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Pathwise-randomness and models of second-order arithmetic

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arXiv 2021年

作者： Barmpalias, George Wang, Wei State Key Lab of Computer Science Inst. of Software Chinese Acad. of Sciences Beijing China Inst. of Logic & Cognition Dept. of Philosophy Sun Yat-Sen University Guangzhou China

A tree is pathwise-random if all of its paths are Martin-Löf random. We show that: (a) no weakly 2-random real computes a perfect pathwise-random tree;it follows that the class of perfect pathwise-random trees is null, with respect to any computable measure;(b) there exists a positive-measure pathwise-random tree which does not compute any complete extension of Peano arithmetic;and (c) there exists a perfect pathwise-random tree which does not compute any tree of positive measure and finite randomness deficiency. We then obtain models of second-order arithmetic that separate compactness principles below weak Königs lemma, answering questions by Chong et al. (2019). Copyright © 2021, The Authors. All rights reserved.

关键词： Random processes

A Many-Objective Evolutionary Algorithm Assisted by Ideal Hyperplane

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SSRN

SSRN 2022年

作者： Zhang, Zhixia Wen, Jie Wang, Hui Cai, Xingjuan Cui, Zhihua Zhang, Wensheng School of Computer Science and Technology Taiyuan University of Science and Technology China School of Information Engineering Nanchang Institute of Technology Nanchang330099 China State Key Laboratory of Intelligent Control and Management of Complex System Institute of Automation Chinese Academy of Sciences China State Key Lab. for Novel Software Technology Nanjing University China

In many-objective optimization problems (MaOPs), it is a difficult task for evolutionary algorithms to balance convergence and diversity while rapidly converging to the Pareto front. As the number of objectives increases, the difficulty of evolutionary algorithms increases with individual selection pressure. To address above problems, we propose a many-objective evolution algorithm assisted by an ideal hyperplane (MaOEA-IH). Firstly, the ideal hyperplane as a reference surface to guide the individual to search the Pareto front, which is established from the extremum of each dimension of the objective space. Secondly, a parallel p -norm mating selection strategy is proposed to improve convergence. In addition, two factors are considered in this strategy: 1) different p -norm are used to measure different spatial scales;2) individual selection uncertainty is defined by incorporating a probabilistic perturbation mechanism. Thirdly, the improved shift-based density estimation strategy is used as the evaluation criterion for environmental selection to improve the convergence and diversity of solution sets and enhance selection pressure. To verify the effectiveness of the proposed algorithm, MAOEA-IH is compared with seven excellent algorithms in three benchmark sets (DTLZ, WFG and MaF). The results show that the proposed MAOEA-IH is highly competitive in solving MaOPs. © 2022, The Authors. All rights reserved.

关键词： Geometry

Attention-Based Knowledge-aware Multi-Interest Intelligent Model for Sequential Recommendation

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Attention-Based Knowledge-aware Multi-Interest Intelligent M...

Symposia and Workshops on Ubiquitous, Autonomic and Trusted Computing, UIC-ATC

作者： Yang Li Qianmu Li Shunmei Meng Jun Hou School of Computer Science and Engineering Nanjing University of Science and Technology Nanjing China Intelligent Manufacturing Department Wuyi University Jiangmen China State Key Lab. for Novel Software Technology Nanjing University Nanjing China School of Social Science Nanjing Vocational University of Industry Technology Nanjing China

As a fundamental means of intelligent service, recommender systems have shown a trend of diversification. Sequential recommendation, a class of time-aware methods, aims to predict the user’s next click. Multi-interest representation is a hot topic in recommender systems, but the research on how to apply multi-interest into sequences is still in the minority. And many methods will introduce knowledge graph to improve the representation of items, but how to consider both knowledge graph and user’s multi-interest in sequential recommendation has become a temporary blank. In this paper, we propose an attentive sequential recommendation with knowledge-aware multi-interest module (AKAMI). Items are embedded from the sequence’s structure and user’s interests. Specifically, we represent items by stacking self-attention layers to mine the internal correlation of the sequence. Meanwhile, we segment the sequence via the common neighbors in the knowledge graph and cast the user’s multi-interest based on the aggregation of subsequences. Multi-interests are integrated into item representation by the gating network adaptively. Comprehensive experiments on two real-world datasets show that the proposed model performs better than various representative methods under different evaluation metrics. Additionally, we also visually explain the model through a case study.

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Asymptotically unbiased inst.nce-wise regularized partial AUC optimization: theory and algorithm 22

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Asymptotically unbiased instance-wise regularized partial AU...

Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Huiyang Shao Qianqian Xu Zhiyong Yang Shilong Bao Qingming Huang Key Lab of Intell. Info. Process. Inst. of Comput. Tech. CAS and School of Computer Science and Tech. University of Chinese Academy of Sciences Key Lab of Intell. Info. Process. Inst. of Comput. Tech. CAS School of Computer Science and Tech. University of Chinese Academy of Sciences State Key Lab of Info. Security Inst. of Info. Engineering CAS and School of Cyber Security University of Chinese Academy of Sciences Key Lab of Intell. Info. Process. Inst. of Comput. Tech. CAS and School of Computer Science and Tech. University of Chinese Academy of Sciences and BDKM University of Chinese Academy of Sciences and Peng Cheng Laboratory

ISBN: (纸本)9781713871088

The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive rate interval, which is a widely adopted measure when decision constraints must be considered. Consequentiy, PAUC optimization has naturally attracted increasing attention in the machine learning community within the last few years. Nonetheless, most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllab.e. Fortunately, a recent work presents an unbiased formulation of the PAUC optimization problem via distributional robust optimization. However, it is based on the pair-wise formulation of AUC, which suffers from the limited scalab.lity w.r.t. sample size and a slow convergence rate, especially for TPAUC. To address this issue, we present a simpler reformulation of the problem in an asymptotically unbiased and inst.nce-wise manner. For both OPAUC and TPAUC, we come to a nonconvex strongly concave minimax regularized problem of inst.nce-wise functions. On top of this, we employ an efficient solver enjoys a linear per-iteration computational complexity w.r.t. the sample size and a time-complexity of O(ε-1/3) to reach a ε stationary point. Furthermore, we find that the minimax reformulation also facilitates the theoretical analysis of generalization error as a byproduct. Compared with the existing results, we present new error bounds that are much easier to prove and could deal with hypotheses with real-valued outputs. Finally, extensive experiments on several benchmark datasets demonstrate the effectiveness of our method.

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Bridge the Gap between Supervised and Unsupervised Learning for Fine-Grained Classification

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arXiv 2022年

作者： Wang, Jiabao Li, Yang Wei, Xiu-Shen Li, Hang Miao, Zhuang Zhang, Rui Army Engineering University of PLA Nanjing210007 China PCA Lab Key Lab of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education Nanjing University of Science and Technology Nanjing210094 China Jiangsu Key Lab of Image and Video Understanding for Social Security School of Computer Science and Engineering Nanjing University of Science and Technology Nanjing210094 China State Key Lab. for Novel Software Technology Nanjing University Nanjing210023 China

Unsupervised learning technology has caught up with or even surpassed supervised learning technology in general object classification (GOC) and person re-identification (re-ID). However, it is found that the unsupervised learning of fine-grained visual classification (FGVC) is more challenging than GOC and person re-ID. In order to bridge the gap between unsupervised and supervised learning for FGVC, we investigate the essential factors (including feature extraction, clustering, and contrastive learning) for the performance gap between supervised and unsupervised FGVC. Furthermore, we propose a simple, effective, and practical method, termed as UFCL, to alleviate the gap. Three key issues are concerned and improved: First, we introduce a robust and powerful backbone, ResNet50-IBN, which has an ability of domain adaptation when we transfer ImageNet pre-trained models to FGVC tasks. Next, we propose to introduce HDBSCAN inst.ad of DBSCAN to do clustering, which can generate better clusters for adjacent categories with fewer hyper-parameters. Finally, we propose a weighted feature agent and its updating mechanism to do contrastive learning by using the pseudo lab.ls with inevitable noise, which can improve the optimization process of learning the parameters of the network. The effectiveness of our UFCL is verified on CUB-200-2011, Oxford-Flowers, Oxford-Pets, Stanford-Dogs, Stanford-Cars and FGVC-Aircraft datasets. Under the unsupervised FGVC setting, we achieve state-of-the-art results, and analyze the key factors and the important parameters to provide a practical guidance. Copyright © 2022, The Authors. All rights reserved.

