Researchers often face data fusion problems, where multiple data sources are available, each capturing a distinct subset of variables. While problem formulations typically take the data as given, in practice, data acquisition can be an ongoing process. In this paper, we aim to estimate any functional of a probabilistic model (e.g., a causal effect) as efficiently as possible, by deciding, at each time, which data source to query. We propose online moment selection (OMS), a framework in which structural assumptions are encoded as moment conditions. The optimal action at each step depends, in part, on the very moments that identify the functional of interest. Our algorithms balance exploration with choosing the best action as suggested by current estimates of the moments. We propose two selection strategies: (1) explore-then-commit (OMS-ETC) and (2) explore-then-greedy (OMS-ETG), proving that both achieve zero asymptotic regret as assessed by MSE. We instantiate our setup for average treatment effect estimation, where structural assumptions are given by a causal graph and data sources may include subsets of mediators, confounders, and instrumental variables.
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We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
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.
Counterfactual explanations are usually generated through heuristics that are sensitive to the search's initial conditions. The absence of guarantees of performance and robustness hinders trustworthiness. In this paper, we take a disciplined approach towards counterfactual explanations for tree ensembles. We advocate for a model-based search aiming at "optimal" explanations and propose efficient mixed-integer programming approaches. We show that isolation forests can be modeled within our framework to focus the search on plausible explanations with a low outlier score. We provide comprehensive coverage of additional constraints that model important objectives, heterogeneous data types, structural constraints on the feature space, along with resource and actionability restrictions. Our experimental analyses demonstrate that the proposed search approach requires a computational effort that is orders of magnitude smaller than previous mathematical programming algorithms. It scales up to large data sets and tree ensembles, where it provides, within seconds, systematic explanations grounded on well-defined models solved to optimality.
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.
Training datasets for machine learning often have some form of missingness. For example, to learn a model for deciding whom to give a loan, the available training data includes individuals who were given a loan in the past, but not those who were not. This missingness, if ignored, nullifies any fairness guarantee of the training procedure when the model is deployed. Using causal graphs, we characterize the missingness mechanisms in different real-world scenarios. We show conditions under which various distributions, used in popular fairness algorithms, can or can not be recovered from the training data. Our theoretical results imply that many of these algorithms can not guarantee fairness in practice. Modeling missingness also helps to identify correct design principles for fair algorithms. For example, in multi-stage settings where decisions are made in multiple screening rounds, we use our framework to derive the minimal distributions required to design a fair algorithm. Our proposed algorithm decentralizes the decision-making process and still achieves similar performance to the optimal algorithm that requires centralization and non-recoverable distributions.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
Modern online advertising systems inevitably rely on personalization methods, such as click-through rate (CTR) prediction. Recent progress in CTR prediction enjoys the rich representation capabilities of deep learning and achieves great success in large-scale industrial applications. However, these methods can suffer from lack of exploration. Another line of prior work addresses the exploration-exploitation trade-off problem with contextual bandit methods, which are less studied in the industry recently due to the difficulty in extending their flexibility with deep models. In this paper, we propose a novel Deep Uncertainty-Aware Learning (DUAL) method to learn deep CTR models based on Gaussian processes, which can provide efficient uncertainty estimations along with the CTR predictions while maintaining the flexibility of deep neural networks. By linking the ability to estimate predictive uncertainties of DUAL to well-known bandit algorithms, we further present DUAL-based Ad-ranking strategies to boost up long-term utilities such as the social welfare in advertising systems. Experimental results on several public datasets demonstrate the effectiveness of our methods. Remarkably, an online A/B test deployed in the Alibaba display advertising platform shows an $8.2\%$ social welfare improvement and an $8.0\%$ revenue lift.
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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