Ultra-High Dimensional Feature Selection and Mean Estimation under Missing at Random

Next Generation Sequencing (NGS) provides an effective basis for estimating the survival time of cancer patients, but it also poses the problem of high data dimensionality, in addition to the fact that some patients drop out of the study, making the data missing, so a method for estimating the mean of the response variable with missing values for the ultra-high dimensional datasets is needed. In this paper, we propose a two-stage ultra-high dimensional variable screening method, RF-SIS, based on random forest regression, which effectively solves the problem of estimating missing values due to excessive data dimension. After the dimension reduction process by applying RF-SIS, mean interpolation is executed on the missing responses. The results of the simulated data show that compared with the estimation method of directly deleting missing observations, the estimation results of RF-SIS-MI have significant advantages in terms of the proportion of intervals covered, the average length of intervals, and the average absolute deviation.

Mean estimation over numeric data with personalized local differential privacy

The fast development of the Internet and mobile devices results in a crowdsensing business model,where individuals(users)are willing to contribute their data to help the institution(data collector)analyze and release useful information.However,the reveal of personal data will bring huge privacy threats to users,which will impede the wide application of the crowdsensing model.To settle the problem,the definition of local differential privacy(LDP)is proposed.Afterwards,to respond to the varied privacy preference of users,resear-chers propose a new model,i.e.,personalized local differential privacy(PLDP),which allow users to specify their own privacy parameters.In this paper,we focus on a basic task of calculating the mean value over a single numeric attribute with PLDP.Based on the previous schemes for mean estimation under LDP,we employ PLDP model to design novel schemes(LAP,DCP,PWP)to provide personalized privacy for each user.We then theoretically analysis the worst-case variance of three proposed schemes and conduct experiments on synthetic and real datasets to evaluate the performance of three methods.The theoretical and experimental results show the optimality of PWP in the low privacy regime and a slight advantage of DCP in the high privacy regime.

KSKV:Key-Strategy for Key-Value Data Collection with Local Differential Privacy

In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

SOME INTEGRAL MEAN ESTIMATES FOR POLYNOMIALS

In this paper we establish L^q inequalities for polynomials, which in particular yields interesting generalizations of some Zygmund-type inequalities.

Image enhancement via MMSE estimation of Gaussian scale mixture with Maxwell density in AWGN

In optical techniques,noise signal is a classical problem in medical image processing.Recently,there has been considerable interest in using the wavelet transform with Bayesian estimation as a powerful tool for recovering image from noisy data.In wavelet domain,if Bayesian estimator is used for denoising problem,the solution requires a prior knowledge about the distribution of wavelet coeffcients.Indeed,wavelet coeffcients might be better modeled by super Gaussian density.The super Gaussian density can be generated by Gaussian scale mixture(GSM).So,we present new minimum mean square error(MMSE)estimator for spherically-contoured GSM with Maxwell distribution in additive white Gaussian noise(AWGN).We compare our proposed method to current state-of-the-art method applied on standard test image and we quantify achieved performance improvement.

Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

Using self-location to calibrate the errors of observer positions for source localization

The uncertainty of observers＇ positions can lead to significantly degrading in source localization accuracy. This pa-per proposes a method of using self-location for calibrating the positions of observer stations in source localization to reduce the errors of the observer positions and improve the accuracy of the source localization. The relative distance measurements of the two coordinative observers are used for the linear minimum mean square error （LMMSE） estimator. The results of computer si-mulations prove the feasibility and effectiveness of the proposed method. With the general estimation errors of observers＇ positions, the MSE of the source localization with self-location calibration, which is significantly lower than that without self-location calibra-tion, is approximating to the Cramer-Rao lower bound （CRLB）.

Interference cancellation scheme for uplink cognitive radio systems

This paper investigates the interference cancellation （IC） scheme for uplink cognitive radio systems, using the spectrum underlay strategy where the primary users （PUs） and the secondary users （SUs） coexist and operate in the same spectrum. Joint MMSE-based parallel interference cancellation （PIC） and Turbo decoding scheme is proposed to reduce the interference to the PUs, as well as to the SUs, in which the minimum mean square estimation （MMSE） filter is only employed in the first iteration, regarded as the ＂weakest link＂ of the whole detection process, to improve the quality of the preliminary detections results before they are fed to the Turbo decoder. Simulation results show that the proposed scheme can efficiently eliminate the interference to the PUs, as well as to the SUs.

SOME RESULTS CONCERNING GROWTH OF POLYNOMIALS

In this paper, we establish inequalities for polynomials with restricted zeros, which in particular yields interesting generalizations of some Zygmund type inequalities for polynomial.

Forcibly Re-scrambled Randomized Response Model for Simultaneous Estimation of Means of Two Sensitive Variables

Recently,Ahmed et al.(Commun Stat Theory Methods 47(2):324-343,2018)have introduced the idea of simultaneously estimating means of two sensitive variables by collecting one scrambled response and another pseudo-response.In this paper,we extend their idea to the simultaneous estimation of two means by making use of the forced quantitative randomized response model of Gjestvang and Singh(Metrika 66(2):243-257,2007)but then re-scrambling the scrambled scores.This idea of re-scrambling already scrambled responses seems completely new in the field of randomized response sampling.The performance of the proposed forced quantitative randomized response model has been investigated analytically as well as empirically.

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.

Statistical-mechanical analysis of multiuser channel capacity with imperfect channel state information

In this paper, the effect of imperfect channel state information at the receiver, which is caused by noise and other interference, on the multi-access channel capacity is analysed through a statistical-mechanical approach. Replica analyses focus on analytically studying how the minimum mean square error （MMSE） channel estimation error appears in a multiuser channel capacity formula. And the relevant mathematical expressions are derived. At the same time, numerical simulation results are demonstrated to validate the Replica analyses. The simulation results show how the system parameters, such as channel estimation error, system load and signal-to-noise ratio, affect the channel capacity.

On the Third and Fourth Power Moments of Fourier Coefficients of Cusp Forms

The asymptotic formulae for the third and fourth power moments of Fourier coefficients of cusp forms are proved in this paper.

Bayesian edge detector for SAR imagery using discontinuity-adaptive Markov random feld modeling

Synthetic aperture radar（SAR）image is severely affected by multiplicative speckle noise,which greatly complicates the edge detection.In this paper,by incorporating the discontinuityadaptive Markov random feld（DAMRF）and maximum a posteriori（MAP）estimation criterion into edge detection,a Bayesian edge detector for SAR imagery is accordingly developed.In the proposed detector,the DAMRF is used as the a priori distribution of the local mean reflectivity,and a maximum a posteriori estimation of it is thus obtained by maximizing the posteriori energy using gradient-descent method.Four normalized ratios constructed in different directions are computed,based on which two edge strength maps（ESMs）are formed.The fnal edge detection result is achieved by fusing the results of two thresholded ESMs.The experimental results with synthetic and real SAR images show that the proposed detector could effciently detect edges in SAR images,and achieve better performance than two popular detectors in terms of Pratt＇s fgure of merit and visual evaluation in most cases.