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Will Wei Sun

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6 papers

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TMLR Journal 2023 Journal Article

Binary Classification under Local Label Differential Privacy Using Randomized Response Mechanisms

Shirong Xu
Chendi Wang
Will Wei Sun
Guang Cheng

Label differential privacy is a popular branch of $\epsilon$-differential privacy for protecting labels in training datasets with non-private features. In this paper, we study the generalization performance of a binary classifier trained on a dataset privatized under the label differential privacy achieved by the randomized response mechanism. Particularly, we establish minimax lower bounds for the excess risks of the deep neural network plug-in classifier, theoretically quantifying how privacy guarantee $\epsilon$ affects its generalization performance. Our theoretical result shows: (1) the randomized response mechanism slows down the convergence of excess risk by lessening the multiplicative constant term compared with the non-private case $(\epsilon=\infty)$; (2) as $\epsilon$ decreases, the optimal structure of the neural network should be smaller for better generalization performance; (3) the convergence of its excess risk is guaranteed even if $\epsilon$ is adaptive to the size of training sample $n$ at a rate slower than $O(n^{-1/2})$. Our theoretical results are validated by extensive simulated examples and two real applications.

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NeurIPS Conference 2022 Conference Paper

Contextual Dynamic Pricing with Unknown Noise: Explore-then-UCB Strategy and Improved Regrets

Yiyun Luo
Will Wei Sun
Yufeng Liu

Dynamic pricing is a fast-moving research area in machine learning and operations management. A lot of work has been done for this problem with known noise. In this paper, we consider a contextual dynamic pricing problem under a linear customer valuation model with an unknown market noise distribution $F$. This problem is very challenging due to the difficulty in balancing three tangled tasks of revenue-maximization, estimating the linear valuation parameter $\theta_{0}$, and learning the nonparametric $F$. To address this issue, we develop a novel {\it Explore-then-UCB} (ExUCB) strategy that includes an exploration for $\theta_{0}$-learning and a followed UCB procedure of joint revenue-maximization and $F$-learning. Under Lipschitz and 2nd-order smoothness assumptions on $F$, ExUCB is the first approach to achieve the $\tilde{O}(T^{2/3})$ regret rate. Under the Lipschitz assumption only, ExUCB matches the best existing regret of $\tilde{O}(T^{3/4})$ and is computationally more efficient. Furthermore, for regret lower bounds under the nonparametric $F$, not much work has been done beyond only assuming Lipschitz. To fill this gap, we provide the first $\tilde{\Omega}(T^{3/5})$ lower bound under Lipschitz and 2nd-order smoothness assumptions.

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JMLR Journal 2021 Journal Article

Sparse Tensor Additive Regression

Botao Hao
Boxiang Wang
Pengyuan Wang
Jingfei Zhang
Jian Yang
Will Wei Sun

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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JMLR Journal 2020 Journal Article

Provable Convex Co-clustering of Tensors

Eric C. Chi
Brian J. Gaines
Will Wei Sun
Hua Zhou
Jian Yang

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap by developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising “blessing of dimensionality” phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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JMLR Journal 2018 Journal Article

Simultaneous Clustering and Estimation of Heterogeneous Graphical Models

Botao Hao
Will Wei Sun
Yufeng Liu
Guang Cheng

We consider joint estimation of multiple graphical models arising from heterogeneous and high-dimensional observations. Unlike most previous approaches which assume that the cluster structure is given in advance, an appealing feature of our method is to learn cluster structure while estimating heterogeneous graphical models. This is achieved via a high dimensional version of Expectation Conditional Maximization (ECM) algorithm (Meng and Rubin, 1993). A joint graphical lasso penalty is imposed on the conditional maximization step to extract both homogeneity and heterogeneity components across all clusters. Our algorithm is computationally efficient due to fast sparse learning routines and can be implemented without unsupervised learning knowledge. The superior performance of our method is demonstrated by extensive experiments and its application to a Glioblastoma cancer dataset reveals some new insights in understanding the Glioblastoma cancer. In theory, a non-asymptotic error bound is established for the output directly from our high dimensional ECM algorithm, and it consists of two quantities: statistical error (statistical accuracy) and optimization error (computational complexity). Such a result gives a theoretical guideline in terminating our ECM iterations. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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JMLR Journal 2017 Journal Article

STORE: Sparse Tensor Response Regression and Neuroimaging Analysis

Will Wei Sun
Lexin Li

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non- asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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