Treatment Effect

In this paper, we discuss feature engineering for single-pass uncertainty estimation. For accurate uncertainty estimates, neural networks must extract differences in the feature space that quantify uncertainty. This could be achieved by current single-pass approaches that maintain feature distances between data points as they traverse the network. While initial results are promising, maintaining feature distances within the network representations frequently inhibits information compression and opposes the learning objective. We study this effect theoretically and empirically to arrive at a simple conclusion: preserving feature distances in the output is beneficial when the preserved features contribute to learning the label distribution and act in opposition otherwise. We then propose Transitional Uncertainty with Layered Intermediate Predictions (TULIP) as a simple approach to address the shortcomings of current single-pass estimators. Specifically, we implement feature preservation by extracting features from intermediate representations before information is collapsed by subsequent layers. We refer to the underlying preservation mechanism as transitional feature preservation. We show that TULIP matches or outperforms current single-pass methods on standard benchmarks and in practical settings where these methods are less reliable (imbalances, complex architectures, medical modalities).

In this work, we analyze both theoretically and empirically the effect of tied input-output embeddings—a popular technique that reduces the model size while often improving training. Interestingly, we found that this technique is connected to Harris (1954)’s distributional hypothesis—often portrayed by the famous Firth (1957)’s quote “a word is characterized by the company it keeps”. Specifically, our findings indicate that words (or, more broadly, symbols) with similar semantics tend to be encoded in similar input embeddings, while words that appear in similar contexts are encoded in similar output embeddings (thus explaining the semantic space arising in input and output embedding of foundational language models). As a consequence of these findings, the tying of the input and output embeddings is encouraged only when the distributional hypothesis holds for the underlying data. These results also provide insight into the embeddings of foundation language models (which are known to be semantically organized). Further, we complement the theoretical findings with several experiments supporting the claims.

One of the significant challenges in treatment effect estimation is collider bias, a specific form of sample selection bias induced by the common causes of both the treatment and outcome. Identifying treatment effects under collider bias requires well-defined shadow variables in observational data, which are assumed to be related to the outcome and independent of the sample selection mechanism, conditional on the other observed variables. However, finding a valid shadow variable is not an easy task in real-world scenarios and requires domain-specific knowledge from experts. Therefore, in this paper, we propose a novel method that can automatically learn shadow-variable representations from observational data without prior knowledge. To ensure the learned representations satisfy the assumptions of the shadow variable, we introduce a tester to perform hypothesis testing in the representation learning process. We iteratively generate representations and test whether they satisfy the shadow-variable assumptions until they pass the test. With the help of the learned shadow-variable representations, we propose a novel treatment effect estimator to address collider bias. Experiments show that the proposed methods outperform existing treatment effect estimation methods under collider bias and prove their potential application value.

In the rapidly changing healthcare landscape, the implementation of offline reinforcement learning (RL) in dynamic treatment regimes (DTRs) presents a mix of unprecedented opportunities and challenges. This position paper offers a critical examination of the current status of offline RL in the context of DTRs. We argue for a reassessment of applying RL in DTRs, citing concerns such as inconsistent and potentially inconclusive evaluation metrics, the absence of naive and supervised learning baselines, and the diverse choice of RL formulation in existing research. Through a case study with more than 17,000 evaluation experiments using a publicly available Sepsis dataset, we demonstrate that the performance of RL algorithms can significantly vary with changes in evaluation metrics and Markov Decision Process (MDP) formulations. Surprisingly, it is observed that in some instances, RL algorithms can be surpassed by random baselines subjected to policy evaluation methods and reward design. This calls for more careful policy evaluation and algorithm development in future DTR works. Additionally, we discussed potential enhancements toward more reliable development of RL-based dynamic treatment regimes and invited further discussion within the community. Code is available at https://github.com/GilesLuo/ReassessDTR.

Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(sd / nm\varepsilon^2)$. This can be challenging for high-dimensional data, where the dimension $d$ is extremely large. In this work, we investigate user-level locally differentially private sparse linear regression. We show that with $n$ users each contributing $m$ samples, the linear dependency of dimension $d$ can be eliminated, yielding an error upper bound of $\mathcal{O}(s/ nm\varepsilon^2)$. We propose a framework that first selects candidate variables and then conducts estimation in the narrowed low-dimensional space, which is extendable to general sparse estimation problems with tight error bounds. Experiments on both synthetic and real datasets demonstrate the superiority of the proposed methods. Both the theoretical and empirical results suggest that, with the same number of samples, locally private sparse estimation is better conducted when multiple samples per user are available.

