A/B testing has become the gold standard for modern technological industries for policy evaluation. Motivated by the widespread use of switchback experiments in A/B testing, this paper conducts a comprehensive comparative analysis of various switchback designs in Markovian environments. Unlike many existing works which derive the optimal design based on specific and relatively simple estimators, our analysis covers a range of state-of-the-art estimators developed in the reinforcement learning literature. It reveals that the effectiveness of different switchback designs depends crucially on (i) the size of the carryover effect and (ii) the autocorrelations among reward errors over time. Meanwhile, these findings are estimator-agnostic, i.e., they apply to all the aforementioned estimators. Based on these insights, we provide a workflow to offer guidelines for practitioners on designing switchback experiments in A/B testing.

The growing prevalence of streaming data and increasing concerns over data privacy pose significant challenges for traditional nonparametric regression methods, which are often ill-suited for real-time, privacy-aware learning. In this paper, we tackle these issues by first proposing a novel one-pass online functional stochastic gradient descent algorithm that leverages the Huber loss (H-FSGD), to improve robustness against outliers and heavy-tailed errors in dynamic environments. To further accommodate privacy constraints, we introduce a locally differentially private extension, Private H-FSGD (PH-FSGD), designed to real-time, privacy-preserving estimation. Theoretically, we conduct a comprehensive non-asymptotic convergence analysis of the proposed estimators, establishing finite-sample guarantees and identifying optimal step size schedules that achieve optimal convergence rates. In particular, we provide practical insights into the impact of key hyperparameters, such as step size and privacy budget, on convergence behavior. Extensive experiments validate our theoretical findings, demonstrating that our methods achieve strong robustness and privacy protection without sacrificing efficiency.

Differential privacy is a particular data privacy-preserving technology which enables synthetic data or statistical analysis results to be released with a minimum disclosure of private information from individual records. The tradeoff between privacy-preserving and utility guarantee is always a challenge for differential privacy technology, especially for synthetic data generation. In this paper, we propose a differentially private data synthesis algorithm for mixed-type data with correlation based on latent factor models. The proposed method can add a relatively small amount of noise to synthetic data under a given level of privacy protection while capturing correlation information. Moreover, the proposed algorithm can generate synthetic data preserving the same data type as mixed-type original data, which greatly improves the utility of synthetic data. The key idea of our method is to perturb the factor matrix and factor loading matrix to construct a synthetic data generation model, and to utilize link functions with privacy protection to ensure consistency of synthetic data type with original data. The proposed method can generate privacy-preserving synthetic data at low computation cost even when the original data is high-dimensional. In theory, we establish differentially private properties of the proposed method. Our numerical studies also demonstrate superb performance of the proposed method on the utility guarantee of the statistical analysis based on privacy-preserved synthetic data.

Recommender systems have been extensively used by the entertainment industry, business marketing and the biomedical industry. In addition to its capacity of providing preference based recommendations as an unsupervised learning methodology, it has been also proven useful in sales forecasting, product introduction and other production related businesses. Since some consumers and companies need a recommendation or prediction for future budget, labor and supply chain coordination, dynamic recommender systems for precise forecasting have become extremely necessary. In this article, we propose a new recommendation method, namely the dynamic tensor recommender system (DTRS), which aims particularly at forecasting future recommendation. The proposed method utilizes a tensor-valued function of time to integrate time and contextual information, and creates a time-varying coefficient model for temporal tensor factorization through a polynomial spline approximation. Major advantages of the proposed method include competitive future recommendation predictions and effective prediction interval estimations. In theory, we establish the convergence rate of the proposed tensor factorization and asymptotic normality of the spline coefficient estimator. The proposed method is applied to simulations, IRI marketing data and Last.fm data. Numerical studies demonstrate that the proposed method outperforms existing methods in terms of future time forecasting.

Diffusion tensor imaging (DTI) provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. This paper presents a functional regression framework, called FRATS, for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest, such as age, diagnostic status and gender, in real applications. The functional regression framework consists of four integrated components: the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles, a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates, a global test statistic for testing hypotheses of interest, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy, mean diffusivity, and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. Significant age and gestational age effects on the five diffusion properties were found in both tracts. The resulting analysis pipeline can be used for understanding normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles.

Methods for the analysis of brain morphology, including voxel-based morphology and surface-based morphometries, have been used to detect associations between brain structure and covariates of interest, such as diagnosis, severity of disease, age, IQ, and genotype. The statistical analysis of morphometric measures usually involves two statistical procedures: 1) invoking a statistical model at each voxel (or point) on the surface of the brain or brain subregion, followed by mapping test statistics (e.g., t test) or their associated p values at each of those voxels; 2) correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation. We propose the use of new statistical methods for each of these procedures. We first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion (e.g., cortical or subcortical surfaces) and the covariates of interest. Moreover, we develop a robust test procedure that is based on a resampling method, called wild bootstrapping. This procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest. The value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data, including data from both anatomical and functional magnetic resonance imaging (fMRI). Simulation studies demonstrate that this robust test procedure can accurately control the family-wise error rate. We demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects.