@article{dai_shahzad_liu_li_zhong_chen_2018, title={Identifying and Estimating Persistent Items in Data Streams}, volume={26}, ISSN={["1558-2566"]}, DOI={10.1109/TNET.2018.2865125}, abstractNote={This paper addresses the fundamental problem of finding persistent items and estimating the number of times each persistent item occurred in a given data stream during a given period of time at any given observation point. We propose a novel scheme, PIE, that can not only accurately identify each persistent item with a probability greater than any desired false negative rate (FNR), but can also accurately estimate the number of occurrences of each persistent item. The key idea of PIE is that it uses Raptor codes to encode the ID of each item that appears at the observation point during a measurement period and stores only a few bits of the encoded ID in the memory. The item that is persistent occurs in enough measurement periods that enough encoded bits for the ID can be retrieved from the observation point to decode them correctly and get the ID of the persistent item. To estimate the number of occurrences of any given persistent item, PIE uses maximum likelihood estimation-based statistical techniques on the information already recorded during the measurement periods. We implemented and evaluated PIE using three real network traffic traces and compared its performance with three prior schemes. Our results show that PIE not only achieves the desire FNR in every scenario, its average FNR can be 19.5 times smaller than the FNR of the adapted prior scheme. Our results also show that PIE achieves any desired success probability in estimating the number of occurrences of persistent items.}, number={6}, journal={IEEE-ACM TRANSACTIONS ON NETWORKING}, author={Dai, Haipeng and Shahzad, Muhammad and Liu, Alex X. and Li, Meng and Zhong, Yuankun and Chen, Guihai}, year={2018}, month={Dec}, pages={2429–2442} }
 @article{li_ghosal_2017, title={BAYESIAN DETECTION OF IMAGE BOUNDARIES}, volume={45}, ISSN={["0090-5364"]}, DOI={10.1214/16-aos1523}, abstractNote={Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a $d$-dimensional image ($d=2,3,\ldots$), the boundary can often be described by a closed smooth $(d-1)$-dimensional manifold. In this paper, we propose a nonparametric Bayesian approach based on priors indexed by $\mathbb{S}^{d-1}$, the unit sphere in $\mathbb{R}^{d}$. We derive optimal posterior contraction rates for Gaussian processes or finite random series priors using basis functions such as trigonometric polynomials for 2-dimensional images and spherical harmonics for 3-dimensional images. For 2-dimensional images, we show a rescaled squared exponential Gaussian process on $\mathbb{S}^{1}$ achieves four goals of guaranteed geometric restriction, (nearly) minimax optimal rate adapting to the smoothness level, convenience for joint inference and computational efficiency. We conduct an extensive study of its reproducing kernel Hilbert space, which may be of interest by its own and can also be used in other contexts. Several new estimates on modified Bessel functions of the first kind are given. Simulations confirm excellent performance and robustness of the proposed method.}, number={5}, journal={ANNALS OF STATISTICS}, author={Li, Meng and Ghosal, Subhashis}, year={2017}, month={Oct}, pages={2190–2217} }
 @article{li_staicu_bondell_2015, title={Incorporating covariates in skewed functional data models}, volume={16}, DOI={10.1093/biostatistics/kxu055}, abstractNote={We introduce a class of covariate-adjusted skewed functional models (cSFM) designed for functional data exhibiting location-dependent marginal distributions. We propose a semi-parametric copula model for the pointwise marginal distributions, which are allowed to depend on covariates, and the functional dependence, which is assumed covariate invariant. The proposed cSFM framework provides a unifying platform for pointwise quantile estimation and trajectory prediction. We consider a computationally feasible procedure that handles densely as well as sparsely observed functional data. The methods are examined numerically using simulations and is applied to a new tractography study of multiple sclerosis. Furthermore, the methodology is implemented in the R package cSFM, which is publicly available on CRAN.}, number={3}, journal={Biostatistics (Oxford, England)}, author={Li, M. and Staicu, Ana-Maria and Bondell, H. D.}, year={2015}, pages={413–426} }
 @article{li_ghosal_2014, title={Bayesian Multiscale Smoothing of Gaussian Noised Images}, volume={9}, ISSN={["1936-0975"]}, DOI={10.1214/14-ba871}, abstractNote={We propose a multiscale model for Gaussian noised images under a Bayesian framework for both 2-dimensional (2D) and 3-dimensional (3D) images. We use a Chinese restaurant process prior to randomly generate ties among intensity values at neighboring pixels in the image. The resulting Bayesian estimator enjoys some desirable asymptotic properties for identifying precise structures in the image. The proposed Bayesian denoising procedure is completely data-driven. A conditional conjugacy property allows analytical computation of the posterior distribution without involving Markov chain Monte Carlo (MCMC) methods, making the method computationally efficient. Simulations on Shepp-Logan phantom and Lena test images confirm that our smoothing method is comparable with the best available methods for light noise and outperforms them for heavier noise both visually and numerically. The proposed method is further extended for 3D images. A simulation study shows that the proposed method is numerically better than most existing denoising approaches for 3D images. A 3D Shepp-Logan phantom image is used to demonstrate the visual and numerical performance of the proposed method, along with the computational time. MATLAB toolboxes are made available online (both 2D and 3D) to implement the proposed method and reproduce the numerical results.}, number={3}, journal={BAYESIAN ANALYSIS}, author={Li, Meng and Ghosal, Subhashis}, year={2014}, pages={733–758} }