arXiv subjects

Jinhui Xu

Publications and source records attributed to Jinhui Xu.

At least 37 records · Page 2Linked to original sources

arXiv2023

On Stability and Generalization of Bilevel Optimization Problem

(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.

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arXiv2022

Lafite2: Few-shot Text-to-Image Generation

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.

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arXiv2022

On PAC Learning Halfspaces in Non-interactive Local Privacy Model with Public Unlabeled Data

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.

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arXiv2022

Estimating Smooth GLM in Non-interactive Local Differential Privacy Model with Public Unlabeled Data

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.

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arXiv2022

Progressive Voronoi Diagram Subdivision: Towards A Holistic Geometric Framework for Exemplar-free Class-Incremental Learning

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.

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arXiv2022

In-Range Farthest Point Queries and Related Problem in High Dimensions

Range-aggregate query is an important type of queries with numerous applications. It aims to obtain some structural information (defined by an aggregate function $F(\cdot)$) of the points (from a point set $P$) inside a given query range $B$. In this paper, we study the range-aggregate query problem in high dimensional space for two aggregate functions: (1) $F(P \cap B)$ is the farthest point in $P \cap B$ to a query point $q$ in $\mathbb{R}^d$ and (2) $F(P \cap B)$ is the minimum enclosing ball (MEB) of $P \cap B$. For problem (1), called In-Range Farthest Point (IFP) Query, we develop a bi-criteria approximation scheme: For any $ε>0$ that specifies the approximation ratio of the farthest distance and any $γ>0$ that measures the "fuzziness" of the query range, we show that it is possible to pre-process $P$ into a data structure of size $\tilde{O}_{ε,γ}(dn^{1+ρ})$ in $\tilde{O}_{ε,γ}(dn^{1+ρ})$ time such that given any $\mathbb{R}^d$ query ball $B$ and query point $q$, it outputs in $\tilde{O}_{ε,γ}(dn^ρ)$ time a point $p$ that is a $(1-ε)$-approximation of the farthest point to $q$ among all points lying in a $(1+γ)$-expansion $B(1+γ)$ of $B$, where $0<ρ<1$ is a constant depending on $ε$ and $γ$ and the hidden constants in big-O notations depend only on $ε$, $γ$ and $\text{Polylog}(nd)$. For problem (2), we show that the IFP result can be applied to develop query scheme with similar time and space complexities to achieve a $(1+ε)$-approximation for MEB.

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arXiv2022

LAFITE: Towards Language-Free Training for Text-to-Image Generation

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.

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arXiv2022

Improving Uncertainty Calibration of Deep Neural Networks via Truth Discovery and Geometric Optimization

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.

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arXiv2022

Few-shot Learning as Cluster-induced Voronoi Diagrams: A Geometric Approach

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.

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arXiv2022

Differentially Private (Gradient) Expectation Maximization Algorithm with Statistical Guarantees

(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.

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arXiv2022

Differentially Private $\ell_1$-norm Linear Regression with Heavy-tailed Data

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.

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arXiv2021

A Generic Approach for Enhancing GANs by Regularized Latent Optimization

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.

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arXiv2021

Learning High-Dimensional Distributions with Latent Neural Fokker-Planck Kernels

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.

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arXiv2021

Learning Manifold Implicitly via Explicit Heat-Kernel Learning

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.

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arXiv2021

Meta-Learning with Neural Tangent Kernels

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.

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arXiv2020

Empirical Risk Minimization in the Non-interactive Local Model of Differential Privacy

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.

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arXiv2020

On Differentially Private Stochastic Convex Optimization with Heavy-tailed Data

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.

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arXiv2020

Estimating Stochastic Linear Combination of Non-linear Regressions Efficiently and Scalably

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.

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