Jinhui Xu

Yufan Zhou, Bingchen Liu, Yizhe Zhu et al.

We present Corgi, a novel method for text-to-image generation. Corgi is based on our proposed shifted diffusion model, which achieves better image embedding generation from input text. Unlike the baseline diffusion model used in DALL-E 2, our method seamlessly encodes prior knowledge of the pre-trained CLIP model in its diffusion process by designing a new initialization distribution and a new transition step of the diffusion. Compared to the strong DALL-E 2 baseline, our method performs better in generating image embedding from the text in terms of both efficiency and effectiveness, resulting in better text-to-image generation. Extensive large-scale experiments are conducted and evaluated in terms of both quantitative measures and human evaluation, indicating a stronger generation ability of our method compared to existing ones. Furthermore, our model enables semi-supervised and language-free training for text-to-image generation, where only part or none of the images in the training dataset have an associated caption. Trained with only 1.7% of the images being captioned, our semi-supervised model obtains FID results comparable to DALL-E 2 on zero-shot text-to-image generation evaluated on MS-COCO. Corgi also achieves new state-of-the-art results across different datasets on downstream language-free text-to-image generation tasks, outperforming the previous method, Lafite, by a large margin.

Yufan Zhou, Chunyuan Li, Changyou Chen et al.

Text-to-image generation models have progressed considerably in recent years, which can now generate impressive realistic images from arbitrary text. Most of such models are trained on web-scale image-text paired datasets, which may not be affordable for many researchers. In this paper, we propose a novel method for pre-training text-to-image generation model on image-only datasets. It considers a retrieval-then-optimization procedure to synthesize pseudo text features: for a given image, relevant pseudo text features are first retrieved, then optimized for better alignment. The low requirement of the proposed method yields high flexibility and usability: it can be beneficial to a wide range of settings, including the few-shot, semi-supervised and fully-supervised learning; it can be applied on different models including generative adversarial networks (GANs) and diffusion models. Extensive experiments illustrate the effectiveness of the proposed method. On MS-COCO dataset, our GAN model obtains Fréchet Inception Distance (FID) of 6.78 which is the new state-of-the-art (SoTA) of GANs under fully-supervised setting. Our diffusion model obtains FID of 8.42 and 4.28 on zero-shot and supervised setting respectively, which are competitive to SoTA diffusion models with a much smaller model size.

Chunwei Ma, Zhanghexuan Ji, Ziyun Huang et al.

Exemplar-free Class-incremental Learning (CIL) is a challenging problem because rehearsing data from previous phases is strictly prohibited, causing catastrophic forgetting of Deep Neural Networks (DNNs). In this paper, we present iVoro, a holistic framework for CIL, derived from computational geometry. We found Voronoi Diagram (VD), a classical model for space subdivision, is especially powerful for solving the CIL problem, because VD itself can be constructed favorably in an incremental manner -- the newly added sites (classes) will only affect the proximate classes, making the non-contiguous classes hardly forgettable. Further, in order to find a better set of centers for VD construction, we colligate DNN with VD using Power Diagram and show that the VD structure can be optimized by integrating local DNN models using a divide-and-conquer algorithm. Moreover, our VD construction is not restricted to the deep feature space, but is also applicable to multiple intermediate feature spaces, promoting VD to be multi-centered VD (CIVD) that efficiently captures multi-grained features from DNN. Importantly, iVoro is also capable of handling uncertainty-aware test-time Voronoi cell assignment and has exhibited high correlations between geometric uncertainty and predictive accuracy (up to ~0.9). Putting everything together, iVoro achieves up to 25.26%, 37.09%, and 33.21% improvements on CIFAR-100, TinyImageNet, and ImageNet-Subset, respectively, compared to the state-of-the-art non-exemplar CIL approaches. In conclusion, iVoro enables highly accurate, privacy-preserving, and geometrically interpretable CIL that is particularly useful when cross-phase data sharing is forbidden, e.g. in medical applications. Our code is available at https://machunwei.github.io/ivoro.

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.

Meng Ding, Mingxi Lei, Yunwen Lei et al.

