Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model. Hence, a factor importance measure ought to characterize the feature's predictive potential without relying on a specific prediction algorithm. Such algorithm-agnostic importance is termed as intrinsic importance in Williamson et al. (2023), but their estimator again requires model fitting. To bypass the modeling step, we present the equivalence between predictiveness potential and total Sobol' indices from global sensitivity analysis, and introduce a novel consistent estimator that can be directly estimated from noisy data. Integrating with forward selection and backward elimination gives rise to FIRST, Factor Importance Ranking and Selection using Total (Sobol') indices. Extensive simulations are provided to demonstrate the effectiveness of FIRST on regression and binary classification problems, and a clear advantage over the state-of-the-art methods.

In multivariate functional data analysis, different functional covariates can be homogeneous. The hidden homogeneity structure is informative about the connectivity or association of different covariates. The covariates with pronounced homogeneity can be analyzed jointly within the same group, which gives rise to a way of parsimoniously modeling multivariate functional data. In this paper, a novel grouped multivariate functional regression model with a new regularization approach termed "coefficient shape alignment" is developed to tackle the potential homogeneity of different functional covariates. The modeling procedure includes two main steps: first detect the unknown grouping structure with the new regularization approach to aggregate covariates into disjoint groups; and then the grouped multivariate functional regression model is established based on the detected grouping structure. In this new grouped model, the coefficient functions of covariates in the same homogeneous group share the same shape invariant to scaling. The new regularization approach builds on penalizing the discrepancy of coefficient shape. The consistency property of the detected grouping structure is thoroughly investigated, and the conditions that guarantee uncovering the underlying true grouping structure are developed. The asymptotic properties of the model estimates are also developed. Extensive simulation studies are conducted to investigate the finite-sample properties of the developed methods. The practical utility of the proposed methods is illustrated in the real data analysis on sugar quality evaluation. This work provides a novel means for analyzing the underlying homogeneity of functional covariates and developing parsimonious model structures for multivariate functional data.

A popular approach for finding a minimizer of an EMO problem is based on the mean-field Langevin dynamics. When the problem is convex, Hu et al. (2019) show the mean-field Langevin dynamics convergences to the minimizer asymptotically; and when the problem satisfies a uniform logarithmic Sobolev inequality, several works have established an exponentially fast convergence (Chizat, 2022; Nitanda et al., 2022; Chen et al., 2022). The mean-field Langevin dynamics, however, cannot be implemented and bridging this gap requires both space and time discretizations of the dynamics. A time-discretization of the mean-field Langevin dynamics was analyzed by Nitanda et al. (2022) who extend the interpolation argument introduced by Vempala and Wibisono (2019) to a non-linear Fokker-Planck equation. They establish the non-asymptotic convergence of the time-discretized dynamics in the energy gap. A space-discretization was studied by Chen et al. (2022) who show that the finite-particle approximation to the density of the mean-field Langevin dynamics (referred to as a uniform-in-time propagation of chaos) converges exponentially fast, with a bias related to the number of particles. More practically, Suzuki et al. (2023) analyze a space-time discretization of the mean-field Langevin dynamics and establish the non-asymptotic convergence 1

The causal inference literature frequently focuses on estimating the mean of the potential outcome, whereas the quantiles of the potential outcome may carry important additional information. We propose a universal approach, based on the inverse estimating equations, to generalize a wide class of causal inference solutions from estimating the mean of the potential outcome to its quantiles. We assume that an identifying moment function is available to identify the mean of the threshold-transformed potential outcome, based on which a convenient construction of the estimating equation of quantiles of potential outcome is proposed. In addition, we also give a general construction of the efficient influence functions of the mean and quantiles of potential outcomes, and identify their connection. We motivate estimators for the quantile estimands with the efficient influence function, and develop their asymptotic properties when either parametric models or data-adaptive machine learners are used to estimate the nuisance functions. A broad implication of our results is that one can rework the existing result for mean causal estimands to facilitate causal inference on quantiles, rather than starting from scratch. Our results are illustrated by several examples.

We present a Transfer Causal Learning (TCL) framework when target and source domains share the same covariate/feature spaces, aiming to improve causal effect estimation accuracy in limited data. Limited data is very common in medical applications, where some rare medical conditions, such as sepsis, are of interest. Our proposed method, named \texttt{$\ell_1$-TCL}, incorporates $\ell_1$ regularized TL for nuisance models (e.g., propensity score model); the TL estimator of the nuisance parameters is plugged into downstream average causal/treatment effect estimators (e.g., inverse probability weighted estimator). We establish non-asymptotic recovery guarantees for the \texttt{$\ell_1$-TCL} with generalized linear model (GLM) under the sparsity assumption in the high-dimensional setting, and demonstrate the empirical benefits of \texttt{$\ell_1$-TCL} through extensive numerical simulation for GLM and recent neural network nuisance models. Our method is subsequently extended to real data and generates meaningful insights consistent with medical literature, a case where all baseline methods fail.

