arXiv subjects

Puning Zhao

Publications and source records attributed to Puning Zhao.

31 records · Page 2Linked to original sources

arXiv2024

Learn Suspected Anomalies from Event Prompts for Video Anomaly Detection

Most models for weakly supervised video anomaly detection (WS-VAD) rely on multiple instance learning, aiming to distinguish normal and abnormal snippets without specifying the type of anomaly. However, the ambiguous nature of anomaly definitions across contexts may introduce inaccuracy in discriminating abnormal and normal events. To show the model what is anomalous, a novel framework is proposed to guide the learning of suspected anomalies from event prompts. Given a textual prompt dictionary of potential anomaly events and the captions generated from anomaly videos, the semantic anomaly similarity between them could be calculated to identify the suspected events for each video snippet. It enables a new multi-prompt learning process to constrain the visual-semantic features across all videos, as well as provides a new way to label pseudo anomalies for self-training. To demonstrate its effectiveness, comprehensive experiments and detailed ablation studies are conducted on four datasets, namely XD-Violence, UCF-Crime, TAD, and ShanghaiTech. Our proposed model outperforms most state-of-the-art methods in terms of AP or AUC (86.5\%, \hl{90.4}\%, 94.4\%, and 97.4\%). Furthermore, it shows promising performance in open-set and cross-dataset cases. The data, code, and models can be found at: \url{https://github.com/shiwoaz/lap}.

cs.CV↗

arXiv2024

Sequential Federated Learning in Hierarchical Architecture on Non-IID Datasets

In a real federated learning (FL) system, communication overhead for passing model parameters between the clients and the parameter server (PS) is often a bottleneck. Hierarchical federated learning (HFL) that poses multiple edge servers (ESs) between clients and the PS can partially alleviate communication pressure but still needs the aggregation of model parameters from multiple ESs at the PS. To further reduce communication overhead, we bring sequential FL (SFL) into HFL for the first time, which removes the central PS and enables the model training to be completed only through passing the global model between two adjacent ESs for each iteration, and propose a novel algorithm adaptive to such a combinational framework, referred to as Fed-CHS. Convergence results are derived for strongly convex and non-convex loss functions under various data heterogeneity setups, which show comparable convergence performance with the algorithms for HFL or SFL solely. Experimental results provide evidence of the superiority of our proposed Fed-CHS on both communication overhead saving and test accuracy over baseline methods.

cs.LG↗

arXiv2024

Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates

We study convex optimization problems under differential privacy (DP). With heavy-tailed gradients, existing works achieve suboptimal rates. The main obstacle is that existing gradient estimators have suboptimal tail properties, resulting in a superfluous factor of $d$ in the union bound. In this paper, we explore algorithms achieving optimal rates of DP optimization with heavy-tailed gradients. Our first method is a simple clipping approach. Under bounded $p$-th order moments of gradients, with $n$ samples, it achieves $\tilde{O}(\sqrt{d/n}+\sqrt{d}(\sqrt{d}/nε)^{1-1/p})$ population risk with $ε\leq 1/\sqrt{d}$. We then propose an iterative updating method, which is more complex but achieves this rate for all $ε\leq 1$. The results significantly improve over existing methods. Such improvement relies on a careful treatment of the tail behavior of gradient estimators. Our results match the minimax lower bound in \cite{kamath2022improved}, indicating that the theoretical limit of stochastic convex optimization under DP is achievable.

cs.LG↗

arXiv2024

Minimax Optimal Q Learning with Nearest Neighbors

Analyzing the Markov decision process (MDP) with continuous state spaces is generally challenging. A recent interesting work \cite{shah2018q} solves MDP with bounded continuous state space by a nearest neighbor $Q$ learning approach, which has a sample complexity of $\tilde{O}(\frac{1}{ε^{d+3}(1-γ)^{d+7}})$ for $ε$-accurate $Q$ function estimation with discount factor $γ$. In this paper, we propose two new nearest neighbor $Q$ learning methods, one for the offline setting and the other for the online setting. We show that the sample complexities of these two methods are $\tilde{O}(\frac{1}{ε^{d+2}(1-γ)^{d+2}})$ and $\tilde{O}(\frac{1}{ε^{d+2}(1-γ)^{d+3}})$ for offline and online methods respectively, which significantly improve over existing results and have minimax optimal dependence over $ε$. We achieve such improvement by utilizing the samples more efficiently. In particular, the method in \cite{shah2018q} clears up all samples after each iteration, thus these samples are somewhat wasted. On the other hand, our offline method does not remove any samples, and our online method only removes samples with time earlier than $βt$ at time $t$ with $β$ being a tunable parameter, thus our methods significantly reduce the loss of information. Apart from the sample complexity, our methods also have additional advantages of better computational complexity, as well as suitability to unbounded state spaces.

cs.LG↗

arXiv2024

Learning with User-Level Local Differential Privacy

User-level privacy is important in distributed systems. Previous research primarily focuses on the central model, while the local models have received much less attention. Under the central model, user-level DP is strictly stronger than the item-level one. However, under the local model, the relationship between user-level and item-level LDP becomes more complex, thus the analysis is crucially different. In this paper, we first analyze the mean estimation problem and then apply it to stochastic optimization, classification, and regression. In particular, we propose adaptive strategies to achieve optimal performance at all privacy levels. Moreover, we also obtain information-theoretic lower bounds, which show that the proposed methods are minimax optimal up to logarithmic factors. Unlike the central DP model, where user-level DP always leads to slower convergence, our result shows that under the local model, the convergence rates are nearly the same between user-level and item-level cases for distributions with bounded support. For heavy-tailed distributions, the user-level rate is even faster than the item-level one.

stat.ML↗

arXiv2024

Enhancing Learning with Label Differential Privacy by Vector Approximation

Label differential privacy (DP) is a framework that protects the privacy of labels in training datasets, while the feature vectors are public. Existing approaches protect the privacy of labels by flipping them randomly, and then train a model to make the output approximate the privatized label. However, as the number of classes $K$ increases, stronger randomization is needed, thus the performances of these methods become significantly worse. In this paper, we propose a vector approximation approach, which is easy to implement and introduces little additional computational overhead. Instead of flipping each label into a single scalar, our method converts each label into a random vector with $K$ components, whose expectations reflect class conditional probabilities. Intuitively, vector approximation retains more information than scalar labels. A brief theoretical analysis shows that the performance of our method only decays slightly with $K$. Finally, we conduct experiments on both synthesized and real datasets, which validate our theoretical analysis as well as the practical performance of our method.

cs.LG↗

arXiv2024

A Huber Loss Minimization Approach to Byzantine Robust Federated Learning

Federated learning systems are susceptible to adversarial attacks. To combat this, we introduce a novel aggregator based on Huber loss minimization, and provide a comprehensive theoretical analysis. Under independent and identically distributed (i.i.d) assumption, our approach has several advantages compared to existing methods. Firstly, it has optimal dependence on $ε$, which stands for the ratio of attacked clients. Secondly, our approach does not need precise knowledge of $ε$. Thirdly, it allows different clients to have unequal data sizes. We then broaden our analysis to include non-i.i.d data, such that clients have slightly different distributions.

cs.LG↗

arXiv2023

Robust Nonparametric Regression under Poisoning Attack

This paper studies robust nonparametric regression, in which an adversarial attacker can modify the values of up to $q$ samples from a training dataset of size $N$. Our initial solution is an M-estimator based on Huber loss minimization. Compared with simple kernel regression, i.e. the Nadaraya-Watson estimator, this method can significantly weaken the impact of malicious samples on the regression performance. We provide the convergence rate as well as the corresponding minimax lower bound. The result shows that, with proper bandwidth selection, $\ell_\infty$ error is minimax optimal. The $\ell_2$ error is optimal with relatively small $q$, but is suboptimal with larger $q$. The reason is that this estimator is vulnerable if there are many attacked samples concentrating in a small region. To address this issue, we propose a correction method by projecting the initial estimate to the space of Lipschitz functions. The final estimate is nearly minimax optimal for arbitrary $q$, up to a $\ln N$ factor.

math.ST↗

arXiv2021

Optimal Stochastic Nonconvex Optimization with Bandit Feedback

In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting method. We then propose an adaptive bin splitting method, which can significantly improve the performance. Furthermore, a minimax lower bound is derived, which shows that our new adaptive method achieves locally minimax optimal expected cumulative regret.

cs.LG↗

arXiv2020

Analysis of KNN Density Estimation

We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the probability density function has a bounded support and is bounded away from zero. We show that kNN density estimation is minimax optimal under both $\ell_1$ and $\ell_\infty$ criteria, if the support set is known. If the support set is unknown, then the convergence rate of $\ell_1$ error is not affected, while $\ell_\infty$ error does not converge. In the second case, the probability density function can approach zero and is smooth everywhere. Moreover, the Hessian is assumed to decay with the density values. For this case, our result shows that the $\ell_\infty$ error of kNN density estimation is nearly minimax optimal. The $\ell_1$ error does not reach the minimax lower bound, but is better than kernel density estimation.

stat.ML↗

arXiv2020

Minimax Optimal Estimation of KL Divergence for Continuous Distributions

Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples. In this paper, we analyze the convergence rates of the bias and variance of this estimator. Furthermore, we derive a lower bound of the minimax mean square error and show that kNN method is asymptotically rate optimal.

cs.IT↗

arXiv2019

Analysis of KNN Information Estimators for Smooth Distributions

KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away from zero in its support. In practice, however, KSG estimator also performs well for a much broader class of distributions, including not only those with bounded support and densities bounded away from zero, but also those with bounded support but densities approaching zero, and those with unbounded support. In this paper, we analyze the convergence rate of the error of KSG estimator for smooth distributions, whose support of density can be both bounded and unbounded. As KSG mutual information estimator can be viewed as an adaptive recombination of KL entropy estimators, in our analysis, we also provide convergence analysis of KL entropy estimator for a broad class of distributions.

stat.ML↗

arXiv2019

Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regression

k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has bounded support and the probability density function is bounded away from zero in its support, the convergence rate of the standard kNN method, in which k is the same for all test samples, is minimax optimal. On the contrary, if the distribution has unbounded support, we show that there is a gap between the convergence rate achieved by the standard kNN method and the minimax bound. To close this gap, we propose an adaptive kNN method, in which different k is selected for different samples. Our selection rule does not require precise knowledge of the underlying distribution of features. The new proposed method significantly outperforms the standard one. We characterize the convergence rate of the proposed adaptive method, and show that it matches the minimax lower bound.

math.ST↗