关键词： Image classification

Reach-avoid Verification Based on Convex Optimization

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arXiv 2022年

作者： Xue, Bai Zhan, Naijun Fränzle, Martin Wang, Ji Liu, Wanwei State Key Lab. of Computer Science Institute of Software Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China Carl von Ossietzky Universität Oldenburg Oldenburg Germany National University of Defense Technology Changsha China

In this paper we propose novel optimization-based methods for verifying reach-avoid (or, eventuality) properties of continuous-time systems modelled by ordinary differential equations. Given a system, an initial set, a safe set and a target set of states, we say that the reach-avoid property holds if for all initial conditions in the initial set, any trajectory of the system starting at them will eventually, i.e. in unbounded yet finite time, enter the target set while remaining inside the safe set until that first target hit. Based on a discount value function, two sets of quantified constraints are derived for verifying the reach-avoid property via the computation of exponential/asymptotic guidance-barrier functions (they form a barrier escorting the system to the target set safely at an exponential or asymptotic rate). It is interesting to find that one set of constraints whose solution is termed exponential guidance-barrier functions is just a simplified version of the existing one derived from the moment based method, while the other one whose solution is termed asymptotic guidance-barrier functions is completely new. Furthermore, built upon this new set of constraints, we derive a set of more expressive constraints, which includes the aforementioned two sets of constraints as special inst.nces, providing more chances for verifying the reach-avoid properties successfully. When the involved datum are polynomials, i.e., the initial set, safe set and target set are semi-algebraic, and the system has polynomial dynamics, the problem of solving these sets of constraints can be framed as a semi-definite optimization problem using sum-of-squares decomposition techniques and thus can be efficiently solved in polynomial time via interior point methods. Finally, several examples demonstrate the theoretical developments and performance of proposed methods. Copyright © 2022, The Authors. All rights reserved.

关键词： Ordinary differential equations

A Characterization of Robust Regions of Attraction for Discrete-Time Systems Based on Bellman Equations

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IFAC-PapersOnLine 2020年第2期53卷 6390-6397页

作者： Bai Xue Naijun Zhan Yangjia Li State Key Lab. of Computer Science Institute of Software CAS China University of Chinese Academy of Sciences Beijing China

In this paper we present a Bellman equation for computing robust regions of attraction for state-constrained perturbed discrete-time systems. The robust region of attraction of interest is a set of states such that every trajectory initialized in it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. In this approach, the interior of the maximal robust region of attraction is characterized as the strict one sub-level set of the unique bounded and continuous solution to a Bellman equation.

关键词： Robust Regions of Attraction state-Constrained Perturbed Discrete-Time Systems Bellman Equations

Robust Regions of Attraction Generation for state-Constrained Perturbed Discrete-Time Polynomial Systems

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IFAC-PapersOnLine 2020年第2期53卷 6327-6333页

作者： Bai Xue Naijun Zhan Yangjia Li University of Chinese Academy of Sciences Beijing China State Key Lab. of Computer Science Institute of Software CAS China

In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that every possible trajectory initialized in it will approach an equilibrium state while never violating the specified state constraint, regardless of the actual perturbation. Based on a Bellman equation which characterizes the interior of the maximal robust region of attraction as the strict one sub-level set of its unique bounded and continuous solution, we construct a semi-definite program for computing robust regions of attraction. Under appropriate assumptions, the existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate and converge to the interior of the maximal robust region of attraction in measure. Finally, we demonstrate the method by two examples.

关键词： Robust Regions of Attraction state-Constrained Perturbed Discrete-Time Polynomial Systems Convex Programming

User-inspired posterior network for recommendation reason generation

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arXiv 2021年

作者： Zhan, Haolan Zhang, Hainan Chen, Hongshen Shen, Lei Lan, Yanyan Ding, Zhuoye Yin, Dawei State Key Lab. of Computer Science Institute of Software Chinese Academy of Sciences Institute of Computing Technology Chinese Academy of Sciences University of Chinese Academy of Sciences Data Science Lab *** Baidu Inc. Beijing China

Recommendation reason generation, aiming at showing the selling points of products for customers, plays a vital role in attracting customers’ attention as well as improving user experience. A simple and effective way is to extract keywords directly from the knowledge-base of products, i.e., attributes or title, as the recommendation reason. However, generating recommendation reason from product knowledge doesn’t naturally respond to users’ interests. Fortunately, on some E-commerce websites, there exists more and more user-generated content (user-content for short), i.e., product question-answering (QA) discussions, which reflect user-cared aspects. Therefore, in this paper, we consider generating the recommendation reason by taking into account not only the product attributes but also the customer-generated product QA discussions. In reality, adequate user-content is only possible for the most popular commodities, whereas large sums of long-tail products or new products cannot gather a sufficient number of user-content. To tackle this problem, we propose a user-inspired multi-source posterior transformer (MSPT), which induces the model reflecting the users’ interests with a posterior multiple QA discussions module, and generating recommendation reasons containing the product attributes as well as the user-cared aspects. Experimental results show that our model is superior to traditional generative models. Additionally, the analysis also shows that our model can focus more on the user-cared aspects than baselines. Copyright © 2021, The Authors. All rights reserved.

关键词： Sales