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Selecting Optimal Subset to releaseunder Differentially Private M-estimators

from Hybrid DatasetsMeng Wang, Zhanglong Ji, Hyeon-Eui Kim, Shuang Wang, Li Xiong, Xiaoqian Jiang

Abstract—Privacy concern in data sharing especially for health data gains particularly increasing attention nowadays.Now some patients agree to open their information for research use, which gives rise to a new question of how toeffectively use the public information to better understand the private dataset without breaching privacy. In this paper, wespecialize this question as selecting an optimal subset of the public dataset for M-estimators in the framework ofdifferential privacy (DP) in [1]. From a perspective of non-interactive learning, we first construct the weighted privatedensity estimation from the hybrid datasets under DP. Along the same line as [2], we analyze the accuracy of the DPM-estimators based on the hybrid datasets. Our main contributions are (i) we find that the bias-variance tradeoff in theperformance of our M-estimators can be characterized in the sample size of the released dataset; (2) based on thisfinding, we develop an algorithm to select the optimal subset of the public dataset to release under DP. Our simulationstudies and application to the real datasets confirm our findings and set a guideline in the real application.

Index Terms—differential privacy, M-estimators, hybrid datasets.

F

1 INTRODUCTION

A common challenge in clinical studies is accessingsufficient amount of data of the subjects with a condi-tion of interest. This becomes even more challengingwhen the study is set in a limited setting of a singleinstitution and targets a rare disease. Hence, datasharing is of great interest to biomedical research foraccelerating scientific discovery which can be trans-lated into novel treatment methods. However, reveal-ing sensitive information about patients or individualsis an important privacy concern in sharing healthcaredata. This concern is gaining particularly increasing at-tention in healthcare as shown in [3–8]. Nowadays, toprotect private information to some extent, accessingraw data from multiple institutions requires not onlyInstitutional Review Boards (IRBs) approval but alsoconforming to the institutional Data Use Agreement(DUA) conditions, which becomes a time-consumingand laborious process. It would be ideal to have amechanism to support healthcare data analysis in a

• M. Wang was with the Department of Biomedical Informatics,University of California at San Diego, CA, 92093 U.S., and now iswith the Department of Genetics, Stanford University, CA, 94305,U.S.E-mail: mengw1@stanford.edu

• Z. Ji, H. Kim, S. Wang, X. Jiang are with the Department ofBiomedical Informatics, University of California at San Diego, CA,92093 U.S.;

• L. Xiong is with the Department of Computer Science, EmoryUniversity, GA, 30322 U.S.,

Manuscript revised September, 2017.

privacy-preserving manner by maximizing the utilityof available dataset while reducing the burden of un-dergoing the complex process around IRB and DUA.

In the literature of protecting private informationfrom synthetic data, Rubin first proposed the idea offully synthetic data to represent “no actual individual”[9], which attracted a lot of attentions. Later, Reiterprovided guidance on specifying the number and sizeof Rubin’s synthetic data generation model to ensurevalid statistical procedures [10]. But Abowd and Vil-huber discussed potential “disclosure risk” of suchmethod through inference disclosure [11]. In the impu-tation model. [12] described partial synthesis of surveydata collected by the Cancer Care OutcomesResearchand Surveillance (CanCORS) project and discussed thekey steps of selecting variables for synthesis, specifi-cation of imputation models, measurements of datautility, and disclosure risk.

Due to the risk concerns that were previouslyidentified, modern synthetic data generation methodsmostly driven by differential privacy. Differential pri-vacy (DP) [1] uses perturbation techniques giving amathematically rigorous privacy guarantee even if anattacker has arbitrarily auxiliary information. Thereare many and an increasing number of research fieldsin applying the concept of DP and DP mechanisms tomachine learning [13], statistics [14; 15] and medicineapplication [6; 16–18]. Under the framework of DP,Mohammed et al. developed decide-tree based syn-

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thetic data release using a top down model that dy-namically specifies sibling nodes and perturbs countssatisfying differential privacy [19]. Machanavajjhalaet al. introduced another synthetic data generationmodel for commuting patterns of the population ofthe United States [20], which are very sparse in nature.Hall et al. developed yet another method to releasedifferentially private functional data in the reproduc-ing kernel Hilbert space (RKHS) by introducing an ap-propriate Gaussian process to the function of interestin [21]. These methods only retain utility for specialclasses of functions, which are not generalizable tomedical data at large.

In reality, some patients are willing to sign the openconsents to make their information freely available,which gives rise to a new problem of integrating thepublic information to infer from the private infor-mation. Several works show that hybridizing publicand private information can significantly improve theutility of the DP mechanisms in specific learning goals.In logistic regression, Ji et al. [22] developed DP algo-rithm based on importance sampling for the hybriddatasets. A recent work [23] modified the update stepin Newton-Raphson method in logistic regression un-der DP based on public data and private data together.Another similar work [24] developed a hybrid DPsupport vector machine (SVM) model that also takesadvantage of aforementioned hybrid datasets. Thesemodels are still specific to certain machine learningmodels.

Different from existing task-specific models, wepropose a new algorithm to publish data under DPusing public and private datasets. It is not designedfor a special task but the algorithm works for a gen-eral task such as estimation, regression and classifi-cation. To achieve this goal, we construct a weightedprivate density from the hybrid datasets under DP(in Section 3). We focus on protecting privacy in M-estimators, which are well studied in statistics [25]without privacy concerns. Under some regularities,M-estimators are robust to the outliers. This propertymakes it possible for M-estimators to maintain highutility under DP as discussed in [14].

Our workflow to infer the M-estimators under DPis summarized in Figure 1. Consider a situation thatthe researcher (the data user) would like to conductexploratory data analysis to get M-estimators (for ex-ample, the coefficients of the covariates in the logisticregression) over a private dataset before making theformal IRB application. The researcher asks for a bestmodel under DP from a trusted third party (TTP),which can access both public and private datasets. Oneway is to directly infer the M-estimators from a privatedataset under DP. [2] provides a good frameworkfor low dimensional data by perturbing the privatehistogram but this method could become useless for

high dimensional data. Noticing the related publicinformation, the TTP could take the result from thepublic dataset to represent that for the private dataset.However, we need to be extra careful here. If thedistribution of the public dataset is the same as that ofthe private dataset, it will be perfect to directly inferfrom the public dataset without costing any privacybudget. But in most cases, the open-consent popu-lation itself could have bias, such as the young andhigh educated people are probably more willing tomake their information open for research so that somecovariate in the open-consent population has smallervariation than that in the private population. Henceif we directly learn from the data from consentedpopulation, the results could not fully represent theprivate data.

