Machine learning (ML) is playing an increasingly important role in scientific research. In conjunction with classical statistical approaches, ML-assisted analytical strategies have shown great promise in accelerating research findings. This has also opened up a whole new field of methodological research focusing on integrative approaches that leverage both ML and statistics to tackle data science challenges. One type of study that has quickly gained popularity employs ML to predict unobserved outcomes in massive samples and then uses the predicted outcomes in downstream statistical inference. However, existing methods designed to ensure the validity of this type of post-prediction inference are limited to very basic tasks such as linear regression analysis. This is because any extension of these approaches to new, more sophisticated statistical tasks requires task-specific algebraic derivations and software implementations, which ignores the massive library of existing software tools already developed for complex inference tasks and severely constrains the scope of post-prediction inference in real applications. To address this challenge, we propose a novel statistical framework for task-agnostic ML-assisted inference. It provides a post-prediction inference solution that can be easily plugged into almost any established data analysis routine. It delivers valid and efficient inference that is robust to arbitrary choices of ML models, while allowing nearly all existing analytical frameworks to be incorporated into the analysis of ML-predicted outcomes. Through extensive experiments, we showcase the validity, versatility, and superiority of our method compared to existing approaches.

Despite their benefits in terms of simplicity, low computational cost and data requirement, parametric machine learning algorithms, such as linear discriminant analysis, quadratic discriminant analysis or logistic regression, suffer from serious drawbacks including linearity, poor fit of features to the usually imposed normal distribution and high dimensionality. Batch kernel-based nonparametric classifier, which overcomes the linearity and normality of features constraints, represent an interesting alternative for supervised classification problem. However, it suffers from the ``curse of dimension". The problem can be alleviated by the explosive sample size in the era of big data, while large-scale data size presents some challenges in the storage of data and the calculation of the classifier. These challenges make the classical batch nonparametric classifier no longer applicable. This motivates us to develop a fast algorithm adapted to the real-time calculation of the nonparametric classifier in massive as well as streaming data frameworks. This online classifier includes two steps. First, we consider an online principle components analysis to reduce the dimension of the features with a very low computation cost. Then, a stochastic approximation algorithm is deployed to obtain a real-time calculation of the nonparametric classifier. The proposed methods are evaluated and compared to some commonly used machine learning algorithms for real-time fetal well-being monitoring. The study revealed that, in terms of accuracy, the offline (or Batch), as well as, the online classifiers are good competitors to the random forest algorithm. Moreover, we show that the online classifier gives the best trade-off accuracy/computation cost compared to the offline classifier.

Counterfactual explanations have emerged as an important tool to understand, debug, and audit complex machine learning models. To offer global counterfactual explainability, state-of-the-art methods construct summaries of local explanations, offering a trade-off among conciseness, counterfactual effectiveness, and counterfactual cost or burden imposed on instances. In this work, we provide a concise formulation of the problem of identifying global counterfactuals and establish principled criteria for comparing solutions, drawing inspiration from Pareto dominance. We introduce innovative algorithms designed to address the challenge of finding global counterfactuals for either the entire input space or specific partitions, employing clustering and decision trees as key components. Additionally, we conduct a comprehensive experimental evaluation, considering various instances of the problem and comparing our proposed algorithms with state-of-the-art methods. The results highlight the consistent capability of our algorithms to generate meaningful and interpretable global counterfactual explanations.

This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic framework that generates prediction intervals for datasets with complete or missing data. SEMF extends the Expectation-Maximization (EM) algorithm, traditionally used in unsupervised learning, to a supervised context, enabling it to extract latent representations for uncertainty estimation. The framework demonstrates robustness through extensive empirical evaluation across 11 tabular datasets, achieving$\unicode{x2013}$in some cases$\unicode{x2013}$narrower normalized prediction intervals and higher coverage than traditional quantile regression methods. Furthermore, SEMF integrates seamlessly with existing machine learning algorithms, such as gradient-boosted trees and neural networks, exemplifying its usefulness for real-world applications. The experimental results highlight SEMF's potential to advance state-of-the-art techniques in uncertainty quantification.

We develop algorithms for online linear regression which achieve optimal static and dynamic regret guarantees \emph{even in the complete absence of prior knowledge}. We present a novel analysis showing that a discounted variant of the Vovk-Azoury-Warmuth forecaster achieves dynamic regret of the form $R_{T}(\vec{u})\le O\left(d\log(T)\vee \sqrt{dP_{T}^{\gamma}(\vec{u})T}\right)$, where $P_{T}^{\gamma}(\vec{u})$ is a measure of variability of the comparator sequence, and show that the discount factor achieving this result can be learned on-the-fly. We show that this result is optimal by providing a matching lower bound. We also extend our results to \emph{strongly-adaptive} guarantees which hold over every sub-interval $[a,b]\subseteq[1,T]$ simultaneously.

