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1. A unifying framework of high-dimensional sparse estimation with dierence-of-convex (DC) regularization

   Cao, Shanshan ; Huo, Xiaoming ; Pang, Jong-Shi ( August 2021 , Statistical science)

   null (Ed.)

   Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients. Non-convex penalties in specic forms are well-studied in the literature for sparse estimation. A recent work, Ahn, Pang, and Xin (2017), has pointed out that nearly all existing non-convex penalties can be represented as difference-of-convex (DC) functions, which are the difference of two convex functions, while itself may not be convex. There is a large existing literature on optimization problems when their objectives and/or constraints involve DC functions. Efficient numerical solutions have been proposed. Under the DC framework, directional-stationary (d-stationary) solutions are considered, and they are usually not unique. In this paper, we show that under some mild conditions, a certain subset of d-stationary solutions in an optimization problem (with a DC objective) has some ideal statistical properties: namely, asymptotic estimation consistency, asymptotic model selection consistency, asymptotic efficiency. Our assumptions are either weaker than or comparable with those conditions that have been adopted in other existing works. This work shows that DC is a nice framework to offer a unied approach to these existing works where non-convex penalties are involved. Our work bridges the communities of optimization and statistics. 

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2. Algorithm and Hardware Co-Design for FPGA Acceleration of Hamiltonian Monte Carlo Based No-U-Turn Sampler

   Wang, Y. ; Li, P. ( July 2021 , The 32nd IEEE International Conference on Application-specific Systems, Architectures and Processors)

   null (Ed.)

   Monte Carlo (MC) methods are widely used in many research areas such as physical simulation, statistical analysis, and machine learning. Application of MC methods requires drawing fast mixing samples from a given probability distribution. Among existing sampling methods, the Hamiltonian Monte Carlo (HMC) utilizes gradient information during Hamiltonian simulation and can produce fast mixing samples at the highest efficiency. However, without carefully chosen simulation parameters for a specific problem, HMC generally suffers from simulation locality and computation waste. As a result, the No-U-Turn Sampler (NUTS) has been proposed to automatically tune these parameters during simulation and is the current state-of-the-art sampling algorithm. However, application of NUTS requires frequent gradient calculation of a given distribution and high-volume vector processing, especially for large-scale problems, leading to drawing an expensively large number of samples and a desire of hardware acceleration. While some hardware acceleration works have been proposed for traditional Markov Chain Monte Carlo (MCMC) and HMC methods, there is no existing work targeting hardware acceleration of the NUTS algorithm. In this paper, we present the first NUTS accelerator on FPGA while addressing the high complexity of this state-of-the-art algorithm. Our hardware and algorithm co-optimizations include an incremental resampling technique which leads to a more memory efficient architecture and pipeline optimization for multi-chain sampling to maximize the throughput. We also explore three levels of parallelism in the NUTS accelerator to further boost performance. Compared with optimized C++ NUTS package: RSTAN, our NUTS accelerator can reach a maximum speedup of 50.6X and an energy improvement of 189.7X. 

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3. U-PASS: unified power analysis and forensics for qualitative traits in genetic association studies

   https://doi.org/10.1093/bioinformatics/btz637  

   Gao, Zheng ; Terhorst, Jonathan ; Van Hout, Cristopher V. ; Stoev, Stilian ; Schwartz, ed., Russell ( August 2019 , Bioinformatics)

   Despite the availability of existing calculators for statistical power analysis in genetic association studies, there has not been a model-invariant and test-independent tool that allows for both planning of prospective studies and systematic review of reported findings. In this work, we develop a web-based application U-PASS (Unified Power analysis of ASsociation Studies), implementing a unified framework for the analysis of common association tests for binary qualitative traits. The application quantifies the shared asymptotic power limits of the common association tests, and visualizes the fundamental statistical trade-off between risk allele frequency and odds ratio. The application also addresses the applicability of asymptotics-based power calculations in finite samples, and provides guidelines for single-SNP-based association tests. In addition to designing prospective studies, U-PASS enables researchers to retrospectively assess the statistical validity of previously reported associations.

   U-PASS is an open-source R Shiny application. A live instance is hosted at https://power.stat.lsa.umich.edu. Source is available on https://github.com/Pill-GZ/U-PASS.

   Supplementary data are available at Bioinformatics online.

    

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4. Differentially Private L2-Heavy Hitters in the Sliding Window Model

   Blocki, Jeremiah ; Lee, Seunghoon ; Mukherjee, Tamalika ; Zhou, Samson ( February 2023 , Eleventh International Conference on Learning Representations (ICLR 2023))

   The data management of large companies often prioritize more recent data, as a source of higher accuracy prediction than outdated data. For example, the Facebook data policy retains user search histories for months while the Google data retention policy states that browser information may be stored for up to months. These policies are captured by the sliding window model, in which only the most recent statistics form the underlying dataset. In this paper, we consider the problem of privately releasing the L2-heavy hitters in the sliding window model, which include Lp-heavy hitters for p<=2 and in some sense are the strongest possible guarantees that can be achieved using polylogarithmic space, but cannot be handled by existing techniques due to the sub-additivity of the L2 norm. Moreover, existing non-private sliding window algorithms use the smooth histogram framework, which has high sensitivity. To overcome these barriers, we introduce the first differentially private algorithm for L2-heavy hitters in the sliding window model by initiating a number of L2-heavy hitter algorithms across the stream with significantly lower threshold. Similarly, we augment the algorithms with an approximate frequency tracking algorithm with significantly higher accuracy. We then use smooth sensitivity and statistical distance arguments to show that we can add noise proportional to an estimation of the norm. To the best of our knowledge, our techniques are the first to privately release statistics that are related to a sub-additive function in the sliding window model, and may be of independent interest to future differentially private algorithmic design in the sliding window model. 

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5. A study of disproportionately affected populations by race/ethnicity during the SARS-CoV-2 pandemic using multi-population SEIR modeling and ensemble data assimilation

   https://doi.org/10.3934/fods.2021022  

   Fleurantin, Emmanuel ; Sampson, Christian ; Maes, Daniel Paul ; Bennett, Justin ; Fernandes-Nunez, Tayler ; Marx, Sophia ; Evensen, Geir ( January 2021 , Foundations of Data Science)

   null (Ed.)

   The disparity in the impact of COVID-19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number (\begin{document}$ R_t $\end{document}), can be hard to calculate from this data especially for individual populations. Furthermore, disparities in the availability of testing, record keeping infrastructure, or government funding in disadvantaged populations can produce incomplete data sets. In this work, we apply ensemble data assimilation techniques which optimally combine model and data to produce a more complete data set providing better estimates of the critical metrics used by public health officials and epidemiologists. We employ a multi-population SEIR (Susceptible, Exposed, Infected and Recovered) model with a time dependent reproductive number and age stratified contact rate matrix for each population. We assimilate the daily death data for populations separated by ethnic/racial groupings using a technique called Ensemble Smoothing with Multiple Data Assimilation (ESMDA) to estimate model parameters and produce an \begin{document}$R_t(n)$\end{document} for the \begin{document}$n^{th}$\end{document} population. We do this with three distinct approaches, (1) using the same contact matrices and prior \begin{document}$R_t(n)$\end{document} for each population, (2) assigning contact matrices with increased contact rates for working age and older adults to populations experiencing disparity and (3) as in (2) but with a time-continuous update to \begin{document}$R_t(n)$\end{document}. We make a study of 9 U.S. states and the District of Columbia providing a complete time series of the pandemic in each and, in some cases, identifying disparities not otherwise evident in the aggregate statistics.

    

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