Due to the possible bias from public dataset, howto effectively use the public information to betterunderstand the private information without releasingprivacy is a challenging question. Our main contri-butions (in Section 4) are (i) we provide a theoreticalsupport that there could exist an optimal subset of thepublic dataset, not always the whole public dataset,giving the highly accurate and privacy protected M-estimators and (ii) we further develop a DP selectionprocedure to obtain this optimal subset. Given theprivate data of interest, our method generates a DPhybrid cohort by referencing the public data to pickthe most representative samples to facilitate the study,which ensures the valid statistical procedures and pre-vents against inference disclosure problem in Rubin’scase [9]. The simulation studies and an applicationin real datasets in logistic regression (in Section 5)show that the optimal public subset from our selectionprocedure performs better than the perturbed his-togram method in [2] and promisingly our procedurecan be applied in high dimensional data. We discussfuture directions and limitations and finally make aconclusion in Section 6.

2 PRELIMINARY

2.1 Setting of the problemLet D = {x1, . . . , xnD} be the private dataset andE = {y1, . . . , ynE} the public dataset where y’s aredistinct. Each data point xi ∈ D is a realization of arandom variable X from a density function fD andyi ∈ E a realization of Y from fE . We generally callthe density function for the probability mass functionof a discrete variable. We assume Xi

iid∼ fD, Yiiid∼ fE

and X’s and Y ’s are independent. Due to the biasfrom open-consent preselection, we consider generallyfD 6= fE . Denote the sample space of X by XD and Yby XE .

Notation. The symbol | · | of a set means the cardi-nality of the set. For a, b ∈ R, denote a∨b = max{a, b}.

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Fig. 1. Workflow of the proposed framework. (1) A trusted third party (TTP) can access both public and private datasets. (2) A datauser would like to infer an M-estimator over a private dataset. (3)The TTP compares the results from (i) directly learning from thepublic dataset (ii) applying our DP selection procedure to learn from an optimal subset of the public dataset (iii) in low dimension,applying the perturbed histogram method only learning from the private dataset. (4) The TTP reports the user the best model underDP to learn the private information.

For two sequences of reals (an) and (bn): an ∼ bnwhen an/bn → 1; an = o(bn) when an/bn → 0;an = O(bn) when an/bn is bounded. For two realrandom sequences (an), (bn), an = Op(bn) if an/bn isbounded in probability, i.e., supn P(|an/bn| > x) → 0as x → ∞. For a random variable X and densityfunction f , X ∼ f means X has density F . X ∼Laplace(λ) means X has density 1

2λ exp (−|x|/λ).

2.2 Differential PrivacyDifferential privacy proposed by [1] provides guaran-tees on the privacy of the dataset against any arbitraryexternal attacks. The concept of differential privacy(DP) is designed to protect the worst case that the at-tacker knows the information of all the patients exceptone. To protect this case, DP considers two neighbordatasets D and D′ which differ in only one patient.The rigorous definition of ε-differential privacy is inDefinition 1. The definition of DP is symmetric inD and D′. By the comparability property of DP inDefinition 4, it is easily applied to the case where Dand D′ differ in more than one patients.

Laplace mechanism [1] in Definition 3 is one ofmechanisms that achieve ε-differential privacy byadding Laplace noise on private information, whichis the mechanism we use in this paper. The amount ofnoise added is determined by the privacy parameterε, and the sensitivity of the statistics in Definition 2which characterizes the worst case among all neighbordatasets.

Definition 1. (Differential Privacy [1]) A randomizedmechanism M is ε-differentially private if, for all datasetsD and D′ which differ on at most one individual and forany measurable subset S of the range ofM,∣∣∣∣ log

P(M(D) ∈ S)

P(M(D′) ∈ S)

∣∣∣∣ ≤ ε, ∀S ⊆ range(M).

In Definition 1, D and D′ are called neighbor datasetswith Hamming distance H(D,D′) = |D \ D′| =

|D′ \D| = 1. ε is the privacy parameter. Small ε tellsthe distribution of M(D) and M(D′) is not easilydistinguishable so that in some sense this protectsthe information of the patients that D and D′ aredifferent in. Note here the randomness ofM is in theperturbation added to protect privacy not in the dataitself.

Definition 2. (Sensitivity for Laplace Mechanism [1]) Thesensitivity of a statistic T in the Laplace Mechanism is thesmallest number S(T ) such that

‖T (D)− T (D′)‖1 ≤ S(T ),

for all D,D′ with H(D,D′) = 1.

Definition 3. (Laplace Mechanism [1]) Releasing(T (D) + noise) where noise has Laplace(S(T )/ε) dis-tribution is an ε-differentially private mechanism satisfyingDefinition 1, where S(T ) is the sensitivity of T in Defini-tion 2.

Definition 4. (Sequential Composition [1]) If we ap-ply k independent statistics T1, . . . , Tk with correspond-ing privacy parameters ε1, . . . , εk, then any functiong(T1, . . . , Tk) is

∑ki=1 εi-differentially private.

2.3 M-estimator

In our case, the parameter we are interest in is the onefor the private distribution,

θ∗(XD) = arg minθ∈Θ

MXD (θ),

where MXD (θ) =

∫XD

m(x, θ)fD(x)dx, (1)

and Θ is the parameter space of θ and m(x, θ)is called contrast function. Given the private datasetD = {x1, . . . , xnD} and under the independence as-

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sumption of X’s, the M-estimator for θ∗(XD) is theminima of the sum of contrast functions,

θ(D) = arg minθ∈Θ

MD(θ),

where MD(θ) =∑xi∈D

1

nDm(xi, θ). (2)

For example, taking m(x, θ) as absolute loss function|x − θ|, θ is the sample median; taking m(x, θ) assquared loss function (x − θ)2, θ is the sample mean;taking m(x, θ) as the negative log-likelihood function,θ is maximum likelihood estimator. More examplesand properties of M-estimators can be found in [25].

Since D is private, we can not release θ(D) in (2)without any privacy protection. We take θ(D) as abaseline to evaluate the performance of the privacyprotected M-estimator. Our goal is to develop a M-estimate under DP integrating public information toachieve high utility.

3 DP M-ESTIMATOR FROM HYBRIDDATASETS

3.1 Our DP M-estimator

In a non-interactive fashion, a direct way to releasea DP version of the M-estimator is to perturb thedensity function. Once we get a privacy protecteddensity, based on the synthetic data points, we cannot only ask for the mean, the median of the privatedataset, but also learn the private dataset form linearregression, logistic regression, in a series of estimatingM-estimators.