Recent work has focused on the very common practice of prediction-based inference: that is, (i) using a pre-trained machine learning model to predict an unobserved response variable, and then (ii) conducting inference on the association between that predicted response and some covariates. As pointed out by Wang et al. (2020), applying a standard inferential approach in (ii) does not accurately quantify the association between the unobserved (as opposed to the predicted) response and the covariates. In recent work, Wang et al. (2020) and Angelopoulos et al. (2023) propose corrections to step (ii) in order to enable valid inference on the association between the unobserved response and the covariates. Here, we show that the method proposed by Angelopoulos et al. (2023) successfully controls the type 1 error rate and provides confidence intervals with correct nominal coverage, regardless of the quality of the pre-trained machine learning model used to predict the unobserved response. However, the method proposed by Wang et al. (2020) provides valid inference only under very strong conditions that rarely hold in practice: for instance, if the machine learning model perfectly estimates the true regression function in the study population of interest.

This paper introduces an iterative algorithm designed to train additive models with favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient descent, applied to the coefficients of a truncated basis expansion of the component functions. We show that the resulting estimator satisfies an oracle inequality that allows for model mispecification. In the well-specified setting, by choosing the learning rate carefully across three distinct stages of training, we prove that its risk is minimax optimal in terms of the dependence on the dimensionality of the data and the size of the training sample.

Highway traffic crashes exert a considerable impact on both transportation systems and the economy. In this context, accurate and dependable emergency responses are crucial for effective traffic management. However, the influence of crashes on traffic status varies across diverse factors and may be biased due to selection bias. Therefore, there arises a necessity to accurately estimate the heterogeneous causal effects of crashes, thereby providing essential insights to facilitate individual-level emergency decision-making. This paper proposes a novel causal machine learning framework to estimate the causal effect of different types of crashes on highway speed. The Neyman-Rubin Causal Model (RCM) is employed to formulate this problem from a causal perspective. The Conditional Shapley Value Index (CSVI) is proposed based on causal graph theory to filter adverse variables, and the Structural Causal Model (SCM) is then adopted to define the statistical estimand for causal effects. The treatment effects are estimated by Doubly Robust Learning (DRL) methods, which combine doubly robust causal inference with classification and regression machine learning models. Experimental results from 4815 crashes on Highway Interstate 5 in Washington State reveal the heterogeneous treatment effects of crashes at varying distances and durations. The rear-end crashes cause more severe congestion and longer durations than other types of crashes, and the sideswipe crashes have the longest delayed impact. Additionally, the findings show that rear-end crashes affect traffic greater at night, while crash to objects has the most significant influence during peak hours. Statistical hypothesis tests, error metrics based on matched "counterfactual outcomes", and sensitive analyses are employed for assessment, and the results validate the accuracy and effectiveness of our method.

Epilepsy is one of the most common neurological diseases globally, affecting around 50 million people worldwide. Fortunately, up to 70 percent of people with epilepsy could live seizure-free if properly diagnosed and treated, and a reliable technique to monitor the onset of seizures could improve the quality of life of patients who are constantly facing the fear of random seizure attacks. The scalp-based EEG test, despite being the gold standard for diagnosing epilepsy, is costly, necessitates hospitalization, demands skilled professionals for operation, and is discomforting for users. In this paper, we propose EarSD, a novel lightweight, unobtrusive, and socially acceptable ear-worn system to detect epileptic seizure onsets by measuring the physiological signals from behind the user's ears. EarSD includes an integrated custom-built sensing, computing, and communication PCB to collect and amplify the signals of interest, remove the noises caused by motion artifacts and environmental impacts, and stream the data wirelessly to the computer or mobile phone nearby, where data are uploaded to the host computer for further processing. We conducted both in-lab and in-hospital experiments with epileptic seizure patients who were hospitalized for seizure studies. The preliminary results confirm that EarSD can detect seizures with up to 95.3 percent accuracy by just using classical machine learning algorithms.

Recent research at CHU Sainte Justine's Pediatric Critical Care Unit (PICU) has revealed that traditional machine learning methods, such as semi-supervised label propagation and K-nearest neighbors, outperform Transformer-based models in artifact detection from PPG signals, mainly when data is limited. This study addresses the underutilization of abundant unlabeled data by employing self-supervised learning (SSL) to extract latent features from these data, followed by fine-tuning on labeled data. Our experiments demonstrate that SSL significantly enhances the Transformer model's ability to learn representations, improving its robustness in artifact classification tasks. Among various SSL techniques, including masking, contrastive learning, and DINO (self-distillation with no labels)-contrastive learning exhibited the most stable and superior performance in small PPG datasets. Further, we delve into optimizing contrastive loss functions, which are crucial for contrastive SSL. Inspired by InfoNCE, we introduce a novel contrastive loss function that facilitates smoother training and better convergence, thereby enhancing performance in artifact classification. In summary, this study establishes the efficacy of SSL in leveraging unlabeled data, particularly in enhancing the capabilities of the Transformer model. This approach holds promise for broader applications in PICU environments, where annotated data is often limited.