Data used to train predictive models via empirical risk minimization (ERM) often contain sensitive personal information. While differential privacy (DP) provides mathematically provable bounds to protect such data, previous work has focused almost exclusively on unweighted ERM. We consider weighted ERM (wERM) -- an important generalization where individual contributions to the objective function vary. We propose the first DP algorithm for general wERM with formal privacy guarantees and derive both its empirical and population utility bounds. Crucially, this general wERM framework provides a pathway for deriving privacy-preserving learning methods for individualized treatment rules, including the popular outcome-weighted learning (OWL) approach. We evaluate DP-wERM applied to OWL in simulated and real data experiments. Our empirical results demonstrate that training OWL models via wERM provides strong DP guarantees while maintaining robust performance, proving the method is practical for sensitive, real-world data.

OBJECTIVE: We propose a new health informatics framework to analyze physical activity (PA) from accelerometer devices. Accelerometry data enables scientists to extract personal digital features useful for precision health decision making. Existing methods in accelerometry data analysis typically begin with discretizing summary counts by certain fixed cutoffs into activity categories. One well-known limitation is that the chosen cutoffs are often validated under restricted settings, and cannot be generalizable across populations, devices, or studies. METHODS: We develop a data-driven approach to overcome this bottleneck in PA data analysis, in which we holistically summarize a subject's activity profile using Occupation-Time curves (OTCs), which describe the percentage of time spent at or above a continuum of activity count levels. We develop multi-step adaptive learning algorithms to perform supervised learning via a scalar-on-function model that involves OTC as the functional predictor of interest as well as other scalar covariates. Our learning analytic first incorporates a hybrid approach of fused lasso for clustering and Hidden Markov Model for changepoint detection, then executes refinement procedures to determine activity windows of interest. RESULTS: We evaluate and illustrate the performance of the proposed learning analytic through simulation experiments and real-world data analyses to assess the influence of PA on biological aging. Our findings indicate a different directional relationship between biological age and PA depending on the specific outcome of interest. SIGNIFICANCE: Our bioinformatics methodology involves the biomedical outcome of interest to detect different critical points, and is thus adaptive to the specific data, study population, and health outcome under investigation.

OBJECTIVE: We propose a new analytic framework, "Artificial Synthetic Imaging Data (ASID) Workflow," for sleep classification from a wearable device comprising: 1) the creation of ASID from data collected by a non-invasive wearable device that permits real-time multi-modal physiological monitoring on heart rate (HR), 3-axis accelerometer, electrodermal activity, and skin temperature, denoted as "Temporal E4 Data" (TED) and 2) the use of an image classification supervised learning algorithm, convolutional neural network (CNN), to classify periods of sleep. METHODS: We investigate ASID Workflow under 6 settings (3 data resolutions × 2 HR scenarios). Competing machine/deep learning classification algorithms, including logistic regression, support vector machine, random forest, k-nearest neighbors, and Long Short-Term Memory, are applied to TED as comparisons, termed "Competing Workflow." RESULTS: The ASID Workflow achieves excellent performance with mean weighted accuracy across settings of 94.7%, and is superior to the Competing Workflow with high and low resolution data regardless of the inclusion of HR modality. This superiority is maximized for low resolution data without HR. Additionally, CNN has a relatively low subject-wise test computational cost compared with competing algorithms. CONCLUSION: We demonstrate the utility of creating ASID from multi-modal physiological data and applying a preexisting image classification algorithm to achieve better classification accuracy. We shed light on the influence of data resolution and HR modality on the Workflow's performance. SIGNIFICANCE: Applying CNN to ASID allows us to capture both temporal and spatial dependency among physiological variables and modalities by using 2D images' topological structure that competing algorithms fail to utilize.

Sparse representation has been widely used in data compression, signal and image denoising, dimensionality reduction and computer vision. While overcomplete dictionaries are required for sparse representation of multidimensional data, orthogonal bases represent one-dimensional data well. In this paper, we propose a data-driven sparse representation using orthonormal bases under the lossless compression constraint. We show that imposing such constraint under the Minimum Description Length (MDL) principle leads to a unique and optimal sparse representation for one-dimensional data, which results in discriminative features useful for data discovery.