(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on this problem only focused on analyzing the convergence or improving the convergence rate, while little effort has been devoted to understanding its generalization behaviors. In this paper, we conduct a thorough analysis on the generalization of first-order (gradient-based) methods for the bilevel optimization problem. We first establish a fundamental connection between algorithmic stability and generalization error in different forms and give a high probability generalization bound which improves the previous best one from $\bigO(\sqrt{n})$ to $\bigO(\log n)$, where $n$ is the sample size. We then provide the first stability bounds for the general case where both inner and outer level parameters are subject to continuous update, while existing work allows only the outer level parameter to be updated. Our analysis can be applied in various standard settings such as strongly-convex-strongly-convex (SC-SC), convex-convex (C-C), and nonconvex-nonconvex (NC-NC). Our analysis for the NC-NC setting can also be extended to a particular nonconvex-strongly-convex (NC-SC) setting that is commonly encountered in practice. Finally, we corroborate our theoretical analysis and demonstrate how iterations can affect the generalization error by experiments on meta-learning and hyper-parameter optimization.

Jinyan Su, Jinhui Xu, Di Wang

In this paper, we study the problem of PAC learning halfspaces in the non-interactive local differential privacy model (NLDP). To breach the barrier of exponential sample complexity, previous results studied a relaxed setting where the server has access to some additional public but unlabeled data. We continue in this direction. Specifically, we consider the problem under the standard setting instead of the large margin setting studied before. Under different mild assumptions on the underlying data distribution, we propose two approaches that are based on the Massart noise model and self-supervised learning and show that it is possible to achieve sample complexities that are only linear in the dimension and polynomial in other terms for both private and public data, which significantly improve the previous results. Our methods could also be used for other private PAC learning problems.

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.

Ruijia Zhang, Mingxi Lei, Meng Ding et al.

In this paper, we study the problem of (finite sum) minimax optimization in the Differential Privacy (DP) model. Unlike most of the previous studies on the (strongly) convex-concave settings or loss functions satisfying the Polyak-Lojasiewicz condition, here we mainly focus on the nonconvex-strongly-concave one, which encapsulates many models in deep learning such as deep AUC maximization. Specifically, we first analyze a DP version of Stochastic Gradient Descent Ascent (SGDA) and show that it is possible to get a DP estimator whose $l_2$-norm of the gradient for the empirical risk function is upper bounded by $\tilde{O}(\frac{d^{1/4}}{({nε})^{1/2}})$, where $d$ is the model dimension and $n$ is the sample size. We then propose a new method with less gradient noise variance and improve the upper bound to $\tilde{O}(\frac{d^{1/3}}{(nε)^{2/3}})$, which matches the best-known result for DP Empirical Risk Minimization with non-convex loss. We also discussed several lower bounds of private minimax optimization. Finally, experiments on AUC maximization, generative adversarial networks, and temporal difference learning with real-world data support our theoretical analysis.

Meng Ding, Mingxi Lei, Shaowei Wang et al.

In this paper, we investigate one of the most fundamental nonconvex learning problems, ReLU regression, in the Differential Privacy (DP) model. Previous studies on private ReLU regression heavily rely on stringent assumptions, such as constant bounded norms for feature vectors and labels. We relax these assumptions to a more standard setting, where data can be i.i.d. sampled from $O(1)$-sub-Gaussian distributions. We first show that when $\varepsilon = \tilde{O}(\sqrt{\frac{1}{N}})$ and there is some public data, it is possible to achieve an upper bound of $\tilde{O}(\frac{d^2}{N^2 \varepsilon^2})$ for the excess population risk in $(ε, δ)$-DP, where $d$ is the dimension and $N$ is the number of data samples. Moreover, we relax the requirement of $ε$ and public data by proposing and analyzing a one-pass mini-batch Generalized Linear Model Perceptron algorithm (DP-MBGLMtron). Additionally, using the tracing attack argument technique, we demonstrate that the minimax rate of the estimation error for $(\varepsilon, δ)$-DP algorithms is lower bounded by $Ω(\frac{d^2}{N^2 \varepsilon^2})$. This shows that DP-MBGLMtron achieves the optimal utility bound up to logarithmic factors. Experiments further support our theoretical results.

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.

