Jinhui Xu

Liyang Zhu, Meng Ding, Vaneet Aggarwal et al.

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is $1$-sparse, and extending such bounds to the more general $k$-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the $ε$ non-interactive LDP model and provide a lower bound of $Ω(\frac{\sqrt{dk\log d}}{\sqrt{n}ε})$ on the $\ell_2$-norm estimation error for sub-Gaussian data, where $n$ is the sample size and $d$ is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of $\tilde{O}({\frac{d\sqrt{k}}{\sqrt{n}ε}})$ for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of $O(\sqrt{d})$ if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of $Ω({\frac{\sqrt{dk}}{\sqrt{n}ε}})$. As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of $\tilde{O}(\frac{k\sqrt{d}}{\sqrt{n}ε})$. Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

Chunwei Ma, Ziyun Huang, Jiayi Xian et al.

Deep Neural Networks (DNNs), despite their tremendous success in recent years, could still cast doubts on their predictions due to the intrinsic uncertainty associated with their learning process. Ensemble techniques and post-hoc calibrations are two types of approaches that have individually shown promise in improving the uncertainty calibration of DNNs. However, the synergistic effect of the two types of methods has not been well explored. In this paper, we propose a truth discovery framework to integrate ensemble-based and post-hoc calibration methods. Using the geometric variance of the ensemble candidates as a good indicator for sample uncertainty, we design an accuracy-preserving truth estimator with provably no accuracy drop. Furthermore, we show that post-hoc calibration can also be enhanced by truth discovery-regularized optimization. On large-scale datasets including CIFAR and ImageNet, our method shows consistent improvement against state-of-the-art calibration approaches on both histogram-based and kernel density-based evaluation metrics. Our codes are available at https://github.com/horsepurve/truly-uncertain.

Jiaming Zhang, Mingxi Lei, Meng Ding et al.

Reinforcement Learning with Human Feedback (RLHF) has emerged as an influential technique, enabling the alignment of large language models (LLMs) with human preferences. Despite the promising potential of RLHF, how to protect user preference privacy has become a crucial issue. Most previous work has focused on using differential privacy (DP) to protect the privacy of individual data. However, they have concentrated primarily on item-level privacy protection and have unsatisfactory performance for user-level privacy, which is more common in RLHF. This study proposes a novel framework, AUP-RLHF, which integrates user-level label DP into RLHF. We first show that the classical random response algorithm, which achieves an acceptable performance in item-level privacy, leads to suboptimal utility when in the user-level settings. We then establish a lower bound for the user-level label DP-RLHF and develop the AUP-RLHF algorithm, which guarantees $(\varepsilon, δ)$ user-level privacy and achieves an improved estimation error. Experimental results show that AUP-RLHF outperforms existing baseline methods in sentiment generation and summarization tasks, achieving a better privacy-utility trade-off.

Mingxi Lei, Chunwei Ma, Meng Ding et al.

Deep learning models often struggle with generalization when deploying on real-world data, due to the common distributional shift to the training data. Test-time adaptation (TTA) is an emerging scheme used at inference time to address this issue. In TTA, models are adapted online at the same time when making predictions to test data. Neighbor-based approaches have gained attention recently, where prototype embeddings provide location information to alleviate the feature shift between training and testing data. However, due to their inherit limitation of simplicity, they often struggle to learn useful patterns and encounter performance degradation. To confront this challenge, we study the TTA problem from a geometric point of view. We first reveal that the underlying structure of neighbor-based methods aligns with the Voronoi Diagram, a classical computational geometry model for space partitioning. Building on this observation, we propose the Test-Time adjustment by Voronoi Diagram guidance (TTVD), a novel framework that leverages the benefits of this geometric property. Specifically, we explore two key structures: 1) Cluster-induced Voronoi Diagram (CIVD): This integrates the joint contribution of self-supervision and entropy-based methods to provide richer information. 2) Power Diagram (PD): A generalized version of the Voronoi Diagram that refines partitions by assigning weights to each Voronoi cell. Our experiments under rigid, peer-reviewed settings on CIFAR-10-C, CIFAR-100-C, ImageNet-C, and ImageNet-R shows that TTVD achieves remarkable improvements compared to state-of-the-art methods. Moreover, extensive experimental results also explore the effects of batch size and class imbalance, which are two scenarios commonly encountered in real-world applications. These analyses further validate the robustness and adaptability of our proposed framework.