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and analyze its concentration rates, demonstrating adaptiveness to the unknown sparsity level of the regression coefficient vector. Furthermore, we extend our investigation to establish concentration outcomes for parameter estimation using specific distance measures. These findings are in line with recent discoveries in frequentist studies. Additionally, by employing techniques to address model misspecification through a fractional posterior, we broaden our analysis through oracle inequalities to encompass the critical aspect of model misspecification for the regular posterior. Our novel findings are demonstrated using two different types of sparsity priors: a shrinkage prior and a spike-and-slab prior.

A common way to evaluate a dataset in ML involves training a model on this dataset and assessing the model's performance on a test set. However, this approach has two issues: (1) it may incentivize undesirable data manipulation in data marketplaces, as the self-interested data providers seek to modify the dataset to maximize their evaluation scores; (2) it may select datasets that overfit to potentially small test sets. We propose a new data valuation method that provably guarantees the following: data providers always maximize their expected score by truthfully reporting their observed data. Any manipulation of the data, including but not limited to data duplication, adding random data, data removal, or re-weighting data from different groups, cannot increase their expected score. Our method, following the paradigm of proper scoring rules, measures the pointwise mutual information (PMI) of the test dataset and the evaluated dataset. However, computing the PMI of two datasets is challenging. We introduce a novel PMI measuring method that greatly improves tractability within Bayesian machine learning contexts. This is accomplished through a new characterization of PMI that relies solely on the posterior probabilities of the model parameter at an arbitrarily selected value. Finally, we support our theoretical results with simulations and further test the effectiveness of our data valuation method in identifying the top datasets among multiple data providers. Interestingly, our method outperforms the standard approach of selecting datasets based on the trained model's test performance, suggesting that our truthful valuation score can also be more robust to overfitting.

Estimating heterogeneous treatment effects is important to tailor treatments to those individuals who would most likely benefit. However, conditional average treatment effect predictors may often be trained on one population but possibly deployed on different, possibly unknown populations. We use methodology for learning multi-accurate predictors to post-process CATE T-learners (differenced regressions) to become robust to unknown covariate shifts at the time of deployment. The method works in general for pseudo-outcome regression, such as the DR-learner. We show how this approach can combine (large) confounded observational and (smaller) randomized datasets by learning a confounded predictor from the observational dataset, and auditing for multi-accuracy on the randomized controlled trial. We show improvements in bias and mean squared error in simulations with increasingly larger covariate shift, and on a semi-synthetic case study of a parallel large observational study and smaller randomized controlled experiment. Overall, we establish a connection between methods developed for multi-distribution learning and achieve appealing desiderata (e.g. external validity) in causal inference and machine learning.

Forward stagewise regression is a simple algorithm that can be used to estimate regularized models. The updating rule adds a small constant to a regression coefficient in each iteration, such that the underlying optimization problem is solved slowly with small improvements. This is similar to gradient boosting, with the essential difference that the step size is determined by the product of the gradient and a step length parameter in the latter algorithm. One often overlooked challenge in gradient boosting for distributional regression is the issue of a vanishing small gradient, which practically halts the algorithm's progress. We show that gradient boosting in this case oftentimes results in suboptimal models, especially for complex problems certain distributional parameters are never updated due to the vanishing gradient. Therefore, we propose a stagewise boosting-type algorithm for distributional regression, combining stagewise regression ideas with gradient boosting. Additionally, we extend it with a novel regularization method, correlation filtering, to provide additional stability when the problem involves a large number of covariates. Furthermore, the algorithm includes best-subset selection for parameters and can be applied to big data problems by leveraging stochastic approximations of the updating steps. Besides the advantage of processing large datasets, the stochastic nature of the approximations can lead to better results, especially for complex distributions, by reducing the risk of being trapped in a local optimum. The performance of our proposed stagewise boosting distributional regression approach is investigated in an extensive simulation study and by estimating a full probabilistic model for lightning counts with data of more than 9.1 million observations and 672 covariates.

Sleep is a complex physiological process evaluated through various modalities recording electrical brain, cardiac, and respiratory activities. We curate a large polysomnography dataset from over 14,000 participants comprising over 100,000 hours of multi-modal sleep recordings. Leveraging this extensive dataset, we developed SleepFM, the first multi-modal foundation model for sleep analysis. We show that a novel leave-one-out approach for contrastive learning significantly improves downstream task performance compared to representations from standard pairwise contrastive learning. A logistic regression model trained on SleepFM's learned embeddings outperforms an end-to-end trained convolutional neural network (CNN) on sleep stage classification (macro AUROC 0.88 vs 0.72 and macro AUPRC 0.72 vs 0.48) and sleep disordered breathing detection (AUROC 0.85 vs 0.69 and AUPRC 0.77 vs 0.61). Notably, the learned embeddings achieve 48% top-1 average accuracy in retrieving the corresponding recording clips of other modalities from 90,000 candidates. This work demonstrates the value of holistic multi-modal sleep modeling to fully capture the richness of sleep recordings. SleepFM is open source and available at https://github.com/rthapa84/sleepfm-codebase.