Meng Ding, Jinhui Xu, Kaiyi Ji

Continual learning (CL) aims to train models on a sequence of tasks while retaining performance on previously learned ones. A core challenge in this setting is catastrophic forgetting, where new learning interferes with past knowledge. Among various mitigation strategies, data-replay methods, where past samples are periodically revisited, are considered simple yet effective, especially when memory constraints are relaxed. However, the theoretical effectiveness of full data replay, where all past data is accessible during training, remains largely unexplored. In this paper, we present a comprehensive theoretical framework for analyzing full data-replay training in continual learning from a feature learning perspective. Adopting a multi-view data model, we identify the signal-to-noise ratio (SNR) as a critical factor affecting forgetting. Focusing on task-incremental binary classification across $M$ tasks, our analysis verifies two key conclusions: (1) forgetting can still occur under full replay when the cumulative noise from later tasks dominates the signal from earlier ones; and (2) with sufficient signal accumulation, data replay can recover earlier tasks-even if their initial learning was poor. Notably, we uncover a novel insight into task ordering: prioritizing higher-signal tasks not only facilitates learning of lower-signal tasks but also helps prevent catastrophic forgetting. We validate our theoretical findings through synthetic and real-world experiments that visualize the interplay between signal learning and noise memorization across varying SNRs and task correlation regimes.

Meng Ding, Mingxi Lei, Shaopeng Fu et al.

Differentially private Stochastic Gradient Descent (DP-SGD) has become integral to privacy-preserving machine learning, ensuring robust privacy guarantees in sensitive domains. Despite notable empirical advances leveraging features from non-private, pre-trained models to enhance DP-SGD training, a theoretical understanding of feature dynamics in private learning remains underexplored. This paper presents the first theoretical framework to analyze private training through a feature learning perspective. Building on the multi-patch data structure from prior work, our analysis distinguishes between label-dependent feature signals and label-independent noise, a critical aspect overlooked by existing analyses in the DP community. Employing a two-layer CNN with polynomial ReLU activation, we theoretically characterize both feature signal learning and data noise memorization in private training via noisy gradient descent. Our findings reveal that (1) Effective private signal learning requires a higher signal-to-noise ratio (SNR) compared to non-private training, and (2) When data noise memorization occurs in non-private learning, it will also occur in private learning, leading to poor generalization despite small training loss. Our findings highlight the challenges of private learning and prove the benefit of feature enhancement to improve SNR. Experiments on synthetic and real-world datasets also validate our theoretical findings.

Difei Xu, Meng Ding, Zihang Xiang et al.

We study Stochastic Convex Optimization in the Differential Privacy model (DP-SCO). Unlike previous studies, here we assume the population risk function satisfies the Tsybakov Noise Condition (TNC) with some parameter $θ>1$, where the Lipschitz constant of the loss could be extremely large or even unbounded, but the $\ell_2$-norm gradient of the loss has bounded $k$-th moment with $k\geq 2$. For the Lipschitz case with $θ\geq 2$, we first propose an $(\varepsilon, δ)$-DP algorithm whose utility bound is $\Tilde{O}\left(\left(\tilde{r}_{2k}(\frac{1}{\sqrt{n}}+(\frac{\sqrt{d}}{n\varepsilon}))^\frac{k-1}{k}\right)^\fracθ{θ-1}\right)$ in high probability, where $n$ is the sample size, $d$ is the model dimension, and $\tilde{r}_{2k}$ is a term that only depends on the $2k$-th moment of the gradient. It is notable that such an upper bound is independent of the Lipschitz constant. We then extend to the case where $θ\geq \barθ> 1$ for some known constant $\barθ$. Moreover, when the privacy budget $\varepsilon$ is small enough, we show an upper bound of $\tilde{O}\left(\left(\tilde{r}_{k}(\frac{1}{\sqrt{n}}+(\frac{\sqrt{d}}{n\varepsilon}))^\frac{k-1}{k}\right)^\fracθ{θ-1}\right)$ even if the loss function is not Lipschitz. For the lower bound, we show that for any $θ\geq 2$, the private minimax rate for $ρ$-zero Concentrated Differential Privacy is lower bounded by $Ω\left(\left(\tilde{r}_{k}(\frac{1}{\sqrt{n}}+(\frac{\sqrt{d}}{n\sqrtρ}))^\frac{k-1}{k}\right)^\fracθ{θ-1}\right)$.

