处理效应

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.

Byzantine-robust distributed learning (BRDL), in which computing devices are likely to behave abnormally due to accidental failures or malicious attacks, has recently become a hot research topic. However, even in the independent and identically distributed (i.i.d.) case, existing BRDL methods will suffer a significant drop on model accuracy due to the large variance of stochastic gradients. Increasing batch sizes is a simple yet effective way to reduce the variance. However, when the total number of gradient computation is fixed, a too-large batch size will lead to a too-small iteration number (update number), which may also degrade the model accuracy. In view of this challenge, we mainly study the effect of batch size when the total number of gradient computation is fixed in this work. In particular, we show that when the total number of gradient computation is fixed, the optimal batch size corresponding to the tightest theoretical upper bound in BRDL increases with the fraction of Byzantine workers. Therefore, compared to the case without attacks, a larger batch size is preferred when under Byzantine attacks. Motivated by the theoretical finding, we propose a novel method called Byzantine-robust stochastic gradient descent with normalized momentum (ByzSGDnm) in order to further increase model accuracy in BRDL. We theoretically prove the convergence of ByzSGDnm for general non-convex cases under Byzantine attacks. Empirical results show that when under Byzantine attacks, compared to the cases of small batch sizes, setting a relatively large batch size can significantly increase the model accuracy, which is consistent with our theoretical results. Moreover, ByzSGDnm can achieve higher model accuracy than existing BRDL methods when under deliberately crafted attacks. In addition, we empirically show that increasing batch sizes has the bonus of training acceleration.

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse, but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations.

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting — and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based $U$-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics, including a conceptually new cause for progressive sharpening and the edge of stability. We further draw connections to related phenomena including grokking and simplicity bias. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong *Opposing Signals*: consistent, large magnitude features which dominate the network output and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We carefully study these groups' effect on the network's optimization and behavior, and we complement this with a theoretical analysis of a two-layer linear network under a simplified model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

Unobserved confounding is common in many applications, making causal inference from observational data challenging. As a remedy, causal sensitivity analysis is an important tool to draw causal conclusions under unobserved confounding with mathematical guarantees. In this paper, we propose NeuralCSA, a neural framework for generalized causal sensitivity analysis. Unlike previous work, our framework is compatible with (i) a large class of sensitivity models, including the marginal sensitivity model, $f$-sensitivity models, and Rosenbaum's sensitivity model; (ii) different treatment types (i.e., binary and continuous); and (iii) different causal queries, including (conditional) average treatment effects and simultaneous effects on multiple outcomes. This generality is achieved by learning a latent distribution shift that corresponds to a treatment intervention using two conditional normalizing flows. We provide theoretical guarantees that NeuralCSA is able to infer valid bounds on the causal query of interest and also demonstrate this empirically using both simulated and real-world data.

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic refutation framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATE is non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose a neural refutation framework which performs partial identification of CATE or, equivalently, aims at estimating lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our refutation framework is of direct relevance in practice where the validity of CATE estimation is of importance.

Proximal causal learning is a powerful framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatments can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments for proximal causal learning. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the influence function. Further, we propose a new approach to efficiently solve the nuisance functions. We then provide a comprehensive convergence analysis in terms of the mean square error. We demonstrate the utility of our estimator on synthetic datasets and real-world applications.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to $20\times \sim 5000\times$. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Estimating treatment effects has numerous real-world applications in various fields, such as epidemiology and political science. While much attention has been devoted to addressing the challenge using fully observational data, there has been comparatively limited exploration of this issue in cases when the treatment is not directly observed. In this paper, we tackle this problem by developing a general variational framework, which is flexible to integrate with advanced neural network-based approaches, to identify the average dose-response function (ADRF) with the continuously valued error-contaminated treatment. Our approach begins with the formulation of a probabilistic data generation model, treating the unobserved treatment as a latent variable. In this model, we leverage a learnable density estimation neural network to derive its prior distribution conditioned on covariates. This module also doubles as a generalized propensity score estimator, effectively mitigating selection bias arising from observed confounding variables. Subsequently, we calculate the posterior distribution of the treatment, taking into account the observed measurement and outcome. To mitigate the impact of treatment error, we introduce a re-parametrized treatment value, replacing the error-affected one, to make more accurate predictions regarding the outcome. To demonstrate the adaptability of our framework, we incorporate two state-of-the-art ADRF estimation methods and rigorously assess its efficacy through extensive simulations and experiments using semi-synthetic data.

Estimating individual treatment effects in clinical data is essential for understanding how different patients uniquely respond to treatments and identifying the most effective interventions for specific patient subgroups, thereby enhancing the precision and personalization of healthcare. However, counterfactual data are not accessible, and the true calculation of causal effects cannot be performed at the individual level. This paper proposes a linear algebraic framework to generate counterfactual longitudinal data that exactly matches pre-treatment factual data. Because causation travels forward in time, not in reverse, counterfactual predictability is further strengthened by blocking causal effects from flowing back to the past, thus limiting counterfactual dependence on the future. Using simulated LDL cholesterol datasets, we show that our method significantly outperforms the most cited methods of counterfactual generation. We also provide a formula that can estimate the time-varying variance of individual treatment effects, interpreted as a confidence level in the generated counterfactuals compared to true values.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates achieve SOTA performance and great robustness.

Selection bias in recommender system arises from the recommendation process of system filtering and the interactive process of user selection. Many previous studies have focused on addressing selection bias to achieve unbiased learning of the prediction model, but ignore the fact that potential outcomes for a given user-item pair may vary with the treatments assigned to other user-item pairs, named neighborhood effect. To fill the gap, this paper formally formulates the neighborhood effect as an interference problem from the perspective of causal inference, and introduces a treatment representation to capture the neighborhood effect. On this basis, we propose a novel ideal loss that can be used to deal with selection bias in the presence of neighborhood effect. We further develop two new estimators for estimating the proposed ideal loss. We theoretically establish the connection between the proposed and previous debiasing methods ignoring the neighborhood effect, showing that the proposed methods can achieve unbiased learning when both selection bias and neighborhood effects are present, while the existing methods are biased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed methods.

Decision-makers are often experts of their domain and take actions based on their domain knowledge. Doctors, for instance, may prescribe treatments by predicting the likely outcome of each available treatment. Actions of an expert thus naturally encode part of their domain knowledge, and can help make inferences within the same domain: Knowing doctors try to prescribe the best treatment for their patients, we can tell treatments prescribed more frequently are likely to be more effective. Yet in machine learning, the fact that most decision-makers are experts is often overlooked, and “expertise” is seldom leveraged as an inductive bias. This is especially true for the literature on treatment effect estimation, where often the only assumption made about actions is that of overlap. In this paper, we argue that expertise—particularly the type of expertise the decision-makers of a domain are likely to have—can be informative in designing and selecting methods for treatment effect estimation. We formally define two types of expertise, predictive and prognostic, and demonstrate empirically that: (i) the prominent type of expertise in a domain significantly influences the performance of different methods in treatment effect estimation, and (ii) it is possible to predict the type of expertise present in a dataset, which can provide a quantitative basis for model selection.