This paper studies how to approximate pufferfish privacy when the adversary's prior belief of the published data is Gaussian distributed. Using Monge's optimal transport plan, we show that $(\epsilon, \delta)$-pufferfish privacy is attained if the additive Laplace noise is calibrated to the differences in mean and variance of the Gaussian distributions conditioned on every discriminative secret pair. A typical application is the private release of the summation (or average) query, for which sufficient conditions are derived for approximating $\epsilon$-statistical indistinguishability in individual's sensitive data. The result is then extended to arbitrary prior beliefs trained by Gaussian mixture models (GMMs): calibrating Laplace noise to a convex combination of differences in mean and variance between Gaussian components attains $(\epsilon,\delta)$-pufferfish privacy.
相關內容
In this paper, we examine the role of stochastic quantizers for privacy preservation. We first employ a static stochastic quantizer and investigate its corresponding privacy-preserving properties. Specifically, we demonstrate that a sufficiently large quantization step guarantees $(0, \delta)$ differential privacy. Additionally, the degradation of control performance caused by quantization is evaluated as the tracking error of output regulation. These two analyses characterize the trade-off between privacy and control performance, determined by the quantization step. This insight enables us to use quantization intentionally as a means to achieve the seemingly conflicting two goals of maintaining control performance and preserving privacy at the same time; towards this end, we further investigate a dynamic stochastic quantizer. Under a stability assumption, the dynamic stochastic quantizer can enhance privacy, more than the static one, while achieving the same control performance. We further handle the unstable case by additionally applying input Gaussian noise.
This paper proposes a novel convex optimization framework for designing robust Kalman filters that guarantee a user-specified steady-state error while maximizing process and sensor noise. The proposed framework simultaneously determines the Kalman gain and the robustness margin in terms of the process and sensor noise. This is the first paper to present such a joint formulation for Kalman filtering. The proposed methodology is validated through two distinct examples: the Clohessy-Wiltshire-Hill equations for a chaser spacecraft in an elliptical orbit and the longitudinal motion model of an F-16 aircraft.
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly supported distributions, this method also applies when both the predictor and responses are Gaussian distributions on $\mathbb{R}^d$. Our approach generalizes an existing transportation-based regression model to higher dimensions. This model postulates that the conditional Fr\'echet mean of the response distribution is linked to the covariate distribution via an optimal transport map. We establish an upper bound for the rate of convergence of a plug-in estimator. We propose an iterative algorithm for computing the estimator, which is based on DC (Difference of Convex Functions) Programming. In the Gaussian case, the estimator achieves a parametric rate of convergence, and the computation of the estimator simplifies to a finite-dimensional optimization over positive definite matrices, allowing for an efficient solution. The performance of the estimator is demonstrated in a simulation study.
This paper introduces a novel Nussbaum function-based PID control for robotic manipulators. The integration of the Nussbaum function into the PID framework provides a solution with a simple structure that effectively tackles the challenge of unknown control directions. Stability is achieved through a combination of neural network-based estimation and Lyapunov analysis, facilitating automatic gain adjustment without the need for system dynamics. Our approach offers a gain determination with minimum parameter requirements, significantly reducing the complexity and enhancing the efficiency of robotic manipulator control. The paper guarantees that all signals within the closed-loop system remain bounded. Lastly, numerical simulations validate the theoretical framework, confirming the effectiveness of the proposed control strategy in enhancing robotic manipulator control.
This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a general and more realistic setup. Specifically, the comparison graph consists of hyper-edges of possible heterogeneous sizes, and the number of comparisons can be as low as one for a given hyper-edge. Such a setting is pervasive in real applications, circumventing the need to specify the graph randomness and the restrictive homogeneous sampling assumption imposed in the commonly used Bradley-Terry-Luce (BTL) or Plackett-Luce (PL) models. Furthermore, in scenarios where the BTL or PL models are appropriate, we unravel the relationship between the spectral estimator and the Maximum Likelihood Estimator (MLE). We discover that a two-step spectral method, where we apply the optimal weighting estimated from the equal weighting vanilla spectral method, can achieve the same asymptotic efficiency as the MLE. Given the asymptotic distributions of the estimated preference scores, we also introduce a comprehensive framework to carry out both one-sample and two-sample ranking inferences, applicable to both fixed and random graph settings. It is noteworthy that this is the first time effective two-sample rank testing methods have been proposed. Finally, we substantiate our findings via comprehensive numerical simulations and subsequently apply our developed methodologies to perform statistical inferences for statistical journals and movie rankings.
We propose a new and generic approach for detecting multiple change-points in general dependent data, termed random interval distillation (RID). By collecting random intervals with sufficient strength of signals and reassembling them into a sequence of informative short intervals, our new approach captures the shifts in signal characteristics across diverse dependent data forms including locally stationary high-dimensional time series and dynamic networks with Markov formation. We further propose a range of secondary refinements tailored to various data types to enhance the localization precision. Notably, for univariate time series and low-rank autoregressive networks, our methods achieve the minimax optimality as their independent counterparts. For practical applications, we introduce a clustering-based and data-driven procedure to determine the optimal threshold for signal strength, which is adaptable to a wide array of dependent data scenarios utilizing the connection between RID and clustering. Additionally, our method has been extended to identify kinks and changes in signals characterized by piecewise polynomial trends. We examine the effectiveness and usefulness of our methodology via extensive simulation studies and a real data example, implementing it in the R-package rid.
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.
Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191