Minghua Wang, Ziyun Huang, Jinhui Xu

To improve persistence diagram representation learning, we propose Multiset Transformer. This is the first neural network that utilizes attention mechanisms specifically designed for multisets as inputs and offers rigorous theoretical guarantees of permutation invariance. The architecture integrates multiset-enhanced attentions with a pool-decomposition scheme, allowing multiplicities to be preserved across equivariant layers. This capability enables full leverage of multiplicities while significantly reducing both computational and spatial complexity compared to the Set Transformer. Additionally, our method can greatly benefit from clustering as a preprocessing step to further minimize complexity, an advantage not possessed by the Set Transformer. Experimental results demonstrate that the Multiset Transformer outperforms existing neural network methods in the realm of persistence diagram representation learning.

Yufan Zhou, Chunyuan Li, Changyou Chen et al.

With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on improving DGMs by either introducing new objective functions or designing more expressive model architectures. However, such approaches often introduce significantly more computational and/or designing overhead. To resolve such issues, we introduce in this paper a generic framework called {\em generative-model inference} that is capable of enhancing pre-trained GANs effectively and seamlessly in a variety of application scenarios. Our basic idea is to efficiently infer the optimal latent distribution for the given requirements using Wasserstein gradient flow techniques, instead of re-training or fine-tuning pre-trained model parameters. Extensive experimental results on applications like image generation, image translation, text-to-image generation, image inpainting, and text-guided image editing suggest the effectiveness and superiority of our proposed framework.

Yufan Zhou, Ruiyi Zhang, Changyou Chen et al.

One of the major challenges in training text-to-image generation models is the need of a large number of high-quality image-text pairs. While image samples are often easily accessible, the associated text descriptions typically require careful human captioning, which is particularly time- and cost-consuming. In this paper, we propose the first work to train text-to-image generation models without any text data. Our method leverages the well-aligned multi-modal semantic space of the powerful pre-trained CLIP model: the requirement of text-conditioning is seamlessly alleviated via generating text features from image features. Extensive experiments are conducted to illustrate the effectiveness of the proposed method. We obtain state-of-the-art results in the standard text-to-image generation tasks. Importantly, the proposed language-free model outperforms most existing models trained with full image-text pairs. Furthermore, our method can be applied in fine-tuning pre-trained models, which saves both training time and cost in training text-to-image generation models. Our pre-trained model obtains competitive results in zero-shot text-to-image generation on the MS-COCO dataset, yet with around only 1% of the model size and training data size relative to the recently proposed large DALL-E model.

Yufan Zhou, Zhenyi Wang, Jiayi Xian et al.

Model Agnostic Meta-Learning (MAML) has emerged as a standard framework for meta-learning, where a meta-model is learned with the ability of fast adapting to new tasks. However, as a double-looped optimization problem, MAML needs to differentiate through the whole inner-loop optimization path for every outer-loop training step, which may lead to both computational inefficiency and sub-optimal solutions. In this paper, we generalize MAML to allow meta-learning to be defined in function spaces, and propose the first meta-learning paradigm in the Reproducing Kernel Hilbert Space (RKHS) induced by the meta-model's Neural Tangent Kernel (NTK). Within this paradigm, we introduce two meta-learning algorithms in the RKHS, which no longer need a sub-optimal iterative inner-loop adaptation as in the MAML framework. We achieve this goal by 1) replacing the adaptation with a fast-adaptive regularizer in the RKHS; and 2) solving the adaptation analytically based on the NTK theory. Extensive experimental studies demonstrate advantages of our paradigm in both efficiency and quality of solutions compared to related meta-learning algorithms. Another interesting feature of our proposed methods is that they are demonstrated to be more robust to adversarial attacks and out-of-distribution adaptation than popular baselines, as demonstrated in our experiments.

Di Wang, Marco Gaboardi, Adam Smith et al.

In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to achieve error $α$, needs to be exponentially depending on the dimensionality $p$ for general loss functions. In this paper, we make two attempts to resolve this issue by investigating conditions on the loss functions that allow us to remove such a limit. In our first attempt, we show that if the loss function is $(\infty, T)$-smooth, by using the Bernstein polynomial approximation we can avoid the exponential dependency in the term of $α$. We then propose player-efficient algorithms with $1$-bit communication complexity and $O(1)$ computation cost for each player. The error bound of these algorithms is asymptotically the same as the original one. With some additional assumptions, we also give an algorithm which is more efficient for the server. In our second attempt, we show that for any $1$-Lipschitz generalized linear convex loss function, there is an $(ε, δ)$-LDP algorithm whose sample complexity for achieving error $α$ is only linear in the dimensionality $p$. Our results use a polynomial of inner product approximation technique. Finally, motivated by the idea of using polynomial approximation and based on different types of polynomial approximations, we propose (efficient) non-interactive locally differentially private algorithms for learning the set of k-way marginal queries and the set of smooth queries.

