arXiv subjects

Jinyu Wang

Publications and source records attributed to Jinyu Wang.

33 records · Page 2Linked to original sources

arXiv2024

Probabilistic degenerate Bernstein polynomials

In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with $Y$. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable.

math.NT↗

arXiv2024

Neural Probabilistic Logic Learning for Knowledge Graph Reasoning

Knowledge graph (KG) reasoning is a task that aims to predict unknown facts based on known factual samples. Reasoning methods can be divided into two categories: rule-based methods and KG-embedding based methods. The former possesses precise reasoning capabilities but finds it challenging to reason efficiently over large-scale knowledge graphs. While gaining the ability to reason over large-scale knowledge graphs, the latter sacrifices reasoning accuracy. This paper aims to design a reasoning framework called Neural Probabilistic Logic Learning(NPLL) that achieves accurate reasoning on knowledge graphs. Our approach introduces a scoring module that effectively enhances the expressive power of embedding networks, striking a balance between model simplicity and reasoning capabilities. We improve the interpretability of the model by incorporating a Markov Logic Network based on variational inference. We empirically evaluate our approach on several benchmark datasets, and the experimental results validate that our method substantially enhances the accuracy and quality of the reasoning results.

cs.AI↗

arXiv2024

Mildly Constrained Evaluation Policy for Offline Reinforcement Learning

Offline reinforcement learning (RL) methodologies enforce constraints on the policy to adhere closely to the behavior policy, thereby stabilizing value learning and mitigating the selection of out-of-distribution (OOD) actions during test time. Conventional approaches apply identical constraints for both value learning and test time inference. However, our findings indicate that the constraints suitable for value estimation may in fact be excessively restrictive for action selection during test time. To address this issue, we propose a \textit{Mildly Constrained Evaluation Policy (MCEP)} for test time inference with a more constrained \textit{target policy} for value estimation. Since the \textit{target policy} has been adopted in various prior approaches, MCEP can be seamlessly integrated with them as a plug-in. We instantiate MCEP based on TD3BC (Fujimoto & Gu, 2021), AWAC (Nair et al., 2020) and DQL (Wang et al., 2023) algorithms. The empirical results on D4RL MuJoCo locomotion, high-dimensional humanoid and a set of 16 robotic manipulation tasks show that the MCEP brought significant performance improvement on classic offline RL methods and can further improve SOTA methods. The codes are open-sourced at \url{https://github.com/egg-west/MCEP.git}.

cs.LG↗

arXiv2024

Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two chi-squared statistic-based algorithms for testing hypotheses on random shapes. Simulation studies are presented to validate our mathematical derivations and to compare our algorithms with state-of-the-art methods to demonstrate the utility of our proposed framework. As real applications, we analyze a data set of mandibular molars from four genera of primates and show that our algorithms have the power to detect significant shape differences that recapitulate known morphological variation across suborders. Altogether, our discussions bridge the following fields: algebraic and computational topology, probability theory and stochastic processes, Sobolev spaces and functional analysis, analysis of variance for functional data, and geometric morphometrics.

stat.ME↗

arXiv2024

Higher Replay Ratio Empowers Sample-Efficient Multi-Agent Reinforcement Learning

One of the notorious issues for Reinforcement Learning (RL) is poor sample efficiency. Compared to single agent RL, the sample efficiency for Multi-Agent Reinforcement Learning (MARL) is more challenging because of its inherent partial observability, non-stationary training, and enormous strategy space. Although much effort has been devoted to developing new methods and enhancing sample efficiency, we look at the widely used episodic training mechanism. In each training step, tens of frames are collected, but only one gradient step is made. We argue that this episodic training could be a source of poor sample efficiency. To better exploit the data already collected, we propose to increase the frequency of the gradient updates per environment interaction (a.k.a. Replay Ratio or Update-To-Data ratio). To show its generality, we evaluate $3$ MARL methods on $6$ SMAC tasks. The empirical results validate that a higher replay ratio significantly improves the sample efficiency for MARL algorithms. The codes to reimplement the results presented in this paper are open-sourced at https://anonymous.4open.science/r/rr_for_MARL-0D83/.

cs.LG↗

arXiv2023

Statistical Inference on Grayscale Images via the Euler-Radon Transform

Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where pixel intensities instead take on continuous values) have been relatively underdeveloped. In this paper, we introduce the Euler-Radon transform, which generalizes the Euler characteristic transform to grayscale images by using o-minimal structures and Euler integration over definable functions. Coupling the Karhunen-Loeve expansion with our proposed topological representation, we offer hypothesis-testing algorithms based on the chi-squared distribution for detecting significant differences between two groups of grayscale images. We illustrate our framework via extensive numerical experiments and simulations.

stat.ME↗

arXiv2023

Hypothesis testing for medical imaging analysis via the smooth Euler characteristic transform

Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis testing method via the smooth Euler characteristic transform to detect significant differences among collections of shapes. Our proposed method has a solid mathematical foundation and is computationally efficient. Through simulation studies, we illustrate the performance of our proposed method. We apply our method to images of lung cancer tumors from the National Lung Screening Trial database, comparing its performance to a state-of-the-art machine learning model.

stat.ME↗

arXiv2023

An Order-Complexity Model for Aesthetic Quality Assessment of Homophony Music Performance