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, Ruiyi Zhang, Tong Sun et al.

Recent text-to-image generation models have demonstrated impressive capability of generating text-aligned images with high fidelity. However, generating images of novel concept provided by the user input image is still a challenging task. To address this problem, researchers have been exploring various methods for customizing pre-trained text-to-image generation models. Currently, most existing methods for customizing pre-trained text-to-image generation models involve the use of regularization techniques to prevent over-fitting. While regularization will ease the challenge of customization and leads to successful content creation with respect to text guidance, it may restrict the model capability, resulting in the loss of detailed information and inferior performance. In this work, we propose a novel framework for customized text-to-image generation without the use of regularization. Specifically, our proposed framework consists of an encoder network and a novel sampling method which can tackle the over-fitting problem without the use of regularization. With the proposed framework, we are able to customize a large-scale text-to-image generation model within half a minute on single GPU, with only one image provided by the user. We demonstrate in experiments that our proposed framework outperforms existing methods, and preserves more fine-grained details.

Chunwei Ma, Ziyun Huang, Mingchen Gao et al.

Few-shot learning (FSL) is the process of rapid generalization from abundant base samples to inadequate novel samples. Despite extensive research in recent years, FSL is still not yet able to generate satisfactory solutions for a wide range of real-world applications. To confront this challenge, we study the FSL problem from a geometric point of view in this paper. One observation is that the widely embraced ProtoNet model is essentially a Voronoi Diagram (VD) in the feature space. We retrofit it by making use of a recent advance in computational geometry called Cluster-induced Voronoi Diagram (CIVD). Starting from the simplest nearest neighbor model, CIVD gradually incorporates cluster-to-point and then cluster-to-cluster relationships for space subdivision, which is used to improve the accuracy and robustness at multiple stages of FSL. Specifically, we use CIVD (1) to integrate parametric and nonparametric few-shot classifiers; (2) to combine feature representation and surrogate representation; (3) and to leverage feature-level, transformation-level, and geometry-level heterogeneities for a better ensemble. Our CIVD-based workflow enables us to achieve new state-of-the-art results on mini-ImageNet, CUB, and tiered-ImagenNet datasets, with ${\sim}2\%{-}5\%$ improvements upon the next best. To summarize, CIVD provides a mathematically elegant and geometrically interpretable framework that compensates for extreme data insufficiency, prevents overfitting, and allows for fast geometric ensemble for thousands of individual VD. These together make FSL stronger.

Di Wang, Jinhui Xu

We study the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) with heavy-tailed data. Specifically, we focus on the $\ell_1$-norm linear regression in the $ε$-DP model. While most of the previous work focuses on the case where the loss function is Lipschitz, here we only need to assume the variates has bounded moments. Firstly, we study the case where the $\ell_2$ norm of data has bounded second order moment. We propose an algorithm which is based on the exponential mechanism and show that it is possible to achieve an upper bound of $\tilde{O}(\sqrt{\frac{d}{nε}})$ (with high probability). Next, we relax the assumption to bounded $θ$-th order moment with some $θ\in (1, 2)$ and show that it is possible to achieve an upper bound of $\tilde{O}(({\frac{d}{nε}})^\frac{θ-1}θ)$. Our algorithms can also be extended to more relaxed cases where only each coordinate of the data has bounded moments, and we can get an upper bound of $\tilde{O}({\frac{d}{\sqrt{nε}}})$ and $\tilde{O}({\frac{d}{({nε})^\frac{θ-1}θ}})$ in the second and $θ$-th moment case respectively.

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, Changyou Chen, Jinhui Xu

Learning high-dimensional distributions is an important yet challenging problem in machine learning with applications in various domains. In this paper, we introduce new techniques to formulate the problem as solving Fokker-Planck equation in a lower-dimensional latent space, aiming to mitigate challenges in high-dimensional data space. Our proposed model consists of latent-distribution morphing, a generator and a parameterized Fokker-Planck kernel function. One fascinating property of our model is that it can be trained with arbitrary steps of latent distribution morphing or even without morphing, which makes it flexible and as efficient as Generative Adversarial Networks (GANs). Furthermore, this property also makes our latent-distribution morphing an efficient plug-and-play scheme, thus can be used to improve arbitrary GANs, and more interestingly, can effectively correct failure cases of the GAN models. Extensive experiments illustrate the advantages of our proposed method over existing models.