Di Wang, Jiahao Ding, Lijie Hu et al.

(Gradient) Expectation Maximization (EM) is a widely used algorithm for estimating the maximum likelihood of mixture models or incomplete data problems. A major challenge facing this popular technique is how to effectively preserve the privacy of sensitive data. Previous research on this problem has already lead to the discovery of some Differentially Private (DP) algorithms for (Gradient) EM. However, unlike in the non-private case, existing techniques are not yet able to provide finite sample statistical guarantees. To address this issue, we propose in this paper the first DP version of (Gradient) EM algorithm with statistical guarantees. Moreover, we apply our general framework to three canonical models: Gaussian Mixture Model (GMM), Mixture of Regressions Model (MRM) and Linear Regression with Missing Covariates (RMC). Specifically, for GMM in the DP model, our estimation error is near optimal in some cases. For the other two models, we provide the first finite sample statistical guarantees. Our theory is supported by thorough numerical experiments.

Di Wang, Hanshen Xiao, Srini Devadas et al.

In this paper, we consider the problem of designing Differentially Private (DP) algorithms for Stochastic Convex Optimization (SCO) on heavy-tailed data. The irregularity of such data violates some key assumptions used in almost all existing DP-SCO and DP-ERM methods, resulting in failure to provide the DP guarantees. To better understand this type of challenges, we provide in this paper a comprehensive study of DP-SCO under various settings. First, we consider the case where the loss function is strongly convex and smooth. For this case, we propose a method based on the sample-and-aggregate framework, which has an excess population risk of $\tilde{O}(\frac{d^3}{nε^4})$ (after omitting other factors), where $n$ is the sample size and $d$ is the dimensionality of the data. Then, we show that with some additional assumptions on the loss functions, it is possible to reduce the \textit{expected} excess population risk to $\tilde{O}(\frac{ d^2}{ nε^2 })$. To lift these additional conditions, we also provide a gradient smoothing and trimming based scheme to achieve excess population risks of $\tilde{O}(\frac{ d^2}{nε^2})$ and $\tilde{O}(\frac{d^\frac{2}{3}}{(nε^2)^\frac{1}{3}})$ for strongly convex and general convex loss functions, respectively, \textit{with high probability}. Experiments suggest that our algorithms can effectively deal with the challenges caused by data irregularity.

Yufan Zhou, Changyou Chen, Jinhui Xu

Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the flexibility of being directly applicable to down-stream applications. In this paper, we propose the concept of implicit manifold learning, where manifold information is implicitly obtained by learning the associated heat kernel. A heat kernel is the solution of the corresponding heat equation, which describes how "heat" transfers on the manifold, thus containing ample geometric information of the manifold. We provide both practical algorithm and theoretical analysis of our framework. The learned heat kernel can be applied to various kernel-based machine learning models, including deep generative models (DGM) for data generation and Stein Variational Gradient Descent for Bayesian inference. Extensive experiments show that our framework can achieve state-of-the-art results compared to existing methods for the two tasks.

Yufan Zhou, Jiayi Xian, Changyou Chen et al.

Learning on graph structured data has drawn increasing interest in recent years. Frameworks like Graph Convolutional Networks (GCNs) have demonstrated their ability to capture structural information and obtain good performance in various tasks. In these frameworks, node aggregation schemes are typically used to capture structural information: a node's feature vector is recursively computed by aggregating features of its neighboring nodes. However, most of aggregation schemes treat all connections in a graph equally, ignoring node feature similarities. In this paper, we re-interpret node aggregation from the perspective of kernel weighting, and present a framework to consider feature similarity in an aggregation scheme. Specifically, we show that normalized adjacency matrix is equivalent to a neighbor-based kernel matrix in a Krein Space. We then propose feature aggregation as the composition of the original neighbor-based kernel and a learnable kernel to encode feature similarities in a feature space. We further show how the proposed method can be extended to Graph Attention Network (GAT). Experimental results demonstrate better performance of our proposed framework in several real-world applications.

