Alan Hubbard

Ivana Malenica, Rachael V. Phillips, Romain Pirracchio et al.

In this work, we introduce the Personalized Online Super Learner (POSL) -- an online ensembling algorithm for streaming data whose optimization procedure accommodates varying degrees of personalization. Namely, POSL optimizes predictions with respect to baseline covariates, so personalization can vary from completely individualized (i.e., optimization with respect to baseline covariate subject ID) to many individuals (i.e., optimization with respect to common baseline covariates). As an online algorithm, POSL learns in real-time. POSL can leverage a diversity of candidate algorithms, including online algorithms with different training and update times, fixed algorithms that are never updated during the procedure, pooled algorithms that learn from many individuals' time-series, and individualized algorithms that learn from within a single time-series. POSL's ensembling of this hybrid of base learning strategies depends on the amount of data collected, the stationarity of the time-series, and the mutual characteristics of a group of time-series. In essence, POSL decides whether to learn across samples, through time, or both, based on the underlying (unknown) structure in the data. For a wide range of simulations that reflect realistic forecasting scenarios, and in a medical data application, we examine the performance of POSL relative to other current ensembling and online learning methods. We show that POSL is able to provide reliable predictions for time-series data and adjust to changing data-generating environments. We further cultivate POSL's practicality by extending it to settings where time-series enter/exit dynamically over chronological time.

Yue You, Mark van der Laan, Philip Collender et al.

We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution such that the target quantity is identified and the statistical model is unrestricted. We present solutions for linear and non-linear constraints commonly assumed to identify capture-recapture models, including no K-way interaction in linear and log-linear models, independence or conditional independence. We demonstrate that the choice of constraint has a dramatic impact on the value of the estimand, showing that it is crucial that the constraint is known to hold by design. For the commonly assumed constraint of no K-way interaction in a log-linear model, the statistical target parameter is only defined when each of the $2^K - 1$ observable capture patterns is present, and therefore suffers from the curse of dimensionality. We propose a targeted MLE based on undersmoothed lasso model to smooth across the cells while targeting the fit towards the single valued target parameter of interest. For each identification assumption, we provide simulated inference and confidence intervals to assess the performance on the estimator under correct and incorrect identifying assumptions. We apply the proposed method, alongside existing estimators, to estimate prevalence of a parasitic infection using multi-source surveillance data from a region in southwestern China, under the four identification assumptions.

Jeremy R. Coyle, Nima S. Hejazi, Ivana Malenica et al.

Targeted Learning is a subfield of statistics that unifies advances in causal inference, machine learning and statistical theory to help answer scientifically impactful questions with statistical confidence. Targeted Learning is driven by complex problems in data science and has been implemented in a diversity of real-world scenarios: observational studies with missing treatments and outcomes, personalized interventions, longitudinal settings with time-varying treatment regimes, survival analysis, adaptive randomized trials, mediation analysis, and networks of connected subjects. In contrast to the (mis)application of restrictive modeling strategies that dominate the current practice of statistics, Targeted Learning establishes a principled standard for statistical estimation and inference (i.e., confidence intervals and p-values). This multiply robust approach is accompanied by a guiding roadmap and a burgeoning software ecosystem, both of which provide guidance on the construction of estimators optimized to best answer the motivating question. The roadmap of Targeted Learning emphasizes tailoring statistical procedures so as to minimize their assumptions, carefully grounding them only in the scientific knowledge available. The end result is a framework that honestly reflects the uncertainty in both the background knowledge and the available data in order to draw reliable conclusions from statistical analyses - ultimately enhancing the reproducibility and rigor of scientific findings.

Weixin Cai, Nima S. Hejazi, Alan E. Hubbard

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these hypotheses may concern a wide range of parameters, with complex and unknown dependence structures among variables. In analyzing such hypothesis testing procedures, gains in efficiency and power can be achieved by performing variable reduction on the set of hypotheses prior to testing. We present in this paper an approach using data-adaptive multiple testing that serves exactly this purpose. This approach applies data mining techniques to screen the full set of covariates on equally sized partitions of the whole sample via cross-validation. This generalized screening procedure is used to create average ranks for covariates, which are then used to generate a reduced (sub)set of hypotheses, from which we compute test statistics that are subsequently subjected to standard multiple testing corrections. The principal advantage of this methodology lies in its providing valid statistical inference without the \textit{a priori} specifying which hypotheses will be tested. Here, we present the theoretical details of this approach, confirm its validity via a simulation study, and exemplify its use by applying it to the analysis of data on microRNA differential expression.