1. integrating Data for Analysis, Anonymization, and SHaring Supported by the NIH Grant U54HL108460 to the University of California, San Diego Shuang Wang, 1 Xiaoqian Jiang, 1 Yuan Wu, 1 Lijuan Cui, 2 and Samuel Cheng 2, Lucila Ohno-Machado 1 EXpectation Propagation LOgistic REgRession (EXPLORER): distributed privacy-preserving online model learning 1 Division of Biomedical Informatics, University of California–San Diego, La Jolla, California, USA 2 School of Electrical and Computer Engineering, University of Oklahoma, Tulsa, Oklahoma, USA Introduction EXPLORER framework Summary of Conclusions It has been shown in last decade that data privacy cannot be maintained by simply removing patient identities. Thus, training data in one institute cannot be exchanged or shared with other institutions directly for the purposes of global logistic regression model learning. To address such a challenge, numerous privacy-preserving distributed frequentist regression models for horizontally partitioned data have been studied, among which Grid LOgistic RE- gression (GLORE) model [1] and the Secure Pooled Analysis acRoss K-site (SPARK) protocol [2] are the closest work for the method presented here. Despite its simplicity and interpretability, the distributed frequentist logistic regression approach has limitations as shown in Table 1. Table 1: Comparing EXPLORER with GLORE and SPARK References [1] Wu, Y., Jiang, X., Kim, J., Ohno-Machado, L. (2012). Grid Binary LOgistic REgression (GLORE): building shared models without sharing data. JAMIA, 19(5), 758-764. [2] El Emam, K., Samet, S., Arbuckle, L., Tamblyn, R., Earle, C., & Kantarcioglu, M. (2013). A secure distributed logistic regression protocol for the detection of rare adverse drug events. JAMIA, 20(3), 453-461. [3] Wang, S., Jiang, X., Wu, Y., Cui, L., Cheng, S., & Ohno-Machado, L. (2013). EXpectation Propagation LOgistic REgRession (EXPLORER): Distributed privacy-preserving online model learning. JBI, 46(3), 480-496. In summary, EXPLORER offers an alternative tool for privacy-preserving distributed statistical learning. We showed empirically on multiple data sets that the results are very similar to those of ordinary logistic regression. These promising results warrant further validation in larger data sets and further refinement of the methodology. Inability to openly share (i.e., transmit) patient data without onerous processes involving pair-wise agreements between institutions may significantly slow down analyses that could produce important results for healthcare improvement and biomedical research advances. EXPLORER provides a means to mitigate this problem by relying on multiparty computation without need for extensive re-training of models, nor reliance on synchronous communications among sites. Privacy protection Asynchronous communication Online learning GLORE or SPARK ✔ EXPLORER ✔✔✔ We developed an EXpectation Propagation LOgistic REgRession (EXPLORER) model for distributed privacy-preserving online learning [3]. The proposed framework provides a high level guarantee for protecting sensitive information, since the information exchanged between the server and the client is the encrypted posterior distribution of coefficients. Through experimental results, EXPLORER shows the same performance as the traditional frequentist logistic regression model, but provides more flexibility in model updating. That is, EXPLORER can be updated one point at a time rather than having to retrain the entire data set when new observations are recorded. The proposed EXPLORER supports asynchronized communication, which relieves the participants from coordinating with one another, and prevents service breakdown from the absence of participants or interrupted communications Experimental Results Methodology Secured Intermediate iNformation Exchange (SINE) protocol DatasetDataset description# of covariates# of samples 1Simulated i.i.d. data5500 2Simulated correlated data6500 3Simulated binary data151500 4Myocardial infarction91253 Table 2: Summary of datasets used in our experiments Ordinary LREXPLORERtwo-sample Z-test β Prob. Test statistic p-value β1-2.0743 1.000-2.0722 1.000-0.3573 0.7209 β2 0.0452 0.267 0.0527 0.300-0.3669 0.7137 β3 3.0195 1.000 3.0167 1.0000.5919 0.5539 β4-0.0402 0.200-0.0265 0.133-0.7003 0.4837 β5-1.7313 1.000-1.7316 1.0000.1305 0.8962 Table 3: Distributed forward feature selection on data set 1 over 30 trials Table 4: Comparisons of H-L tests and AUCs for simulated dataset 2 with/without interaction using Ordinary LR and 4-site EXPLORER With interactionWithout interaction Ordinary LR EXPLORER H-L testtest statistics22.45940.59515.18418.909 p-value0.289 0.1980.203 0.150 AUC Averaged value0.851 0.8520.794 0.793 Standard deviation0.045 0.058 Z-test statistics-0.0490.075 Z-test p-value0.9610.940 The convergence speed of all 10 coefficients of the data set 4 for an asynchronous 8- site EXPLORE setup β Ordinary LREXPLORERtwo-sample Z test value std. Test statistic p-value β01.577 0.1571.558 0.1530.468 0.64005 β1-1.035 0.082-1.027 0.083-0.359 0.71924 β21.728 0.0721.734 0.072-0.301 0.76344 β30.604 0.0770.607 0.077-0.183 0.85511 β4-1.120 0.096-1.116 0.096-0.139 0.88984 β50.943 0.0900.950 0.091-0.315 0.75262 β62.239 0.1032.249 0.102-0.379 0.70441 β7-0.942 0.089-0.938 0.089-0.192 0.84777 β8-1.535 0.081-1.537 0.0810.073 0.94145 β91.212 0.0871.221 0.087-0.390 0.69690 β101.048 0.0801.055 0.080-0.322 0.74759 β111.343 0.0891.344 0.089-0.043 0.96579 β12-0.066 0.080-0.064 0.080-0.131 0.89593 β13-0.676 0.081-0.669 0.081-0.362 0.71716 β14-3.354 0.111-3.361 0.1090.226 0.82122 β150.362 0.0810.367 0.081-0.222 0.82458 Table 5: Learned model parameter β of dataset 3 using Ordinary LR and 2-site EXPLORER