Estimating the conditional average treatment effect (CATE) from observational data is relevant for many applications such as personalized medicine. Here, we focus on the widespread setting where the observational data come from multiple environments, such as different hospitals, physicians, or countries. Furthermore, we allow for violations of standard causal assumptions, namely, overlap within the environments and unconfoundedness. To this end, we move away from point identification and focus on partial identification. Specifically, we show that current assumptions from the literature on multiple environments allow us to interpret the environment as an instrumental variable (IV). This allows us to adapt bounds from the IV literature for partial identification of CATE by leveraging treatment assignment mechanisms across environments. Then, we propose different model-agnostic learners (so-called meta-learners) to estimate the bounds that can be used in combination with arbitrary machine learning models. We further demonstrate the effectiveness of our meta-learners across various experiments using both simulated and real-world data. Finally, we discuss the applicability of our meta-learners to partial identification in instrumental variable settings, such as randomized controlled trials with non-compliance.

Deep neural networks (DNNs) have become pivotal in machine learning, but the impact of weight precision, such as in networks with rectified linear units (ReLU), remains underexplored. We analytically investigate the interplay of three key factors: the precision of ReLU network weights, the number of neurons, and the time of the preprocessing algorithm that generates the network description. Our study, which, to the best of our knowledge, is the first formal work on weight precision, yields three main results. (1) We present an exponential time preprocessing algorithm that showcases the possibility of trading ReLU nodes for weight precision. Specifically, our method achieves an exponential reduction in neuron count when computing any function of high complexity with boolean input encoding. What is the implication of the above result in theoretical and practical works? (2) In theory of computing, in general, there is no free lunch. In our case, if you significantly reduce the number of neurons then you should pay the cost in weight precision. To address this, we introduce a notion of network size that considers weight precision in addition to the network's number of neurons. We establish that under this redefined notion of network size, it is generally impossible to exchange neurons for weight precision in ReLU networks of the same (redefined) size. (3) In practice, we show that high weight precision alone cannot help in reducing the neuron count. If instead of our exponential time preprocessing algorithm one uses any polynomial time algorithm, then it is impossible to non-trivially reduce the neuron count, regardless of the high weight precision.

Given a dataset of individuals each described by a covariate vector, a treatment, and an observed outcome on the treatment, the goal of the individual treatment effect (ITE) estimation task is to predict outcome changes resulting from a change in treatment. A fundamental challenge is that in the observational data, a covariate’s outcome is observed only under one treatment, whereas we need to infer the difference in outcomes under two different treatments. Several existing approaches address this issue through training with inferred pseudo-outcomes, but their success relies on the quality of these pseudo-outcomes. We propose PairNet, a novel ITE estimation training strategy that minimizes losses over pairs of examples based on their factual observed outcomes. Theoretical analysis for binary treatments reveals that PairNet is a consistent estimator of ITE risk, and achieves smaller generalization error than baseline models. Empirical comparison with thirteen existing methods across eight benchmarks, covering both discrete and continuous treatments, shows that PairNet achieves significantly lower ITE error compared to the baselines. Also, it is model-agnostic and easy to implement.

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.

Resulting from non-random sample selection caused by both the treatment and outcome, collider bias poses a unique challenge to treatment effect estimation using observational data whose distribution differs from that of the target population. In this paper, we rethink collider bias from an out-of-distribution (OOD) perspective, considering that the entire data space of the target population consists of two different environments: The observational data selected from the target population belongs to a seen environment labeled with $S=1$ and the missing unselected data belongs to another unseen environment labeled with $S=0$. Based on this OOD formulation, we utilize small-scale representative data from the entire data space with no environmental labels and propose a novel method, i.e., Coupled Counterfactual Generative Adversarial Model (C$^2$GAM), to simultaneously generate the missing $S=0$ samples in observational data and the missing $S$ labels in the small-scale representative data. With the help of C$^2$GAM, collider bias can be addressed by combining the generated $S=0$ samples and the observational data to estimate treatment effects. Extensive experiments on synthetic and real-world data demonstrate that plugging C$^2$GAM into existing treatment effect estimators achieves significant performance improvements.