Only based on the private dataset D, Lei in [2] pro-posed a method to get DP M-estimator from perturbedhistogram. The key is to perturb the private densityfunction under DP. His strategy is as follows. We firstpartition the sample space (assuming bounded) intocubic cells with equal bandwidth in each dimension,next add Laplace noise to the counts of the points in Dlying in each cell under DP, then generate the syntheticdata by replicating the center point in each cell in thenumber of the DP perturbed count, finally obtain theDP M-estimator from the synthetic points. But thismodel does not scale well if the dimensionality is highsince adding noise to all high dimensional cells mayrender the estimated density useless. In our setting,this problem can be alleviated if we carefully make useof the public dataset. We compare their performancesin the simulation studies in Section 5.

At the presence of the related public dataset, wewould like to take use of the public data points to rep-resent the private data points in a privacy-preservingmanner and construct a DP hybrid weighted densityfunction. Our idea is to assign a weight to each distinctpublic point, where the weight in one public point is

proportional to the count of the private points suchthat they are closer to this point rather than anyother public points. In statistics, the hybrid weighteddensity is formulated in

fhybD (x) =nE∑i=1

wi1{x=yi}, (3)

where wi =|Dyi |nD

, yi ∈ E,

Dyi ={x ∈ D : ‖x− yi‖ ≤ ‖x− yj‖, for all j 6= i}.

By the definition of Dyi , we can see if a point in Esurrounded by more points in D, it gains large weightand otherwise it gains small weight. In this way, itrelieves the bias of estimating from E to some extent.

In (3) to estimate the private density, we relate itsempirical probability to that of the public empiricalprobability by the weight wi. Without privacy con-cerns, there are several ways in density estimation.The book [26] summarizes several approaches, suchas moment matching, probabilistic classification, anddensity-ratio fitting with kernel smoothing. In this pa-per, our contribution is not to find an optimal way toestimate private density under DP but instead underthe constructed hybrid weighted density to establisha procedure to better use the public information toreduce unnecessary privacy budget allocation andtherefore improve the utility.

Definition 5. (DP M-estimator from hybrid datasets.)Under the notation in Section 2, the DP M-estimator fromhybrid datasets is

θ(E, w) = arg minθ∈Θ

M(E,w)(θ), (4)

where M(E,w)(θ) =nE∑i=1

wim(yi, θ), yi ∈ E,

wi = wi + Zi/nD, wi =|Dyi |nD

,

Dyi = {x ∈ D : ‖x− yi‖ ≤ ‖x− yj‖ for all j 6= i}

Ziiid∼ Laplace(2/ε), i = 1, . . . , nE .

Proposition 1. {wi}nEi=1 in Definition 5 satisfies ε-differential privacy.

Proof. To better understand the concept of DP, wegive the proof for Proposition 1. Suppose D′ andD are neighbor datasets, and xi0 ∈ D \ D′ andxi′0 ∈ D′ \ D. Let T (D) = (|Dy1 |, . . . , |DynE

|) andT (D′) = (|D′y1 |, . . . , |D

′ynE|). Since we add indepen-

dent Laplace noise to T , it suffices to show that thesensitivity of T is 2. In the case that xi0 and xi′0 havethe same representative point in E, then T (D) =T (D′). In the other case that they have different rep-resentatives, denote xi0 ∈ Dyj and xi′0 ∈ D

′y′j

, where

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yj 6= y′j . Then |Dyj | = |D′yj |+ 1 and |Dy′j| = |D′y′j | − 1

and T (D) and T (D′) are the same in other elements.Hence, ‖T (D)−T (D′)‖1 ≤ 2 for all neighbor datasetsD and D′, which gives S(T ) = 2 by Definition 2.

As we can see in Definition 5, adding Laplace noisecan lead some weights wi’s negative. Many negativeweights can cause non-convexity ofM(E,w)(θ). Hence,it is necessary to define a truncated version of theweights. Parallel to the perturbed histogram withnonnegative counts in [2], we define the truncatedperturbed weights and obtain the DP M-estimatorfrom hybrid datasets with nonnegative weights inDefinition 6.

Definition 6. (DP M-estimator from hybrid datasets withnonnegative weights.) In the same notation in Definition 5,replacing wi’s by

w+i = wi ∨ 0,

the DP M-estimator from hybrid datasets with nonnegativeweights is

θ(E, w+) = arg minθ∈Θ

M(E,w+)(θ),

where M(E,w+)(θ) =nE∑i=1

w+i m(yi, θ), yi ∈ E.

Proposition 2. {w+i }

nEi=1 in Definition 6 satisfies ε-

differential privacy.

Proof. By Definition 6, w+i is a measurable function of

wi. From Proposition 1, {wi}nEi=1 satisfies DP so does{w+

i }nEi=1 by Definition 1.

3.2 Algorithm to Get Our DP M-estimatorTo obtain the DP M-estimator from hybrid datasetsin practice, we summarize the steps in the Algorithm1. We first rescale both the public dataset and theprivate dataset to [0, 1]p where p is the data dimension;next calculate the weights in Definition 5 from therescales datasets to establish the hybrid density; thenadd Laplace noise to the weights under DP; finallywe obtain the DP M-estimator for the user assignedcontrast function. To obtain the DP M-estimator withnonnegative weights, the steps follow from Algorithm1 except replacing w by w+ in Definition 6.

Before constructing the hybrid density, we add apreprocessing step to rescale the datasets in Step 1.We claim that it is a necessary step from two aspects.In one aspect, rescaling the data in each dimension to[0, 1] makes the scales of all dimensions comparable.For a categorical variable, suppose it has k categories.We first transform the labels to k-dimensional dummyvariables, (1, 0, . . . , 0) for label 1, (0, 1, 0, . . . , 0) forlabel 2, . . . , (0, . . . , 0, 1) for label k. Hence, the l2distance between two different labels is

√2. We further

divide the transformed labels by√

2 so that the l2distance between any two categories inside [0, 1]. Inanother aspect, we need to guarantee privacy protec-tion in each step involving the private dataset. Hencewe rescale the private dataset according to the rangeof the public dataset in case that the private datapoint outside the range of public dataset could exposeprivacy.

