IV) approach. Collider bias comes from non-random sample selection caused by both treatments and outcomes, which can be addressed by using a different type of instruments, i.e., shadow variables. However, in most scenarios, these two biases simultaneously exist in observational data, and the previous methods focusing on either one are inadequate. To the best of our knowledge, no approach has been developed for causal inference when both biases exist. In this paper, we propose a novel IV approach, Two-Stage Shadow Inclusion (2SSI), which can simultaneously address latent confounding bias and collider bias by utilizing the residual of the treatment as a shadow variable. Extensive experimental results on benchmark synthetic datasets and a real-world dataset show that 2SSI achieves noticeable performance improvement when both biases exist compared to existing methods.

In real-world scenarios, the application of reinforcement learning is significantly challenged by complex non-stationarity. Most existing methods attempt to model changes in the environment explicitly, often requiring impractical prior knowledge of environments. In this paper, we propose a new perspective, positing that non-stationarity can propagate and accumulate through complex causal relationships during state transitions, thereby compounding its sophistication and affecting policy learning. We believe that this challenge can be more effectively addressed by implicitly tracing the causal origin of non-stationarity. To this end, we introduce the Causal-Origin REPresentation (COREP) algorithm. COREP primarily employs a guided updating mechanism to learn a stable graph representation for the state, termed as causal-origin representation. By leveraging this representation, the learned policy exhibits impressive resilience to non-stationarity. We supplement our approach with a theoretical analysis grounded in the causal interpretation for non-stationary reinforcement learning, advocating for the validity of the causal-origin representation. Experimental results further demonstrate the superior performance of COREP over existing methods in tackling non-stationarity problems. The code is available at https://github.com/PKU-RL/COREP.

In this work, we investigate the problem of adapting to the presence or absence of causal structure in multi-armed bandit problems. In addition to the usual reward signal, we assume the learner has access to additional variables, observed in each round after acting. When these variables $d$-separate the action from the reward, existing work in causal bandits demonstrates that one can achieve strictly better (minimax) rates of regret (Lu et al., 2020). Our goal is to adapt to this favorable ``conditionally benign'' structure, if it is present in the environment, while simultaneously recovering worst-case minimax regret, if it is not. Notably, the learner has no prior knowledge of whether the favorable structure holds. In this paper, we establish the Pareto optimal frontier of adaptive rates. We prove upper and matching lower bounds on the possible trade-offs in the performance of learning in conditionally benign and arbitrary environments, resolving an open question raised by Bilodeau et al. (2022). Furthermore, we are the first to obtain instance-dependent bounds for causal bandits, by reducing the problem to the linear bandit setting. Finally, we examine the common assumption that the marginal distributions of the post-action contexts are known and show that a nontrivial estimate is necessary for better-than-worst-case minimax rates.

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that provides such guarantees. By introducing a novel change-of-measure inequality, we are able to tightly bound the model loss in terms of the deviation of the treatment propensities over the population, which we show can be empirically limited. Our theory is fully rigorous and holds even in the face of hidden confounding and violations of positivity. We demonstrate our bounds on semi-synthetic and real data, showcasing their remarkable tightness and practical utility.

A topic of great current interest is Causal Representation Learning (CRL), whose goal is to learn a causal model for hidden features in a data-driven manner. Unfortunately, CRL is severely ill-posed since it is a combination of the two notoriously ill-posed problems of representation learning and causal discovery. Yet, finding practical identifiability conditions that guarantee a unique solution is crucial for its practical applicability. Most approaches so far have been based on assumptions on the latent causal mechanisms, such as temporal causality, or existence of supervision or interventions; these can be too restrictive in actual applications. Here, we show identifiability based on novel, weak constraints, which requires no temporal structure, intervention, nor weak supervision. The approach is based on assuming the observational mixing exhibits a suitable grouping of the observational variables. We also propose a novel self-supervised estimation framework consistent with the model, prove its statistical consistency, and experimentally show its superior CRL performances compared to the state-of-the-art baselines. We further demonstrate its robustness against latent confounders and causal cycles.