Yichen Wang

Shuai Tang, Sergul Aydore, Michael Kearns et al. · amazon-science

We revisit the problem of differentially private squared error linear regression. We observe that existing state-of-the-art methods are sensitive to the choice of hyperparameters -- including the ``clipping threshold'' that cannot be set optimally in a data-independent way. We give a new algorithm for private linear regression based on gradient boosting. We show that our method consistently improves over the previous state of the art when the clipping threshold is taken to be fixed without knowledge of the data, rather than optimized in a non-private way -- and that even when we optimize the hyperparameters of competitor algorithms non-privately, our algorithm is no worse and often better. In addition to a comprehensive set of experiments, we give theoretical insights to explain this behavior.

T. Tony Cai, Yichen Wang, Linjun Zhang

Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and non-parametric regression over the Sobolev class.

T. Tony Cai, Yichen Wang, Linjun Zhang

We propose differentially private algorithms for parameter estimation in both low-dimensional and high-dimensional sparse generalized linear models (GLMs) by constructing private versions of projected gradient descent. We show that the proposed algorithms are nearly rate-optimal by characterizing their statistical performance and establishing privacy-constrained minimax lower bounds for GLMs. The lower bounds are obtained via a novel technique, which is based on Stein's Lemma and generalizes the tracing attack technique for privacy-constrained lower bounds. This lower bound argument can be of independent interest as it is applicable to general parametric models. Simulated and real data experiments are conducted to demonstrate the numerical performance of our algorithms.

T. Tony Cai, Yichen Wang, Linjun Zhang

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the $(\varepsilon,δ)$-differential privacy constraint. To this end, we find that classical lower bound arguments fail to yield sharp results, and new technical tools are called for. By refining the "tracing adversary" technique for lower bounds in the theoretical computer science literature, we formulate a general lower bound argument for minimax risks with differential privacy constraints, and apply this argument to high-dimensional mean estimation and linear regression problems. We also design computationally efficient algorithms that attain the minimax lower bounds up to a logarithmic factor. In particular, for the high-dimensional linear regression, a novel private iterative hard thresholding pursuit algorithm is proposed, based on a privately truncated version of stochastic gradient descent. The numerical performance of these algorithms is demonstrated by simulation studies and applications to real data containing sensitive information, for which privacy-preserving statistical methods are necessary.

Dongyang Xu, Pinyi Ren, James A. Ritcey et al.

A pilot spoofer can paralyze the channel estimation in multi-user orthogonal frequency-division multiplexing (OFD- M) systems by using the same publicly-known pilot tones as legitimate nodes. This causes the problem of pilot authentication (PA). To solve this, we propose, for a two-user multi-antenna OFDM system, a code-frequency block group (CFBG) coding based PA mechanism. Here multi-user pilot information, after being randomized independently to avoid being spoofed, are converted into activation patterns of subcarrier-block groups on code-frequency domain. Those patterns, though overlapped and interfered mutually in the wireless transmission environment, are qualified to be separated and identified as the original pilots with high accuracy, by exploiting CFBG coding theory and channel characteristic. Particularly, we develop the CFBG code through two steps, i.e., 1) devising an ordered signal detection technique to recognize the number of signals coexisting on each subcarrier block, and encoding each subcarrier block with the detected number; 2) constructing a zero-false-drop (ZFD) code and block detection based (BD) code via k-dimensional Latin hypercubes and integrating those two codes into the CFBG code. This code can bring a desirable pilot separation error probability (SEP), inversely proportional to the number of occupied subcarriers and antennas with a power of k. To apply the code to PA, a scheme of pilot conveying, separation and identification is proposed. Based on this novel PA, a joint channel estimation and identification mechanism is proposed to achieve high-precision channel recovery and simultaneously enhance PA without occupying extra resources. Simulation results verify the effectiveness of our proposed mechanism.

Yichen Wang, Grady Williams, Evangelos Theodorou et al.

Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic system driven by the point process is steered to a target state. In particular, we exploit the key insight to view the stochastic optimal control problem from the perspective of optimal measure and variational inference. We further propose a convex optimization framework and an efficient algorithm to update the policy adaptively to the current system state. Experiments on synthetic and real-world data show that our algorithm can steer the user activities much more accurately and efficiently than other stochastic control methods.

Niao He, Zaid Harchaoui, Yichen Wang et al.

Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson log-likelihood is concave but not Lipschitz-continuous. Since almost all gradient-based optimization algorithms rely on Lipschitz-continuity, optimizing Poisson likelihood models with a guarantee of convergence can be challenging, especially for large-scale problems. We present a new perspective allowing to efficiently optimize a wide range of penalized Poisson likelihood objectives. We show that an appropriate saddle point reformulation enjoys a favorable geometry and a smooth structure. Therefore, we can design a new gradient-based optimization algorithm with $O(1/t)$ convergence rate, in contrast to the usual $O(1/\sqrt{t})$ rate of non-smooth minimization alternatives. Furthermore, in order to tackle problems with large samples, we also develop a randomized block-decomposition variant that enjoys the same convergence rate yet more efficient iteration cost. Experimental results on several point process applications including social network estimation and temporal recommendation show that the proposed algorithm and its randomized block variant outperform existing methods both on synthetic and real-world datasets.