Tianhang Zheng, Di Wang, Baochun Li et al.

As a certified defensive technique, randomized smoothing has received considerable attention due to its scalability to large datasets and neural networks. However, several important questions remain unanswered, such as (i) whether the Gaussian mechanism is an appropriate option for certifying $\ell_2$-norm robustness, and (ii) whether there is an appropriate randomized (smoothing) mechanism to certify $\ell_\infty$-norm robustness. To shed light on these questions, we argue that the main difficulty is how to assess the appropriateness of each randomized mechanism. In this paper, we propose a generic framework that connects the existing frameworks in \cite{lecuyer2018certified, li2019certified}, to assess randomized mechanisms. Under our framework, for a randomized mechanism that can certify a certain extent of robustness, we define the magnitude of its required additive noise as the metric for assessing its appropriateness. We also prove lower bounds on this metric for the $\ell_2$-norm and $\ell_\infty$-norm cases as the criteria for assessment. Based on our framework, we assess the Gaussian and Exponential mechanisms by comparing the magnitude of additive noise required by these mechanisms and the lower bounds (criteria). We first conclude that the Gaussian mechanism is indeed an appropriate option to certify $\ell_2$-norm robustness. Surprisingly, we show that the Gaussian mechanism is also an appropriate option for certifying $\ell_\infty$-norm robustness, instead of the Exponential mechanism. Finally, we generalize our framework to $\ell_p$-norm for any $p\geq2$. Our theoretical findings are verified by evaluations on CIFAR10 and ImageNet.

Yufan Zhou, Changyou Chen, Jinhui Xu

Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features and implicit spectral distributions that are parameterized by deep neural networks. The constructed network (called KernelNet) can be applied to deep generative modeling in various scenarios, including two popular learning paradigms in deep generative models, MMD-GAN and implicit Variational Autoencoder (VAE). We show that our proposed kernel indeed exists in applications and is guaranteed to be positive definite. Furthermore, the induced Maximum Mean Discrepancy (MMD) can endow the continuity property in weak topology by simple regularization. Extensive experiments indicate that our proposed KernelNet consistently achieves better performance compared to related methods.

Di Wang, Lijie Hu, Huanyu Zhang et al.

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLMs) in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical setting, our model allows the server to access some additional public but unlabeled data. In the first part of the paper we focus on GLMs. Specifically, we first consider the case where each data record is i.i.d. sampled from a zero-mean multivariate Gaussian distribution. Motivated by the Stein's lemma, we present an $(ε, δ)$-NLDP algorithm for GLMs. Moreover, the sample complexity of public and private data for the algorithm to achieve an $\ell_2$-norm estimation error of $α$ (with high probability) is ${O}(p α^{-2})$ and $\tilde{O}(p^3α^{-2}ε^{-2})$ respectively, where $p$ is the dimension of the feature vector. This is a significant improvement over the previously known exponential or quasi-polynomial in $α^{-1}$, or exponential in $p$ sample complexities of GLMs with no public data. Then we consider a more general setting where each data record is i.i.d. sampled from some sub-Gaussian distribution with bounded $\ell_1$-norm. Based on a variant of Stein's lemma, we propose an $(ε, δ)$-NLDP algorithm for GLMs whose sample complexity of public and private data to achieve an $\ell_\infty$-norm estimation error of $α$ is ${O}(p^2α^{-2})$ and $\tilde{O}(p^2α^{-2}ε^{-2})$ respectively, under some mild assumptions and if $α$ is not too small ({\em i.e.,} $α\geq Ω(\frac{1}{\sqrt{p}})$). In the second part of the paper, we extend our idea to the problem of estimating non-linear regressions and show similar results as in GLMs for both multivariate Gaussian and sub-Gaussian cases. Finally, we demonstrate the effectiveness of our algorithms through experiments on both synthetic and real-world datasets.