Motivated by practical applications in clinical trials and online platforms, we study A/B testing with the aim of estimating a confidence interval (CI) for the average treatment effect (ATE) using the minimum expected sample size. This CI should have a width at most $\epsilon$ while ensuring that the probability of the CI not containing the true ATE is at most $\delta$. To answer this, we first establish a lower bound on the expected sample size needed for any adaptive policy which constructs a CI of ATE with desired properties. Specifically, we prove that the lower bound is based on the solution to a max-min non-convex optimization problem for small $\delta$. Tailoring the ``plug-in'' approach for the ATE problem, we construct an adaptive policy that is asymptotically optimal, i.e., matches the lower bound on the expected sample size for small $\delta$. Interestingly, we find that, for small $\epsilon$ and $\delta$, the asymptotically optimal fraction of treatment assignment for A and B is proportional to the standard deviation of the outcome distributions of treatments A and B, respectively. However, as the proposed approach can be computationally intensive, we propose an alternative adaptive policy. This new policy, informed by insights from our lower bound analysis, is computationally efficient while remaining asymptotically optimal for small values of $\epsilon$ and $\delta$. Numerical comparisons demonstrate that both policies perform similarly across practical values of $\epsilon$ and $\delta$, offering efficient solutions for A/B testing.

In many real-world causal inference applications, the primary outcomes (labels) are often partially missing, especially if they are expensive or difficult to collect. If the missingness depends on covariates (i.e., missingness is not completely at random), analyses based on fully observed samples alone may be biased. Incorporating surrogates, which are fully observed post-treatment variables related to the primary outcome, can improve estimation in this case. In this paper, we study the role of surrogates in estimating continuous treatment effects and propose a doubly robust method to efficiently incorporate surrogates in the analysis, which uses both labeled and unlabeled data and does not suffer from the above selection bias problem. Importantly, we establish the asymptotic normality of the proposed estimator and show possible improvements on the variance compared with methods that solely use labeled data. Extensive simulations show our methods enjoy appealing empirical performance.

How would randomly shuffling feature vectors among nodes from the same class affect graph neural networks (GNNs)? The feature shuffle, intuitively, perturbs the dependence between graph topology and features (A-X dependence) for GNNs to learn from. Surprisingly, we observe a consistent and significant improvement in GNN performance following the feature shuffle. Having overlooked the impact of A-X dependence on GNNs, the prior literature does not provide a satisfactory understanding of the phenomenon. Thus, we raise two research questions. First, how should A-X dependence be measured, while controlling for potential confounds? Second, how does A-X dependence affect GNNs? In response, we (i) propose a principled measure for A-X dependence, (ii) design a random graph model that controls A-X dependence, (iii) establish a theory on how A-X dependence relates to graph convolution, and (iv) present empirical analysis on real-world graphs that align with the theory. We conclude that A-X dependence mediates the effect of graph convolution, such that smaller dependence improves GNN-based node classification.

Estimating high-dimensional covariance matrices is crucial in various domains. This work considers a scenario where two collaborating agents access disjoint dimensions of $m$ samples from a high--dimensional random vector, and they can only communicate a limited number of bits to a central server, which wants to accurately approximate the covariance matrix. We analyze the fundamental trade--off between communication cost, number of samples, and estimation accuracy. We prove a lower bound on the error achievable by any estimator, highlighting the impact of dimensions, number of samples, and communication budget. Furthermore, we present an algorithm that achieves this lower bound up to a logarithmic factor, demonstrating its near-optimality in practical settings.

Recently, interest has grown in the use of proxy variables of unobserved confounding for inferring the causal effect in the presence of unmeasured confounders from observational data. One difficulty inhibiting the practical use is finding valid proxy variables of unobserved confounding to a target causal effect of interest. These proxy variables are typically justified by background knowledge. In this paper, we investigate the estimation of causal effects among multiple treatments and a single outcome, all of which are affected by unmeasured confounders, within a linear causal model, without prior knowledge of the validity of proxy variables. To be more specific, we first extend the existing proxy variable estimator, originally addressing a single unmeasured confounder, to accommodate scenarios where multiple unmeasured confounders exist between the treatments and the outcome. Subsequently, we present two different sets of precise identifiability conditions for selecting valid proxy variables of unmeasured confounders, based on the second-order statistics and higher-order statistics of the data, respectively. Moreover, we propose two data-driven methods for the selection of proxy variables and for the unbiased estimation of causal effects. Theoretical analysis demonstrates the correctness of our proposed algorithms. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach.

