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Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a $\varphi$-divergence to an empirical distribution. However, the use of $\varphi$-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an algorithm that exploits the latent-space representation of data points fed into the network, to assess the accuracy of their prediction. Using the latent-space representation generated by the fraction of training set that the network classifies correctly, we build a statistical model that is able to capture the likelihood of a given prediction. We show on a synthetic dataset that commonly used methods are mostly overconfident. Overconfidence occurs also for predictions made on data points that are outside the distribution that generated the training data. In contrast, our method can detect such out-of-distribution data points as inaccurately predicted, thus aiding in the automatic detection of outliers.

Evaluating the utility of synthetic data is critical for measuring the effectiveness and efficiency of synthetic algorithms. Existing results focus on empirical evaluations of the utility of synthetic data, whereas the theoretical understanding of how utility is affected by synthetic data algorithms remains largely unexplored. This paper establishes utility theory from a statistical perspective, aiming to quantitatively assess the utility of synthetic algorithms based on a general metric. The metric is defined as the absolute difference in generalization between models trained on synthetic and original datasets. We establish analytical bounds for this utility metric to investigate critical conditions for the metric to converge. An intriguing result is that the synthetic feature distribution is not necessarily identical to the original one for the convergence of the utility metric as long as the model specification in downstream learning tasks is correct. Another important utility metric is model comparison based on synthetic data. Specifically, we establish sufficient conditions for synthetic data algorithms so that the ranking of generalization performances of models trained on the synthetic data is consistent with that from the original data. Finally, we conduct extensive experiments using non-parametric models and deep neural networks to validate our theoretical findings.

During the past few years, mediation analysis has gained increasing popularity across various research fields. The primary objective of mediation analysis is to examine the direct impact of exposure on outcome, as well as the indirect effects that occur along the pathways from exposure to outcome. There has been a great number of articles that applied mediation analysis to data from hundreds or thousands of individuals. With the rapid development of technology, the volume of avaliable data increases exponentially, which brings new challenges to researchers. Directly conducting statistical analysis for large datasets is often computationally infeasible. Nonetheless, there is a paucity of findings regarding mediation analysis in the context of big data. In this paper, we propose utilizing subsampled double bootstrap and divide-and-conquer algorithms to conduct statistical mediation analysis on large-scale datasets. The proposed algorithms offer a significant enhancement in computational efficiency over traditional bootstrap confidence interval and Sobel test, while simultaneously ensuring desirable confidence interval coverage and power. We conducted extensive numerical simulations to evaluate the performance of our method. The practical applicability of our approach is demonstrated through two real-world data examples.

With the growing availability of large-scale biomedical data, it is often time-consuming or infeasible to directly perform traditional statistical analysis with relatively limited computing resources at hand. We propose a fast subsampling method to effectively approximate the full data maximum partial likelihood estimator in Cox's model, which largely reduces the computational burden when analyzing massive survival data. We establish consistency and asymptotic normality of a general subsample-based estimator. The optimal subsampling probabilities with explicit expressions are determined via minimizing the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator. We propose a two-step subsampling algorithm for practical implementation, which has a significant reduction in computing time compared to the full data method. The asymptotic properties of the resulting two-step subsample-based estimator is also established. Extensive numerical experiments and a real-world example are provided to assess our subsampling strategy.

An approach to parameter optimization for the low-rank matrix recovery method in hyperspectral imaging is discussed. We formulate an optimization problem with respect to the initial parameters of the low-rank matrix recovery method. The performance for different parameter settings is compared in terms of computational times and memory. The results are evaluated by computing the peak signal-to-noise ratio as a quantitative measure. The potential improvement of the performance of the noise reduction method is discussed when optimizing the choice of the initial values. The optimization method is tested on standard and openly available hyperspectral data sets including Indian Pines, Pavia Centre, and Pavia University.

We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no smoothness properties, thus emphasizing the far-reaching regularizing nature of entropy penalization. To derive these results, we employ a novel technique that sidesteps the intricacies linked to empirical process theory and the control of suprema of function classes determined by the cost. Instead, we perform a careful linearization analysis for entropic optimal transport with respect to an empirical $L^2$-norm, which enables a streamlined analysis. As a consequence, our work gives rise to new implications for a multitude of transport-based applications under general costs, including pointwise distributional limits for the empirical entropic optimal transport map estimator, kernel methods as well as regularized colocalization curves. Overall, our research lays the foundation for an expanded framework of statistical inference with empirical entropic optimal transport.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.

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.

The era of big data provides researchers with convenient access to copious data. However, people often have little knowledge about it. The increasing prevalence of big data is challenging the traditional methods of learning causality because they are developed for the cases with limited amount of data and solid prior causal knowledge. This survey aims to close the gap between big data and learning causality with a comprehensive and structured review of traditional and frontier methods and a discussion about some open problems of learning causality. We begin with preliminaries of learning causality. Then we categorize and revisit methods of learning causality for the typical problems and data types. After that, we discuss the connections between learning causality and machine learning. At the end, some open problems are presented to show the great potential of learning causality with data.