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.

Di Wang, Xiangyu Guo, Shi Li et al.

In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a method called Trimmed (Gradient) Expectation Maximization which adds a trimming gradients step and a hard thresholding step to the Expectation step (E-step) and the Maximization step (M-step), respectively. We show that under some mild assumptions and with an appropriate initialization, the algorithm is corruption-proofing and converges to the (near) optimal statistical rate geometrically when the fraction of the corrupted samples $ε$ is bounded by $ \tilde{O}(\frac{1}{\sqrt{n}})$. Moreover, we apply our general framework to three canonical models: mixture of Gaussians, mixture of regressions and linear regression with missing covariates. Our theory is supported by thorough numerical results.

Di Wang, Xiangyu Guo, Chaowen Guan et al.

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new model which is called the \textit{Stochastic Linear Combination of Non-linear Regressions} model. However, due to the high non-convexity of the problem, there is no previous work study how to estimate the model. In this paper, we provide the first study on how to estimate the model efficiently and scalably. Specifically, we first show that with some mild assumptions, if the variate vector $x$ is multivariate Gaussian, then there is an algorithm whose output vectors have $\ell_2$-norm estimation errors of $O(\sqrt{\frac{p}{n}})$ with high probability, where $p$ is the dimension of $x$ and $n$ is the number of samples. The key idea of the proof is based on an observation motived by the Stein's lemma. Then we extend our result to the case where $x$ is bounded and sub-Gaussian using the zero-bias transformation, which could be seen as a generalization of the classic Stein's lemma. We also show that with some additional assumptions there is an algorithm whose output vectors have $\ell_\infty$-norm estimation errors of $O(\frac{1}{\sqrt{p}}+\sqrt{\frac{p}{n}})$ with high probability. We also provide a concrete example to show that there exists some link function which satisfies the previous assumptions. Finally, for both Gaussian and sub-Gaussian cases we propose a faster sub-sampling based algorithm and show that when the sub-sample sizes are large enough then the estimation errors will not be sacrificed by too much. Experiments for both cases support our theoretical results. To the best of our knowledge, this is the first work that studies and provides theoretical guarantees for the stochastic linear combination of non-linear regressions model.

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, Jinhui Xu

In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to achieve a non-trivial $\ell_2$-norm based error bound, which is significantly better than the existing ones from adding noise directly to the empirical covariance matrix. We also extend the $\ell_2$-norm based error bound to a general $\ell_w$-norm based one for any $1\leq w\leq \infty$, and show that they share the same upper bound asymptotically. Our approach can be easily extended to local differential privacy. Experiments on the synthetic datasets show consistent results with our theoretical claims.

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.

Chao Ma, Tianchenghou, Bin Lan et al.

In this paper, we present Deep Extreme Feature Extraction (DEFE), a new ensemble MVA method for searching $τ^{+}τ^{-}$ channel of Higgs bosons in high energy physics. DEFE can be viewed as a deep ensemble learning scheme that trains a strongly diverse set of neural feature learners without explicitly encouraging diversity and penalizing correlations. This is achieved by adopting an implicit neural controller (not involved in feedforward compuation) that directly controls and distributes gradient flows from higher level deep prediction network. Such model-independent controller results in that every single local feature learned are used in the feature-to-output mapping stage, avoiding the blind averaging of features. DEFE makes the ensembles 'deep' in the sense that it allows deep post-process of these features that tries to learn to select and abstract the ensemble of neural feature learners. With the application of this model, a selection regions full of signal process can be obtained through the training of a miniature collision events set. In comparison of the Classic Deep Neural Network, DEFE shows a state-of-the-art performance: the error rate has decreased by about 37\%, the accuracy has broken through 90\% for the first time, along with the discovery significance has reached a standard deviation of 6.0 $σ$. Experimental data shows that, DEFE is able to train an ensemble of discriminative feature learners that boosts the overperformance of final prediction.