To see the effect of rescaling, we first illustrate theoriginal datasets and rescaled ones from a simula-tion in Figure 2. In the simulated data, we considerthe private dataset D containing nD = 104 pointshas a two-dimensional covariate XD generated fromMVN((0, 0)T , diag(1, 1)) where diag(·) denotes a di-agonal matrix and a 0-1 response variable generatedfrom a logistic regression model based on XD and co-efficient βD = (0.2, 0.4), where MVN is the abbrevia-tion for multivariate normal distribution. Similarly forthe public dataset E, nE = 104, XE is generated fromMVN((0, 0)T , diag(0.5, 1)) and βE = (0.5,−0.1). Wesimulate the case that D and E have different distri-butions due to open-consent bias. The lower panels inFigure 2 show the rescaled private and public datasets.We can see since the covariate-1 has less variation inoriginal E than that in original D, after rescaling Daccording to the range of E, several points in D inlarge deviation in covariate-1 are compressed to theboundaries in the rescaled D. Rescaling step changesthe relative positions of two data points. However,what really matters is how much it changes the den-sity weights because the change in the weights willmore or less affect the accuracy of the M-estimator. Toillustrate this idea, we compare the weights calculatedfrom original D and E to those from rescaled D andE and highligt the points with different weights fromtwo ways of calculation in rescaled E in Figure 3.We can see the points with large different weightsmainly lie in the boundaries of covariate-1. (Note that0-1 response variable also contribute to the calculationof the weights.) From this simulation, we get an ideathat the step of rescaling could add more variation onthe weights especially on the points compressed to theboundaries. This is another cost of protecting privacy,besides adding Laplace noise on the weights. If thepublic dataset and the private are not quite differentlike in this simulation, the number of the points thathave more than 2 counts different in weights is only42 out of 104 points. If the model is not extremelysensitive to the outliers, we think a few points withlarge deviated weights could not make a large dif-ference to the final result. On the other hand, thisindicates that if the public dataset and the privateare extremely different such that in some dimensionthey have quite different distributions, rescaling stepmay deteriorate the accuracy in the final estimation.In this case, we suggest finding a more comparable

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public dataset in order to apply the privacy-protectionprocedures. More discussion is in Section 6

Algorithm 1: To obtain DP M-estimator from hybriddatasets.

Input: private dataset D, public dataset E with dis-tinct points, privacy parameter ε and objective func-tion M .Output: DP M-estimator from hybrid datasetsθ(E, w).

1) To rescale D and E to [0, 1]p where p is the dimen-sion of the data points. Combine D and E by thevariables in E. Let zij be i-th observation in j-thvariable of the combined dataset. If j-variable iscontinuous, rescale zij to

zij =ztruncij − ajbj − aj

where aj = mini=1,...,nD+nE

{zij ∈ E},

bj = maxi=1,...,nD+nE

{zij ∈ E},

ztruncij = aj1{zij<aj} + bj1{zij>bj} + zij1{aj≤zij≤bj}

If j-th variable is categorical with k-labels, writezij in terms of k-dimensional dummy variablethen rescale it by dividing

√2.

2) To find the weights wi’s in Definition 5 based onrescaled hybrid datasets from Step 1. Define x’s andy’s are the points in the rescaled dataset D and therescaled E. The weight associated with yi ∈ E iswi = |{x ∈ D : ‖x−yi‖2 ≤ ‖x−yj‖2, i 6= j}|/nD .

3) Adding Laplace noise to the weights. To eachwi obtained in Step 2 adding independentLaplace noise, wi = wi + Zi/nD where Zi

iid∼Laplace(2/ε), i = 1, . . . , nE .

4) To obtain DP M-estimator from hybrid datasets. Min-imizing the objective function M(E,w)(θ) in Def-inition 5 where w is obtained in Step 3, getθ(E, w) = arg minθM(E,w)(θ).

4 OPTIMAL SUBSET IN RELEASING PUBLICDATASET UNDER DPIn the previous section, we establish the DP M-estimator from hybrid datasets. In this section, wefirst evaluate its performance from bias and variancedecomposition Subsection 4.1. We find that this biasand variance tradeoff can be characterized in the num-ber of the public data points to release. This makesit possible that there may exist an optimal subset ofpublic dataset which could give more accurate M-estimators under DP. This is our main contribution.In Subsection 4.2, we further develop an algorithm toselect the optimal subset under DP in practice.

4.1 Bias and Variance TradeoffAt a first look, one may doubt since we have the publicdataset, why only to use part of them. It is true withmore points in the public dataset, they can be morerepresentative of the private dataset. However, underthe framework of DP, we need to add Laplace noise tothe weights of the public data points. More points torelease, more noise to add. Hence, there is a tradeoffbetween bias and variance, where the bias is fromusing public dataset to estimate the private datasetand inadequate sample size while the variance fromadding noise. We find this tradeoff is in the samplesize of the public subset. It is analogous to the casewhere the whole dataset is private where the tradeoffis in the bandwidth of the perturbed histogram in [2].However there how to choose the cell bandwidth isa tricky question in practice but in our case, selectingthe public subset can be optimized.

To analyze the accuracy of our M-estimator, weconsider the contrast function is well-defined in thesame conditions as in [2]. Assume the contrast func-tion m(x, θ) : X × Θ → R where X = XD ∪ XEis the union of the private and public sample spacesand Θ is the parameter space of θ, satisfies condition(A1)− (A3) listed below.

(A1) g(x, θ) := ∂∂θm(x, θ) exists and ‖g(x, θ)‖2 ≤ C1

on X ×Θ where C1 is a constant;(A2) g(x, θ) is Lipschitz in x and θ: ‖g(x1, θ) −

g(x2, θ)‖2 ≤ C2‖x1 − x2‖2 for all θ ∈ Θ and‖g(x, θ1)−g(x, θ2)‖2 ≤ C2‖θ1−θ2‖2 for all x ∈ X ,where C2 is a constant;

(A3) m(x, θ) is convex in θ for all x ∈ X andMXD (θ) is twice continuously differentiable withM′′

XD (θ∗(XD)) :=∫XD fD(x) ∂∂θg(x, θ∗(XD))dx

positive definite where MXD (θ) and θ∗(XD) aredefined in (1).

To quantify the bias from using weighed densityfrom hybrid datasets to estimate the private density,we take the measurement of the distance between twodatasets D and E′ ⊆ E.

d(D,E′) =1

nD

∑x∈D

miny∈E′

‖x− y‖2. (5)

In (5), d(D,E′) takes the average of the distancebetween a point x in D and E′ (i.e., miny∈E′ ‖x− y‖2)over all the points in D. Without considering DP,obviously d(D,E′) ≥ d(D,E) for E′ ⊆ E. Hence,increasing the sample size of the released datasetdecreases the distance to the private dataset D.

