To form precipitation datasets that are accurate and, at the same time, have high spatial densities, data from satellites and gauges are often merged in the literature. However, uncertainty estimates for the data acquired in this manner are scarcely provided, although the importance of uncertainty quantification in predictive modelling is widely recognized. Furthermore, the benefits that machine learning can bring to the task of providing such estimates have not been broadly realized and properly explored through benchmark experiments. The present study aims at filling in this specific gap by conducting the first benchmark tests on the topic. On a large dataset that comprises 15-year-long monthly data spanning across the contiguous United States, we extensively compared six learners that are, by their construction, appropriate for predictive uncertainty quantification. These are the quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM) and quantile regression neural networks (QRNN). The comparison referred to the competence of the learners in issuing predictive quantiles at nine levels that facilitate a good approximation of the entire predictive probability distribution, and was primarily based on the quantile and continuous ranked probability skill scores. Three types of predictor variables (i.e., satellite precipitation variables, distances between a point of interest and satellite grid points, and elevation at a point of interest) were used in the comparison and were additionally compared with each other. This additional comparison was based on the explainable machine learning concept of feature importance. The results suggest that the order from the best to the worst of the learners for the task investigated is the following: LightGBM, QRF, GRF, GBM, QRNN and QR...

Compared to "black-box" models, like random forests and deep neural networks, explainable boosting machines (EBMs) are considered "glass-box" models that can be competitively accurate while also maintaining a higher degree of transparency and explainability. However, EBMs become readily less transparent and harder to interpret in high-dimensional settings with many predictor variables; they also become more difficult to use in production due to increases in scoring time. We propose a simple solution based on the least absolute shrinkage and selection operator (LASSO) that can help introduce sparsity by reweighting the individual model terms and removing the less relevant ones, thereby allowing these models to maintain their transparency and relatively fast scoring times in higher-dimensional settings. In short, post-processing a fitted EBM with many (i.e., possibly hundreds or thousands) of terms using the LASSO can help reduce the model's complexity and drastically improve scoring time. We illustrate the basic idea using two real-world examples with code.

We present a methodology for using unlabeled data to design semi supervised learning (SSL) methods that improve the prediction performance of supervised learning for regression tasks. The main idea is to design different mechanisms for integrating the unlabeled data, and include in each of them a mixing parameter $\alpha$, controlling the weight given to the unlabeled data. Focusing on Generalized Linear Models (GLM) and linear interpolators classes of models, we analyze the characteristics of different mixing mechanisms, and prove that in all cases, it is invariably beneficial to integrate the unlabeled data with some nonzero mixing ratio $\alpha>0$, in terms of predictive performance. Moreover, we provide a rigorous framework to estimate the best mixing ratio $\alpha^*$ where mixed SSL delivers the best predictive performance, while using the labeled and unlabeled data on hand. The effectiveness of our methodology in delivering substantial improvement compared to the standard supervised models, in a variety of settings, is demonstrated empirically through extensive simulation, in a manner that supports the theoretical analysis. We also demonstrate the applicability of our methodology (with some intuitive modifications) to improve more complex models, such as deep neural networks, in real-world regression tasks.

We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. Building on distributionally robust optimization and a regression approach, we propose to optimize the most adverse risk over a family of distributions within bounded Wasserstein distance or KL divergence to the empirical distribution. The worst-case risk accounts for the effect of outliers. The proposed approach applies for general categorical random variables without assuming faithfulness, an ordinal relationship or a specific form of conditional distribution. We present efficient algorithms and show the proposed methods are closely related to the standard regularized regression approach. Under mild assumptions, we derive non-asymptotic guarantees for successful structure learning with logarithmic sample complexities for bounded-degree graphs. Numerical study on synthetic and real datasets validates the effectiveness of our method. Code is available at https://github.com/DanielLeee/drslbn.

Early-exit neural networks (EENNs) facilitate adaptive inference by producing predictions at multiple stages of the forward pass. In safety-critical applications, these predictions are only meaningful when complemented with reliable uncertainty estimates. Yet, due to their sequential structure, an EENN's uncertainty estimates should also be consistent: labels that are deemed improbable at one exit should not reappear within the confidence interval / set of later exits. We show that standard uncertainty quantification techniques, like Bayesian methods or conformal prediction, can lead to inconsistency across exits. We address this problem by applying anytime-valid confidence sequences (AVCSs) to the exits of EENNs. By design, AVCSs maintain consistency across exits. We examine the theoretical and practical challenges of applying AVCSs to EENNs and empirically validate our approach on both regression and classification tasks.

