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When genetic variants in a gene cluster are associated with a disease outcome, the causal pathway from the variants to the outcome can be difficult to disentangle. For example, the chemokine receptor gene cluster contains genetic variants associated with various cytokines. Associations between variants in this cluster and stroke risk may be driven by any of these cytokines. Multivariable Mendelian randomization is an extension of standard univariable Mendelian randomization to estimate the direct effects of related exposures with shared genetic predictors. However, when genetic variants are clustered, a Goldilocks dilemma arises: including too many highly-correlated variants in the analysis can lead to ill-conditioning, but pruning variants too aggressively can lead to imprecise estimates or even lack of identification. We propose multivariable methods that use principal component analysis to reduce many correlated genetic variants into a smaller number of orthogonal components that are used as instrumental variables. We show in simulations that these methods result in more precise estimates that are less sensitive to numerical instability due to both strong correlations and small changes in the input data. We apply the methods to demonstrate the most likely causal risk factor for stroke at the chemokine gene cluster is monocyte chemoattractant protein-1.

We address applied and computational issues for the problem of multiple treatment effect inference under many potential confounders. While there is abundant literature on the harmful effects of omitting relevant controls (under-selection), we show that over-selection can be comparably problematic, introducing substantial variance and a bias related to the non-random over-inclusion controls. We provide a novel empirical Bayes framework to mitigate both under-selection problems in standard high-dimensional methods and over-selection issues in recent proposals, by learning whether each control's inclusion should be encouraged or discouraged. We develop efficient gradient-based and Expectation-Propagation model-fitting algorithms to render the approach practical for a wide class of models. A motivating problem is to estimate the salary gap evolution in recent years in relation to potentially discriminatory characteristics such as gender, race, ethnicity and place of birth. We found that, albeit smaller, some wage differences remained for female and black individuals. A similar trend is observed when analyzing the joint contribution of these factors to deviations from the average salary. Our methodology also showed remarkable estimation robustness to the addition of spurious artificial controls, relative to existing proposals.

We consider two or more forecasters each making a sequence of predictions over time and tackle the problem of how to compare them -- either online or post-hoc. In fields ranging from meteorology to sports, forecasters make predictions on different events or quantities over time, and this work describes how to compare them in a statistically rigorous manner. Specifically, we design a nonasymptotic sequential inference procedure for estimating the time-varying difference in forecast quality when using a relatively large class of scoring rules (bounded scores with a linear equivalent). The resulting confidence intervals can be continuously monitored and yield statistically valid comparisons at arbitrary data-dependent stopping times ("anytime-valid"); this is enabled by adapting recent variance-adaptive confidence sequences (CS) to our setting. In the spirit of Shafer and Vovk's game-theoretic probability, the coverage guarantees for our CSs are also distribution-free, in the sense that they make no distributional assumptions whatsoever on the forecasts or outcomes. Additionally, in contrast to a recent preprint by Henzi and Ziegel, we show how to sequentially test a weak null hypothesis about whether one forecaster outperforms another on average over time, by designing different e-processes that quantify the evidence at any stopping time. We examine the validity of our methods over their fixed-time and asymptotic counterparts in synthetic experiments and demonstrate their effectiveness in real-data settings, including comparing probability forecasts on Major League Baseball (MLB) games and comparing statistical postprocessing methods for ensemble weather forecasts.

Methods for extending -- generalizing or transporting -- inferences from a randomized trial to a target population involve conditioning on a large set of covariates that is sufficient for rendering the randomized and non-randomized groups exchangeable. Yet, decision-makers are often interested in examining treatment effects in subgroups of the target population defined in terms of only a few discrete covariates. Here, we propose methods for estimating subgroup-specific potential outcome means and average treatment effects in generalizability and transportability analyses, using outcome model-based (g-formula), weighting, and augmented weighting estimators. We consider estimating subgroup-specific average treatment effects in the target population and its non-randomized subset, and provide methods that are appropriate both for nested and non-nested trial designs. As an illustration, we apply the methods to data from the Coronary Artery Surgery Study to compare the effect of surgery plus medical therapy versus medical therapy alone for chronic coronary artery disease in subgroups defined by history of myocardial infarction.