Simultaneous inference after model selection is of critical importance to address scientific hypotheses involving a set of parameters. In this paper, we consider a high-dimensional linear regression model in which a regularization procedure such as LASSO is applied to yield a sparse model. To establish a simultaneous post-model selection inference, we propose a method of contraction and expansion (MOCE) along the line of debiasing estimation in that we investigate a desirable trade-off between model selection variability and sample variability by the means of forward screening. We establish key theoretical results for the inference from the proposed MOCE procedure. Once the expanded model is properly selected, the theoretical guarantees and simultaneous confidence regions can be constructed by the joint asymptotic normal distribution. In comparison with existing methods, our proposed method exhibits stable and reliable coverage at a nominal significance level and enjoys substantially less computational burden. Thus, our MOCE approach is trustworthy in solving real-world problems.

While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in realtime. One type of such a continuous stream of information is time series data. Due to the richness of information in time series and inadequacy of summary statistics to encapsulate structures and patterns in such data, development of new approaches to learn time series is of interest. In this paper, we propose a novel method, called pattern tree, to learn patterns in the times-series using a binary-structured tree. While a pattern tree can be used for many purposes such as lossless compression, prediction and anomaly detection, in this paper we focus on its application in time series estimation and forecasting. In comparison to other methods, our proposed pattern tree method improves the mean squared error of estimation.

This paper presents a unified framework for supervised learning and inference procedures using the divide-and-conquer approach for high-dimensional correlated outcomes. We propose a general class of estimators that can be implemented in a fully distributed and parallelized computational scheme. Modeling, computational and theoretical challenges related to high-dimensional correlated outcomes are overcome by dividing data at both outcome and subject levels, estimating the parameter of interest from blocks of data using a broad class of supervised learning procedures, and combining block estimators in a closed-form meta-estimator asymptotically equivalent to estimates obtained by Hansen (1982)'s generalized method of moments (GMM) that does not require the entire data to be reloaded on a common server. We provide rigorous theoretical justifications for the use of distributed estimators with correlated outcomes by studying the asymptotic behaviour of the combined estimator with fixed and diverging number of data divisions. Simulations illustrate the finite sample performance of the proposed method, and we provide an R package for ease of implementation.

As data sets of related studies become more easily accessible, combining data sets of similar studies is often undertaken in practice to achieve a larger sample size and higher power. A major challenge arising from data integration pertains to data heterogeneity in terms of study population, study design, or study coordination. Ignoring such heterogeneity in data analysis may result in biased estimation and misleading inference. Traditional techniques of remedy to data heterogeneity include the use of interactions and random effects, which are inferior to achieving desirable statistical power or providing a meaningful interpretation, especially when a large number of smaller data sets are combined. In this paper, we propose a regularized fusion method that allows us to identify and merge inter-study homogeneous parameter clusters in regression analysis, without the use of hypothesis testing approach. Using the fused lasso, we establish a computationally efficient procedure to deal with large-scale integrated data. Incorporating the estimated parameter ordering in the fused lasso facilitates computing speed with no loss of statistical power. We conduct extensive simulation studies and provide an application example to demonstrate the performance of the new method with a comparison to the conventional methods.

BACKGROUND: Numerous nonparametric approaches have been proposed in literature to detect differential gene expression in the setting of two user-defined groups. However, there is a lack of nonparametric procedures to analyze microarray data with multiple factors attributing to the gene expression. Furthermore, incorporating interaction effects in the analysis of microarray data has long been of great interest to biological scientists, little of which has been investigated in the nonparametric framework. RESULTS: In this paper, we propose a set of nonparametric tests to detect treatment effects, clinical covariate effects, and interaction effects for multifactorial microarray data. When the distribution of expression data is skewed or heavy-tailed, the rank tests are substantially more powerful than the competing parametric F tests. On the other hand, in the case of light or medium-tailed distributions, the rank tests appear to be marginally less powerful than the parametric competitors. CONCLUSION: The proposed rank tests enable us to detect differential gene expression and establish interaction effects for microarray data with various non-normally distributed expression measurements across genome. In the presence of outliers, they are advantageous alternative approaches to the existing parametric F tests due to the robustness feature.