The use of machine learning models in high-stake applications (e.g., healthcare, lending, college admission) has raised growing concerns due to potential biases against protected social groups. Various fairness notions and methods have been proposed to mitigate such biases. In this work, we focus on Counterfactual Fairness (CF), a fairness notion that is dependent on an underlying causal graph and first proposed by Kusner et al. [26]; it requires that the outcome an individual perceives is the same in the real world as it would be in a "counterfactual" world, in which the individual belongs to another social group. Learning fair models satisfying CF can be challenging. It was shown in [26] that a sufficient condition for satisfying CF is to not use features that are descendants of sensitive attributes in the causal graph. This implies a simple method that learns CF models only using non-descendants of sensitive attributes while eliminating all descendants. Although several subsequent works proposed methods that use all features for training CF models, there is no theoretical guarantee that they can satisfy CF. In contrast, this work proposes a new algorithm that trains models using all the available features.

Audience expansion is a methodology developed by ad-serving platforms to help advertisers find the best-matched audiences for their ads without looking into audience specifics. The rationale is that if you advertise to people who are similar to ones who already like the product or service you want to sell, chances are the conversion rate will be high. By leveraging this methodology advertisers can effortlessly reach their ideal leads by simply uploading a list of reference individuals, also known as a seed audience, to the platform. Then, the platform expands this seed to an audience of the desired size, typically resulting in a significant reduction in customer acquisition costs compared to other targeting strategies. From a machine learning perspective, a sound strategy for expanding a seed audience is by framing the problem as a binary classification task [Qu et al., 2014, Shen et al., 2015, Liu et al., 2016, Ma et al., 2016b,a]. Essentially, this involves creating a two-class labeled training set, consisting of seed users and non-seed users, and then training a probabilistic classifier, e.g., Logistic Regression [Jiang et al., 2019], to distinguish between the two classes. But instead of generating class predictions, the goal is to estimate the conditional probability that a given user belongs to the positive class. This probability is used to prioritize users for the expanded audience.

We consider the straggler problem in decentralized learning over a logical ring while preserving user data privacy. Especially, we extend the recently proposed framework of differential privacy (DP) amplification by decentralization by Cyffers and Bellet to include overall training latency--comprising both computation and communication latency. Analytical results on both the convergence speed and the DP level are derived for both a skipping scheme (which ignores the stragglers after a timeout) and a baseline scheme that waits for each node to finish before the training continues. A trade-off between overall training latency, accuracy, and privacy, parameterized by the timeout of the skipping scheme, is identified and empirically validated for logistic regression on a real-world dataset and for image classification using the MNIST and CIFAR-10 datasets.

Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to sampling or localized perturbations of data points is captured by Wasserstein DRO (WDRO), which seeks to learn a model that performs uniformly well over a Wasserstein ball centered around the observed data distribution. However, WDRO fails to account for non-geometric perturbations such as adversarial outliers, which can greatly distort the Wasserstein distance measurement and impede the learned model. We address this gap by proposing a novel outlier-robust WDRO framework for decision-making under both geometric (Wasserstein) perturbations and non-geometric (total variation (TV)) contamination that allows an $\varepsilon$-fraction of data to be arbitrarily corrupted. We design an uncertainty set using a certain robust Wasserstein ball that accounts for both perturbation types and derive minimax optimal excess risk bounds for this procedure that explicitly capture the Wasserstein and TV risks. We prove a strong duality result that enables tractable convex reformulations and efficient computation of our outlier-robust WDRO problem. When the loss function depends only on low-dimensional features of the data, we eliminate certain dimension dependencies from the risk bounds that are unavoidable in the general setting. Finally, we present experiments validating our theory on standard regression and classification tasks.

Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing provably valid confidence intervals for quantities such as means, quantiles, and linear and logistic regression coefficients, without making any assumptions on the machine-learning algorithm that supplies the predictions. Furthermore, more accurate predictions translate to smaller confidence intervals. Prediction-powered inference could enable researchers to draw valid and more data-efficient conclusions using machine learning. The benefits of prediction-powered inference are demonstrated with datasets from proteomics, astronomy, genomics, remote sensing, census analysis, and ecology.