Many methods for estimating conditional average treatment effects (CATEs) can be expressed as weighted pseudo-outcome regressions (PORs). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. For example, we point out that R-Learning implicitly performs a POR with inverse-variance weights (IVWs). In the CATE setting, IVWs mitigate the instability associated with inverse-propensity weights, and lead to convenient simplifications of bias terms. We demonstrate the superior performance of IVWs in simulations, and derive convergence rates for IVWs that are, to our knowledge, the fastest yet shown without assuming knowledge of the covariate distribution.

We propose a novel regression adjustment method designed for estimating distributional treatment effect parameters in randomized experiments. Randomized experiments have been extensively used to estimate treatment effects in various scientific fields. However, to gain deeper insights, it is essential to estimate distributional treatment effects rather than relying solely on average effects. Our approach incorporates pre-treatment covariates into a distributional regression framework, utilizing machine learning techniques to improve the precision of distributional treatment effect estimators. The proposed approach can be readily implemented with off-the-shelf machine learning methods and remains valid as long as the nuisance components are reasonably well estimated. Also, we establish the asymptotic properties of the proposed estimator and present a uniformly valid inference method. Through simulation results and real data analysis, we demonstrate the effectiveness of integrating machine learning techniques in reducing the variance of distributional treatment effect estimators in finite samples.

We develop two density ratio estimation (DRE) methods with robustness to outliers. These are based on the divergence with a weight function to weaken the adverse effects of outliers. One is based on the Unnormalized Kullback-Leibler divergence, called Weighted DRE, and its optimization is a convex problem. The other is based on the γ-divergence, called γ-DRE, which improves a normalizing term problem of Weighted DRE. Its optimization is a DC (Difference of Convex functions) problem and needs more computation than a convex problem. These methods have doubly strong robustness, which means robustness to the heavy contamination of both the reference and target distributions. Numerical experiments show that our proposals are more robust than the previous methods.

We study the problem of private vector mean estimation in the shuffle model of privacy where $n$ users each have a unit vector $v^{(i)} \in \mathbb{R}^d$. We propose a new multi-message protocol that achieves the optimal error using $O(\min(n\varepsilon^2,d))$ messages per user. Moreover, we show that any (unbiased) protocol that achieves optimal error must require each user to send $\Omega(\min(n\varepsilon^2,d)/\log(n))$ messages, demonstrating the optimality of our message complexity up to logarithmic factors. Additionally, we study the single-message setting and design a protocol that achieves mean squared error $O(dn^{d/(d+2)}\varepsilon^{-4/(d+2)})$. Moreover, we show that *any* single-message protocol must incur mean squared error $\Omega(dn^{d/(d+2)})$, showing that our protocol is optimal in the standard setting where $\varepsilon = \Theta(1)$. Finally, we study robustness to malicious users and show that malicious users can incur large additive error with a single shuffler.

Semiparametric statistics play a pivotal role in a wide range of domains, including but not limited to missing data, causal inference, and transfer learning, to name a few. In many settings, semiparametric theory leads to (nearly) statistically optimal procedures that yet involve numerically solving Fredholm integral equations of the second kind. Traditional numerical methods, such as polynomial or spline approximations, are difficult to scale to multi-dimensional problems. Alternatively, statisticians may choose to approximate the original integral equations by ones with closed-form solutions, resulting in computationally more efficient, but statistically suboptimal or even incorrect procedures. To bridge this gap, we propose a novel framework by formulating the semiparametric estimation problem as a bi-level optimization problem; and then we propose a scalable algorithm called **D**eep **N**eural-Nets **A**ssisted **S**emiparametric **E**stimation ($\mathsf{DNA\mbox{-}SE}$) by leveraging the universal approximation property of Deep Neural-Nets (DNN) to streamline semiparametric procedures. Through extensive numerical experiments and a real data analysis, we demonstrate the numerical and statistical advantages of $\mathsf{DNA\mbox{-}SE}$ over traditional methods. To the best of our knowledge, we are the first to bring DNN into semiparametric statistics as a numerical solver of integral equations in our proposed general framework.