Lemma 1. Let g(x, θ) = ∂∂θm(x, θ). Under the notation

in Section 2 and condition (A2), we have∥∥∥∥ nE∑i=1

wig(yi, θ)−nD∑j=1

1

nDg(xj , θ)

∥∥∥∥2

= O(d(D,E)),

(6)

1041-4347 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TKDE.2017.2773545, IEEETransactions on Knowledge and Data Engineering

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−5.0

−2.5

0.0

2.5

5.0

−5.0 −2.5 0.0 2.5 5.0

covariate 1

cova

riate

2

in private dataset D

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−5.0

−2.5

0.0

2.5

5.0

−5.0 −2.5 0.0 2.5 5.0

covariate 1

cova

riate

2

in public dataset E

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0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

covariate 1

cova

riate

2

in rescaled private dataset D~

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0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

covariate 1

cova

riate

2

in rescaled public dataset E~

Fig. 2. Scatter plots of two covariates in the original private dataset D (upper left), original public dataset E (upper right) and rescaledprivate dates D (lower left), rescaled public dates E (lower right). The dots in blue indicate response 0 and in red indicate response 1.

indicator for weight difference ● ●FALSE TRUE response ● 0 1

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0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

covariate 1

cova

riate

2

2098 at−most−2−w−different points in rescaled public dataset

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0.00

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1.00

0.00 0.25 0.50 0.75 1.00

covariate 1

cova

riate

2

42 greater−than−2−w−different points in rescaled public dataset

Fig. 3. Scatter plots of two covariates in the rescaled public dataset E. The red dots indicates the points whose weights calculatedfrom (D, E) have at most 2 counts difference (in the left panel), or greater than 2 counts difference (in the right panel), compared tothe corresponding weights calculated from (D,E).

where d(D,E) is defined in (5).

Proof. To prove Lemma 1, recall that wi = |Dyi |/nDin Definition 5 where Dyi = {x ∈ D : ‖x − yi‖2 ≤‖x−yj‖2, i 6= j}. Since the points in E are distinct, foreach xj ∈ D, there exists a unique point ykj ∈ E suchthat ykj = arg miny∈E ‖xj − y‖2. Based on the def-inition of Dyi , |Dyi |g(yi, θ) =

∑{j:xj∈Dyi}

g(ykj , θ).Since g(x, θ) is Lipschitz in x for all θ by condition

(A2), we have

(LHS) in (6) =

∥∥∥∥ nD∑j=1

1

nDg(ykj , θ)−

nD∑j=1

1

nDg(xj , θ)

∥∥∥∥2

≤ C2 ·1

nD

nD∑j=1

‖ykj − xj‖2 = C2 · d(D,E),

which completes the proof.

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Proposition 3. Under the notation in Section 2 and thecontrast function m satisfing conditions (A1)-(A3), thereexists a local minimizer θ(E, w) for M(E,w)(θ) such that

‖θ(E, w)− θ∗(XD)‖2

=Op

(nE log(nE)

nD∨ d(D,E) ∨ 1

√nD

),

as nE , nD →∞,

where M(E,w)(θ) is in Definition 5, the true parameterθ∗(XD) for MXD (θ) in (1) and d(D,E) is defined in (5).The same result holds for θ(E, w+) in Definition 6.

The proof for Proposition 3 is a straightforwardextension of Theorem 3 in [2], hence we only sketchthe key ideas here. To get the convergence rate ofθ(E, w), applying Lemma 9 in [2], it suffices to showthat supθ∗(XD)∈Θ0

‖M ′(E,w)(θ) −M ′XD (θ)‖2 where Θ0

is a compact neighbor set around θ∗(XD), is boundedin the same order as ‖θ(E, w) − θ∗(XD)‖2. Recallwi = wi + Zi/nD where Zi is the Laplace noise andwi = |Dyi |/nD in Definition 6. In our case, we get thebias-variance decomposition in

M ′(E,w)(θ)−M ′XD (θ)

=nE∑i=1

wig(yi, θ)−∫XD

g(x, θ)fD(x)dx

=nE∑i=1

ZinD

g(yi, θ)

+

( nE∑i=1

|Dyi |nD

g(yi, θ)−nD∑i=1

g(xi, θ)

nD

)

+

( nD∑i=1

g(xi, θ)

nD− EfD g(X, θ)

). (7)

The first term in (7) comes from the variation error byadding Laplace noise; the second term in the parenthe-sis comes from the bias by using the weighted densityfrom hybrid datasets; the third term in the parenthesiscomes from the sampling error of inadequate samplesize. The convergence rates in the first and third termsare a direct extension from Theorem 3 in [2] and theerror bound for the second term is from Lemma 1. Theconvergence rate of θ(E, w+), by Definition 6 followsin the same fashion as Theorem 5 in [2].

From Proposition 3, we can see that there is a clearbias-variance tradeoff in the estimation accuracy andit can be characterized by the sample size of the releasedataset. The term (nE log(nE)/nD) in the convergencerate of θ(E, w) is increasing in nE while d(D,E) isdecreasing in nE . This motivates us to find an optimalsubset of public dataset to better estimate the privatedataset especially in practical application.

4.2 Selection AlgorithmTo implement the procedure of selecting optimal pub-lic subset for M-estimators under DP, we summarizethe steps in Algorithm 2. We add Laplace noise in allthe steps that involve private dataset D to make surethe whole process guarantees privacy. Algorithm 2 canbe implemented for the procedure of selecting the op-timal subset from the hybrid density with nonnegativeweights by replacing w by w+ in Definition 6.

To find the optimal public subset under DP, Algo-rithm 2 contains three parts. Part I: to get a sequenceof subset candidates {E(i)}ki=1. After rescaling thedatasets to D and E in step 1, we get the weightsfor all the points in E then add Laplace noise to thoseweights in step 2. We order all the points in E by theirDP weights in step 3. We consider if a data point in Egains more weight, this point is more representative tothe private points and thus should have high priorityto be selected. Assigning a sequence of the samplesizes {ni}ki=1, {E(i)}ki=1 is a sequence of increasingsets of the ordered points, i.e., E(1) contains the pointsin the first n1 largest DP weights and E(2) containsthe points in the first n2 largest DP weights and soon so forth. Regarding to choose {ni}ki=1, we takeinto the consideration of the trend of d(D, E). FromProposition 3, the upper bound of the estimation errordepends on d(D, E), and d(D, E(i)) is increasing inthe size of E(i). Figure 4 shows that d(D, E) decreasesfirst then stays flat in both a low dimension case p = 2and high dimension case p = 100 in the simulationsof multivariate normal (MVN) variables. From ouranalysis, the estimation error from adding Laplacenoise is increasing in ni. Hence, we would expectthat the turning point for the estimation error can nothappen where d(D, E(i)) is flat. Therefore, the trendof d(D, E(i)) gives us a sense on the general range ofthe size of the optimal public subset.

Part II: to get DP M-estimators from candidatesubsets {E(i)}ki=1. In step 4, we apply Algorithm 1 toget M-estimators under DP based on each data pair(E(i), D). Applying the sequential composition rulein Section 2.2 (since we add Laplace noise indepen-dently), we equally arrange the privacy parameter ε2

to the weights of the weighted density under each datapair.