Di Wang, Adam Smith, Jinhui Xu

Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function. Specifically, we consider differentially private algorithms that operate in the local model, where each data record is stored on a separate user device and randomization is performed locally by those devices. We give new protocols for \emph{noninteractive} LDP convex optimization---i.e., protocols that require only a single randomized report from each user to an untrusted aggregator. We study our algorithms' performance with respect to expected loss---either over the data set at hand (empirical risk) or a larger population from which our data set is assumed to be drawn. Our error bounds depend on the form of individuals' contribution to the expected loss. For the case of \emph{generalized linear losses} (such as hinge and logistic losses), we give an LDP algorithm whose sample complexity is only linear in the dimensionality $p$ and quasipolynomial in other terms (the privacy parameters $ε$ and $δ$, and the desired excess risk $α$). This is the first algorithm for nonsmooth losses with sub-exponential dependence on $p$. For the Euclidean median problem, where the loss is given by the Euclidean distance to a given data point, we give a protocol whose sample complexity grows quasipolynomially in $p$. This is the first protocol with sub-exponential dependence on $p$ for a loss that is not a generalized linear loss . Our result for the hinge loss is based on a technique, dubbed polynomial of inner product approximation, which may be applicable to other problems. Our results for generalized linear losses and the Euclidean median are based on new reductions to the case of hinge loss.

Hu Ding, Jinhui Xu

In this paper, we consider a class of constrained clustering problems of points in $\mathbb{R}^{d}$, where $d$ could be rather high. A common feature of these problems is that their optimal clusterings no longer have the locality property (due to the additional constraints), which is a key property required by many algorithms for their unconstrained counterparts. To overcome the difficulty caused by the loss of locality, we present in this paper a unified framework, called {\em Peeling-and-Enclosing (PnE)}, to iteratively solve two variants of the constrained clustering problems, {\em constrained $k$-means clustering} ($k$-CMeans) and {\em constrained $k$-median clustering} ($k$-CMedian). Our framework is based on two standalone geometric techniques, called {\em Simplex Lemma} and {\em Weaker Simplex Lemma}, for $k$-CMeans and $k$-CMedian, respectively. The simplex lemma (or weaker simplex lemma) enables us to efficiently approximate the mean (or median) point of an unknown set of points by searching a small-size grid, independent of the dimensionality of the space, in a simplex (or the surrounding region of a simplex), and thus can be used to handle high dimensional data. If $k$ and $\frac{1}ε$ are fixed numbers, our framework generates, in nearly linear time ({\em i.e.,} $O(n(\log n)^{k+1}d)$), $O((\log n)^{k})$ $k$-tuple candidates for the $k$ mean or median points, and one of them induces a $(1+ε)$-approximation for $k$-CMeans or $k$-CMedian, where $n$ is the number of points. Combining this unified framework with a problem-specific selection algorithm (which determines the best $k$-tuple candidate), we obtain a $(1+ε)$-approximation for each of the constrained clustering problems. We expect that our technique will be applicable to other constrained clustering problems without locality.

Di Wang, Minwei Ye, Jinhui Xu

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared with previous work. For ERM with smooth convex loss function in high-dimensional ($p\gg n$) setting, we give an algorithm which achieves the upper bound with less gradient complexity than previous ones. At last, we generalize the expected excess empirical risk from convex loss functions to non-convex ones satisfying the Polyak-Lojasiewicz condition and give a tighter upper bound on the utility than the one in \cite{ijcai2017-548}.

Di Wang, Marco Gaboardi, Jinhui Xu

In this paper, we study the Empirical Risk Minimization problem in the non-interactive local model of differential privacy. In the case of constant or low dimensionality ($p\ll n$), we first show that if the ERM loss function is $(\infty, T)$-smooth, then we can avoid a dependence of the sample complexity, to achieve error $α$, on the exponential of the dimensionality $p$ with base $1/α$ (i.e., $α^{-p}$), which answers a question in [smith 2017 interaction]. Our approach is based on polynomial approximation. Then, we propose player-efficient algorithms with $1$-bit communication complexity and $O(1)$ computation cost for each player. The error bound is asymptotically the same as the original one. Also with additional assumptions we show a server efficient algorithm. Next we consider the high dimensional case ($n\ll p$), we show that if the loss function is Generalized Linear function and convex, then we could get an error bound which is dependent on the Gaussian width of the underlying constrained set instead of $p$, which is lower than that in [smith 2017 interaction].

Di Wang, Jinhui Xu

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new method called two-step preconditioning to achieve an approximate solution with a time complexity lower than that of the state-of-the-art techniques for the low precision case. Our idea can also be extended to the high precision case, which gives an alternative implementation to the Iterative Hessian Sketch (IHS) method with significantly improved time complexity. Experiments on benchmark and synthetic datasets suggest that our methods indeed outperform existing ones considerably in both the low and high precision cases.