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn about this separating hyperplane. Exact likelihood or least squares methods to estimate the thresholding parameter involve an indicator function which make them difficult to optimize and are, therefore, often tackled by using a surrogate loss that uses a smooth approximation to the indicator. In this paper, we demonstrate that the resulting estimator is asymptotically normal with a near optimal rate of convergence: $n^{-1}$ up to a log factor, in both classification and regression thresholding models. This is substantially faster than the currently established convergence rates of smoothed estimators for similar models in the statistics and econometrics literatures. We also present a real-data application of our approach to an environmental data set where $CO_2$ emission is explained in terms of a separating hyperplane defined through per-capita GDP and urban agglomeration.

We attempt to give a unifying view of the various recent attempts to (i) improve the interpretability of tree-based models and (ii) debias the the default variable-importance measure in random Forests, Gini importance. In particular, we demonstrate a common thread among the out-of-bag based bias correction methods and their connection to local explanation for trees. In addition, we point out a bias caused by the inclusion of inbag data in the newly developed explainable AI for trees algorithms.

We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function (or its score function) and then, we use concentration inequality on M-estimators to investigate the robust estimation of the mean in high dimension in a corrupted setting (adversarial corruption setting) for bounded and unbounded score functions. For a sample of size $n$ and covariance matrix $\Sigma$, we attain the minimax speed $\sqrt{Tr(\Sigma)/n}+\sqrt{\|\Sigma\|_{op}\log(1/\delta)/n}$ with probability larger than $1-\delta$ in a heavy-tailed setting. One of the major advantages of our approach compared to others recently proposed is that our estimator is tractable and fast to compute even in very high dimension with a complexity of $O(nd\log(Tr(\Sigma)))$ where $n$ is the sample size and $\Sigma$ is the covariance matrix of the inliers. In practice, the code that we make available for this article proves to be very fast.

The problem of Sequential Estimation under Multiple Resources (SEMR) is defined in a federated setting. SEMR could be considered as the intersection of statistical estimation and bandit theory. In this problem, an agent is confronting with k resources to estimate a parameter $\theta$. The agent should continuously learn the quality of the resources by wisely choosing them and at the end, proposes an estimator based on the collected data. In this paper, we assume that the resources' distributions are Gaussian. The quality of the final estimator is evaluated by its mean squared error. Also, we restrict our class of estimators to unbiased estimators in order to define a meaningful notion of regret. The regret measures the performance of the agent by the variance of the final estimator in comparison to the optimal variance. We propose a lower bound to determine the fundamental limit of the setting even in the case that the distributions are not Gaussian. Also, we offer an order-optimal algorithm to achieve this lower bound.

Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.

Active learning has long been a topic of study in machine learning. However, as increasingly complex and opaque models have become standard practice, the process of active learning, too, has become more opaque. There has been little investigation into interpreting what specific trends and patterns an active learning strategy may be exploring. This work expands on the Local Interpretable Model-agnostic Explanations framework (LIME) to provide explanations for active learning recommendations. We demonstrate how LIME can be used to generate locally faithful explanations for an active learning strategy, and how these explanations can be used to understand how different models and datasets explore a problem space over time. In order to quantify the per-subgroup differences in how an active learning strategy queries spatial regions, we introduce a notion of uncertainty bias (based on disparate impact) to measure the discrepancy in the confidence for a model's predictions between one subgroup and another. Using the uncertainty bias measure, we show that our query explanations accurately reflect the subgroup focus of the active learning queries, allowing for an interpretable explanation of what is being learned as points with similar sources of uncertainty have their uncertainty bias resolved. We demonstrate that this technique can be applied to track uncertainty bias over user-defined clusters or automatically generated clusters based on the source of uncertainty.