Part III: to release the estimation error from eachcandidate subsets {E(i)}ki=1 under DP and pick theoptimal subset. In step 4, we evaluate the performanceof θ(E(i), w) by comparing to the baseline θ(D). Onecan take criterion as ‖θ(E(i), w)− θ(D)‖2. But in orderto release the criterions, we need to perturb themunder DP in step 5. Considering the case that thesensitivity of the criterion is large, then selecting theoptimal subset based on the noisy criterions could beuseless. From the prospective of privacy, we consider

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●

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0.00

00.

005

0.01

00.

015

0.02

0

in dimension p = 2

sample size in scaled public dataset E~

(i)

d(D~

, E~(i)

)

100 1600 3100 4600 6100 7600 9100

●

●

●

●

●

●●

●●

● ● ● ● ● ● ● ● ● ● ●3.30

3.35

3.40

3.45

3.50

3.55

3.60

in dimension p = 100

sample size in scaled public dataset E~

(i)

d(D~

, E~(i)

)

100 1600 3100 4600 6100 7600 9100

Fig. 4. d(D, E(i)) decreases with the sample size of E(i) under dimension p = 2, 100, where E(i) is the scaled subset of E withsorted points defined in Algorithm 2 and the sample sizes of {E(i)} start from 100 to nE with increment 500. In this simulation, D is aset of 104 points independently generated from MVN((0, . . . , 0)>, Ip×p) and E is a set of 104 points independently generated fromMVN((0, . . . , 0)>, 0.5Ip×p), where Ip×p is the identity matrix.

a transformation function h on θ with small sensitivityto guarantee a certain utility. We require the functionh is Lipschitz then ‖h(θ(E(i), w)) − h(θ(D))‖2 sharesthe same convergence rate as ‖θ(E(i), w)− θ(D)‖2 andthus the bias-variation tradeoff could still exist. In step6, the subset with the smallest criterion is the optimalset to release.

Algorithm 2: To obtain optimal subset of publicdataset for M-estimators under DP.

Input: private dataset D, public dataset E with dis-tinct points, privacy parameters ε1, ε2, ε3, objectivefunction M and transformation function h.Output: Optimal subset of E with associated weightsunder DP.

1) To rescale D and E to D and E according to Step1 in Algorithm 1.

2) To get noisy weights wi = wi(E, D) for the pointsin E according to Step 2-3 in Algorithm 1 underprivacy parameter ε1.

3) To sort the points in E in the order of w(E, D)obtained in Step 2 in decreasing order.

4) Consider a sequence of increasing sets {E(i)}ki=1

of ordered points in E. To apply Algorithm 1 toeach data pair (E(i), D) under privacy parame-ter ε2/k to get its M-estimator θ(E(i), w) wherew = w(E(i), D). To evaluate the performance ofθ(E(i), w) by the criterion ti := ‖h(θ(E(i), w)) −h(θ(D))‖2, i = 1, . . . , k.

5) To add independent Laplace noise to the perfor-mance criterion ti’s obtained in Step 4. Releas-ing ti = ti + Zi, i = 1, . . . , k, where Zi

iid∼Laplace(S(ti)/ε3) and S(ti) is the sensitivity ofti.

6) To select the optimal subset E(i∗) where i∗ =

arg mini=1,...,k ti and release E(i∗) and its noisyweights.

5 SIMULATION AND APPLICATION

In this section, we take logistic regression as an exam-ple to implement Algorithm 1-2. Both simulation stud-ies and application on the real datasets are coherent toour finding that bias-variance tradeoff phenomenoncan be characterized in the sample size of the releaseddataset. Our example sets a guideline to select optimalsubset under DP in practice.

5.1 Simulation Studies

We simulate the private dataset D and public datasetE from logistic regression model. We set nD = 104,nE = 104 and consider the covariates in a lowdimensional space with p = 2 and a high dimen-sional space with p = 100. In the low dimen-sional case, to get D, we first generate independentcovariates (XD

i1 , XDi2 ) from N ((0, 0)>, diag(1, 1)),

i = 1, . . . , nD . Given (XDi1 , X

Di2 ), we gener-

ate Y Di |(XDi1 , X

Di2 ) ∼ Bernoulli(pDi ) and model

logit(pDi ) = βD1 XDi1 + βD2 X

Di2 setting βD1 , β

D2

iid∼Unif(−1, 1) where logit(p) = log

( p1−p

). Then D is

a set of nD (Y Di , XDi1 , X

Di2 )’s. Similarly, to get E, we

first generate independent covariates (XEi1, X

Ei2) from

N ((0, 0)>, diag(0.5, 1)), i = 1, . . . , nE then generateY Ei |(XE

i1, XEi2) ∼ Bernoulli(pEi ). Model logit(pEi ) =

βE1 XEi1 + βE2 X

Ei2 setting βE1 , β

E2

iid∼ Unif(0, 1/2). ThenE is a set of nE (Y Ei , X

Ei1, X

Ei2)’s. In the high dimen-

sional case, for D, we consider (XDi1 , . . . , X

Di100) from

N ((0, . . . , 0)>100, I100×100) and βDiiid∼ Unif(−1, 1), i =

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1, . . . , nD . For E, we consider (XEi1, . . . , X

Ei100) from

N ((0, . . . , 0)>100, 0.5I100×100) and βEiiid∼ Unif(0, 1/2),

i = 1, . . . , nE .Based on the simulated datasets, we investigate

how the sample size of released public dataset effectsthe performance of logistic regression under DP. In thesimulation, we set (ε1, ε2, ε3) = (0.8ε, 0.2ε, ε) whereε = 0.5, 1, 3, so the total privacy parameter is 2ε bythe sequential composition of DP. Here we put moreweight to ε1 than ε2 from our practical experience.How to optimize the allocation of the total privacybudget can be further investigated. To ImplementAlgorithm 2, for p = 10, we start our search of optimalsubset candidates {E(i)}ki=1 from the size 10 up to3000 with increment 50, and for p = 100, start from thesize 100 up to 10000 with increment 200. In the simula-tions we choose a large range to get the optimal subsetbut with the information of the decreasing range ofd(D, E) in Figure 4, we can further narrow down oursearch to save more privacy budget. For each datapair (E(i), D), we get DP M-estimators from hybriddatasets with nonnegative weights β(E(i), w

+).To evaluate the performance on the sequence of

subset candidates, we consider the total predictionerror defined by ti = ‖(δh)‖2 for candidate E(i),where (δh) = hD(β(E(i), w

+)) − hD(β(D)). Insteadof directly measuring difference in β from differentdatasets, we take the transformation function hD(β) =eX

