Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Learning without Recall by Random Walks on Directed Graphs

We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations. This occurs when some other states are observationally equivalent to the true state from the agent's perspective. To overcome this shortcoming, agents must communicate with each other to benefit from local observations. We propose a model where each agent selects one of her neighbors randomly at each time. Then, she refines her opinion using her private signal and the prior of that particular neighbor. The proposed rule can be thought of as a Bayesian agent who cannot recall the priors based on which other agents make inferences. This learning without recall approach preserves some aspects of the Bayesian inference while being computationally tractable. By establishing a correspondence with a random walk on the network graph, we prove that under the described protocol, agents learn the truth exponentially fast in the almost sure sense. The asymptotic rate is expressed as the sum of the relative entropies between the signal structures of every agent weighted by the stationary distribution of the random walk.Comment: 6 pages, To Appear in Conference on Decision and Control 201

Private Estimation and Inference in High-Dimensional Regression with FDR Control

This paper presents novel methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We start by proposing a differentially private Bayesian Information Criterion (BIC) for selecting the unknown sparsity parameter in DP-Lasso, eliminating the need for prior knowledge of model sparsity, a requisite in the existing literature. Then we propose a differentially private debiased LASSO algorithm that enables privacy-preserving inference on regression parameters. Our proposed method enables accurate and private inference on the regression parameters by leveraging the inherent sparsity of high-dimensional linear regression models. Additionally, we address the issue of multiple testing in high-dimensional linear regression by introducing a differentially private multiple testing procedure that controls the false discovery rate (FDR). This allows for accurate and privacy-preserving identification of significant predictors in the regression model. Through extensive simulations and real data analysis, we demonstrate the efficacy of our proposed methods in conducting inference for high-dimensional linear models while safeguarding privacy and controlling the FDR

An Account of Opinion Implicatures

While previous sentiment analysis research has concentrated on the interpretation of explicitly stated opinions and attitudes, this work initiates the computational study of a type of opinion implicature (i.e., opinion-oriented inference) in text. This paper described a rule-based framework for representing and analyzing opinion implicatures which we hope will contribute to deeper automatic interpretation of subjective language. In the course of understanding implicatures, the system recognizes implicit sentiments (and beliefs) toward various events and entities in the sentence, often attributed to different sources (holders) and of mixed polarities; thus, it produces a richer interpretation than is typical in opinion analysis.Comment: 50 Pages. Submitted to the journal, Language Resources and Evaluatio

Enabling Social Applications via Decentralized Social Data Management

An unprecedented information wealth produced by online social networks, further augmented by location/collocation data, is currently fragmented across different proprietary services. Combined, it can accurately represent the social world and enable novel socially-aware applications. We present Prometheus, a socially-aware peer-to-peer service that collects social information from multiple sources into a multigraph managed in a decentralized fashion on user-contributed nodes, and exposes it through an interface implementing non-trivial social inferences while complying with user-defined access policies. Simulations and experiments on PlanetLab with emulated application workloads show the system exhibits good end-to-end response time, low communication overhead and resilience to malicious attacks.Comment: 27 pages, single ACM column, 9 figures, accepted in Special Issue of Foundations of Social Computing, ACM Transactions on Internet Technolog