Dβ

1+eXDβwhere XD is the covariate matrix of D and

thus hD(β) is a vector of nD elements. The predictionerror of a candidate public subset measures the sumof total differences between the predicted probabilitieswith β estimated from the candidate under DP onthe private covariates for dataset D and those withβ estimated from D and its private covariates acrossall the observations. As we take β(D) as the baseline,β(D) itself contains private information. To comparethe difference to β(D), we need to add additional per-turbation when report this difference. Taking a trans-formation on measuring error ‖β(E(i), w

+)− β(D)‖.,we need the transformation function maintains itstradeoff property and has a small sensitivity. It iseasy to check that h is Lipschitz in this case that XD

is bounded (note XD is not random when addingLaplace noise). Hence (δh) captures the tradeoff. De-fine (δh) and (δh)′ as neighbor vectors only differingin j0-th component and denote their common compo-nents as (δh)−j0 . Noticing that (δh)j0 , (δh)

′

j0∈ [0, 1],

we have

|ti((δh))− ti((δh)′)|

=|√‖(δh)−j0‖22 + (δh)2

j0−√‖(δh)−j0‖22 + (δh)

′2j0|

≤|(δh)j0 − (δh)′

j0 | ≤ 1,

where for the first inequality, the equality achieveswhen ‖(δh)−j0‖2 = 0. Hence the sensitivity of ti is1 and we perturb ti by adding noise Laplace(1/ε3).From the privacy-protected releasing curve of ti’s, wetake the optimal subset as the one with the smallestprediction error.

In the simulation study for logistic regression, wecompare the performance of the estimators for β:(1) β(E) naıvely from public dataset, (2) β(E(i), w)

from weighted density of data pair (E(i), D) withoutadding noise, and (3) β(E(i), w

+) from weighted den-sity of data pair (E(i), D) under DP, and (4) underthe low dimensional case, β(perturbed D) from [2].To make it fair to the perturbed histogram method, weestimate β under privacy parameter ε1 +ε2. We reporttheir average performance in terms of prediction errort from 10 repeats on the whole procedure. We cansee from Figure 5 and Figure 6 that there is a cleartradeoff in the performance of β(E(i), w

+) in the redcurve under DP, i.e. the prediction error decreases firstthen increases with the released sample size, whenthe privacy parameter ε is not too small. Increasingε, the performance of β(E(i), w

+) approaches to thatof β(E(i), w) as expected. The blue line is the per-formance of β(E). Since it does not change with thesubset of E, it is a straight line. We can see due to thebias of public dataset, directly estimating from publicdataset to represent private dataset has large predic-tion error compared to our selecting subset procedure.Figure 5 and Figure 6 indicate that under a smallprivacy parameter, releasing about 10% public pointscould give a better performance under DP. In the caseof p = 2, Figure 5 shows the prediction error fromthe optimal subset of the public dataset is smaller thanthat from the method in [2] only perturbing the privatedataset (in pink line). Under the high dimensionalcase, our DP procedure of selecting the optimal subsetto release shows its priority. When p = 100, addingnoise to say 10p cubes where to partition 10 bins ineach dimension would make the perturbed histogramuseless but the tradeoff curve could still exist whichmakes our selection doable.

5.2 Applying to Real Datasets

We have two clinical datasets from different institutesin the diagnosis of acute myocardial infarction from[27]. One is from Edinburgh institute with 1253 pa-tients and the other is from Sheffield institute with500 patients. We are interested in selecting an optimalpublic dataset in a logistic regression model. The re-sponse in logistic regression is 0-1 disease variable andthe covariates in this study are Pain in left arm, Painin right arm, Nausea, Hypo perfusion, ST elevation,New Q waves, ST depression, T wave inversion and

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●

●

from hybrid datasets under DPfrom hybrid datasets w/o noisefrom public datasetfrom perturbed histgram on private dataset

p = 2

Fig. 5. Prediction error varies with the released points from the public dataset under privacy parameter (ε1, ε2, ε3) = (0.8ε, 0.2ε, ε)where ε = 0.5, 1, 3 from replicating 10 times on the whole procedure. The black dotted curve is the prediction error from the M-estimator from the hybrid datasets without adding noise. The red dotted curve is from the M-estimator from the hybrid datasets underDP. The blue line is from the public dataset. The pink line is from the perturbed private dataset.

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from hybrid datasets under DPfrom hybrid datasets w/o noisefrom public dataset

p = 100

Fig. 6. Prediction error varies with the released points from the public dataset under privacy parameter (ε1, ε2, ε3) = (0.8ε, 0.2ε, ε)where ε = 0.5, 1, 3 from replicating 10 times on the whole procedure.

Sweeting, which are all 0-1 categorical variables andall measured in both institutes.

Since the data is collected from different sites, thereis an intrinsic bias if using one dataset to approximatethe other. In our study, we mimic the case that onedataset is public while the other is private. We firsttake Sheffield dataset as public and Edinburgh asprivate and then converse their roles. Note that sincethe datasets are of discrete variables, it is necessaryto remove the replicates in the public dataset whengetting the weights for the weighted density to avoidambiguity of assigning the weights. The distinct datapoints in Sheffield institute are 153 and for Edinburghare 181. We compare the performance of three M-estimators (from the public dataset, from the hybriddataset without adding noise to the weights and fromthe hybrid datasets under DP) in logistic regressionfor the real datasets, in the same manner as in theprevious section of simulation studies.

In Figure 7, it demonstrates the case that Sheffielddataset is public while Edinburgh is private, and inFigure 8, it demonstrates the case that Edinburghdataset is public while Sheffield is private. In bothcases, applying Algorithm 1-2, we consider ε1 =ε2 = ε3 and set the total of privacy parameter is 3εwhere ε = (1, 3, 10). We add 10 points each time to

the sequence sorted subsets of the public dataset. Tomimic the real application, we report the predictionerror defined in Algorithm 2) from one repeat.

From both Figure 7 and Figure 8, we can see thetradeoff phenomenon in the performance of the DPM-estimator from hybrid datasets (the red curve) isstill clear, as we discussed in the previous section. Toselect the optimal subset under DP, the performance ofthe M-estimator from hybrid datasets without addingnoise (the black curve) can not be released since it hasprivate information. However, the turning point in thered curve suggests an optimal sample size to release.In reality to protect the privacy, we can only see thered curve and the blue line for the performance of M-estimator from the public dataset. Comparing thoseperformance gives us a guideline to select the optimalsubset under DP.

6 DISCUSSION AND CONCLUSION

In this paper, we discuss a privacy problem in asituation where both the private and public datasetsare present. How to effectively take use of the publicinformation to better understand the private informa-tion without releasing privacy is a prime challengeand especially important in the healthcare data anal-ysis. In our work, we formulate this big question

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from hybrid datasets under DPfrom hybrid datasets w/o noisefrom public dataset

Fig. 8. Edinburgh dataset is public while Sheffield is private. The sum privacy parameter is 3ε, where ε = (1, 3, 10).

to how to effectively select public data points underthe framework of differential privacy in the analysisof M-estimator. We first proposed our DP weighteddensity estimation based on the hybrid datasets whichmake it possible to do non interactive learning. Alongthe same line as [2], we gave the convergence rateof our DP M-estimator from hybrid datasets. Basedon that, we found that the bias-variance tradeoff canbe characterized in the sample size of the releaseddataset. This inspired us to explore an algorithm toimplement the selection procedure. The framework ofour Algorithm 1-2 gives a guideline for answeringmore general questions. As we previously pointed,this paper focused on a small question but can be gen-eralized to more variants in both statistical interestsand privacy concerns.

To integrate public and private information, inSection 3, we used the public points to estimate theprivate density weighing them by how they are rep-resentative to the private points in (3). In Section 4,we defined a distance d(D,E) in (5) to measuresimilarity of these two datasets and we showed theaccuracy of the DP M-estimator highly depends ond(D,E). However, in reality, how the public dataset athand is representative to the private dataset is a data-dependent question. As we saw in our investigation

in the effect of rescaling in Subsection 3.2, when thesetwo sets are not extremely different, our proposedprocedure still could provide a DP M-estimation inhigh utility. If we consider a case that only males arein the public dataset while both males and femalesin the private dataset, then we can never infer thecoefficient for the female in the private dataset fromthe public dataset. In this case under the concern ofprivacy, either we do not consider the gender effect ortry to find another more related public dataset. Ourwork intends to give a general framework to selectthe optimal public subset to provide another optionbesides directly learning from the public dataset andonly from the private dataset itself, as we explained inthe workflow in Figure 1.

From a statistical point of view, to estimate theprivate density from public data points, we took theweighted empirical probabilities in (3). As we men-tioned in the Section 3, one can further develop otherdensity estimation methods in the context of DP to geta better convergence rate.

From the privacy concerns, more work can bedone in effectively distribute the privacy parameters(ε1, ε2, ε3) in Algorithm 2. Since the privacy parametercontrols of the utility of the randomized mechanism,the question in how to optimize the distribution of theprivacy parameter should be further investigated. For

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example, instead of releasing the entire performancecurve (the red curve in our simulation studies) to pickthe optimal sample size, one can apply other DP mech-anism such as exponential mechanism to improve theutility.

In conclusion, we proposed Algorithm 1-2 as astrategy to select an optimal public subset to get DPM-estimator in high utility, which serves as a guidelineto real world applications.

ACKNOWLEDGMENTS

We would like to thank the associate editor andthe reviewers. MW would like to thank Ery Arias-Castro and Anthony Gamst for helpful discussionand the training from UCSD. XJ was supported inpart by the Patient-Centered Outcomes Research In-stitute (PCORI) under contract ME-1310-07058, theNational Institute of Health (NIH) under award num-ber R01HG008802, R01GM114612, R01GM118574, andU01EB023685.

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Meng Wang is a postdoctoral fellow in thedepartment of genetics at Stanford Uni-versity from February, 2016 to now. Shereceived the B.S. degree in mathematicalstatistics from Nankai University, China in2010, and the Ph.D. degree in mathemat-ics specialized in statistics from Univer-sity of California at San Diego (UCSD) in2014. She was a postdoctoral fellow in thedepartment of biomedical informatics atUCSD, 2014-2015. Her research interests

include statistics, high-dimensional data, statistical application inhealthcare data privacy and biology.

Zhanglong Ji is a PhD student in De-partment of Computer Science at the Uni-versity of California, San Diego. Beforecoming to UCSD, he majored in Statisticsin Peking University. His research focuseson differential privacy and machine learn-ing.

Hyeoneui Kim received the B.S. de-gree in nursing (BSN) and the Mas-ters degree in Public Health (MPH) fromSeoul National University, South Korea.She earned PhD in Health Informaticsfrom the University of Minnesota at TwinCities. She received post-doctoral trainingfrom Brigham and Women’s Hospital inBoston. Dr. Kim is currently an associateprofessor of Division of Biomedical Infor-matics at UC San Diego. Her research

focuses on standardized data representation, secondary use ofhealthcare data, clinical informatics and consumer health infor-matics.

Shuang Wang (S’08–M’12) received theB.S. degree in applied physics and theM.S. degree in biomedical engineeringfrom the Dalian University of Technology,China, and the Ph.D. degree in electricaland computer engineering from the Uni-versity of Oklahoma, OK, USA, in 2012.He was worked as a postdoc researcherwith the Department of Biomedical Infor-matics (DBMI), University of California,San Diego (UCSD), CA, USA, 2012 -

2015. Currently, he is an assistant professor at the DBMI, UCSD.His research interests include machine learning, and health-care data privacy/security. He has published more than 60 jour-nal/conference papers and 2 book chapters. He was awarded aNGHRI K99/R00 career grant. Dr. Wang is a senior member ofIEEE.

Li Xiong Li Xiong is Professor of Com-puter Science (and Biomedical Informat-ics) and holds a Winship DistinguishedResearch Professorship at Emory Univer-sity. She has a PhD from Georgia Instituteof Technology, an MS from Johns Hop-kins University, and a BS from Universityof Science and Technology of China, allin Computer Science. She and her re-search group, Assured Information Man-agement and Sharing (AIMS), conduct re-

search that addresses both fundamental and applied questionsat the interface of data privacy and security, spatiotemporal datamanagement, and health informatics. She is a recipient of aGoogle Research Award, IBM Faculty Innovation Award, CiscoResearch Award, and Woodrow Wilson Fellowship. Her researchis supported by NSF (National Science Foundation), NIH (Na-tional Institute of Health), AFOSR (Air Force Office of ScientificResearch), and PCORI (Patient-Centered Outcomes ResearchInstitute).

Xiaoqian Jiang is an assistant profes-sor in the Department of Biomedical In-formatics at the University of CaliforniaSan Diego. He received his PhD in Com-puter Science from Carnegie Mellon Uni-versity. He is an associate editor of BMCMedical Informatics and Decision Makingand serves as an editorial board mem-ber of Journal of American Medical Infor-matics Association. He works primarily inhealth data privacy and predictive models

in biomedicine. Dr. Jiang is a recipient of NIH K99/R00 awardand he won the distinguished paper award from American Med-ical Informatics Association Clinical Research Informatics (CRI)Summit in 2012 and 2013.