Although computational aesthetics evaluation has made certain achievements in many fields, its research of music performance remains to be explored. At present, subjective evaluation is still a ultimate method of music aesthetics research, but it will consume a lot of human and material resources. In addition, the music performance generated by AI is still mechanical, monotonous and lacking in beauty. In order to guide the generation task of AI music performance, and to improve the performance effect of human performers, this paper uses Birkhoff's aesthetic measure to propose a method of objective measurement of beauty. The main contributions of this paper are as follows: Firstly, we put forward an objective aesthetic evaluation method to measure the music performance aesthetic; Secondly, we propose 10 basic music features and 4 aesthetic music features. Experiments show that our method performs well on performance assessment.

cs.SD↗

arXiv2023

An Order-Complexity Model for Aesthetic Quality Assessment of Symbolic Homophony Music Scores

Computational aesthetics evaluation has made great achievements in the field of visual arts, but the research work on music still needs to be explored. Although the existing work of music generation is very substantial, the quality of music score generated by AI is relatively poor compared with that created by human composers. The music scores created by AI are usually monotonous and devoid of emotion. Based on Birkhoff's aesthetic measure, this paper proposes an objective quantitative evaluation method for homophony music score aesthetic quality assessment. The main contributions of our work are as follows: first, we put forward a homophony music score aesthetic model to objectively evaluate the quality of music score as a baseline model; second, we put forward eight basic music features and four music aesthetic features.

cs.SD↗

arXiv2022

Multi-access Coded Caching with Optimal Rate and Linear Subpacketization under PDA and Consecutive Cyclic Placement

This work considers the multi-access caching system proposed by Hachem et al., where each user has access to L neighboring caches in a cyclic wrap-around fashion. We first propose a placement strategy called the consecutive cyclic placement, which achieves the maximal local caching gain. Then under the consecutive cyclic placement, we derive the optimal coded caching gain from the perspective of Placement Delivery Array (PDA), thus obtaining a lower bound on the rate of PDA. Finally, under the consecutive cyclic placement, we construct a class of PDA, leading to a multi-access coded caching scheme with linear subpacketization, which achieves our derived lower bound for some parameters; while for other parameters, the achieved coded caching gain is only 1 less than the optimal one. Analytical and numerical comparisons of the proposed scheme with existing schemes are provided to validate the performance.

cs.IT↗

arXiv2021

Novel Frameworks for Coded Caching via Cartesian Product with Reduced Subpacketization

Caching prefetches some library content at users' memories during the off-peak times (i.e., {\it placement phase}), such that the number of transmissions during the peak-traffic times (i.e., {\it delivery phase}) are reduced. A coded caching strategy was originally proposed by Maddah-Ali and Niesen (MN) leading to a multicasting gain compared to the conventional uncoded caching, where each message in the delivery phase is useful to multiple users simultaneously. However, the MN coded caching scheme suffers from the high subpacketization which makes it impractical. In order to reduce the subpacketization while retain the multicast opportunities in the delivery phase, Yan et al. proposed a combinatorial structure called placement delivery array (PDA) to design coded caching schemes. In this paper, we propose two novel frameworks for constructing PDA via Cartesian product, which constructs a PDA for $mK_1$ users by the $m$-fold Cartesian product of a PDA for $K_1$ users. By applying the proposed frameworks to some existing PDAs, three novel caching schemes are obtained which can significantly reduce the subpacketization of the MN scheme while slightly increasing the needed number of transmissions. For instance, for the third scheme which works for any number of users and any memory regime, while reducing the coded caching gain by one, the needed subpacketization is at most $O\left(\sqrt{\frac{K}{q}}2^{-\frac{K}{q}}\right)$ of that of the MN scheme, where $K$ is the number of users, $0<z/q<1$ is the memory ratio of each user, and $q,z$ are coprime.

cs.IT↗

arXiv2021

Coded Caching for Combination Networks with Multiaccess

In a traditional $(H, r)$ combination network, each user is connected to a unique set of $r$ relays. However, few research efforts to consider $(H, r, u)$ multiaccess combination network problem where each $u$ users are connected to a unique set of $r$ relays. A naive strategy to obtain a coded caching scheme for $(H, r, u)$ multiaccess combination network is by $u$ times repeated application of a coded caching scheme for a traditional $(H, r)$ combination network. Obviously, the transmission load for each relay of this trivial scheme is exactly $u$ times that of the original scheme, which implies that as the number of users multiplies, the transmission load for each relay will also multiply. Therefore, it is very meaningful to design a coded caching scheme for $(H, r, u)$ multiaccess combination network with lower transmission load for each relay. In this paper, by directly applying the well known coding method (proposed by Zewail and Yener) for $(H, r)$ combination network, a coded caching scheme (ZY scheme) for $(H, r, u)$ multiaccess combination network is obtained. However, the subpacketization of this scheme has exponential order with the number of users, which leads to a high implementation complexity. In order to reduce the subpacketization, a direct construction of a coded caching scheme for $(H, r, u)$ multiaccess combination network is proposed by means of Combinational Design Theory, where the parameter $u$ must be a combinatorial number. For arbitrary parameter $u$, a hybrid construction of a coded caching scheme for $(H, r, u)$ multiaccess combination network is proposed based on our direct construction. Theoretical and numerical analysis show that our last two schemes have smaller transmission load for each relay compared with the trivial scheme, and have much lower subpacketization compared with ZY scheme.

cs.IT↗

arXiv2021

A framework of constructing placement delivery arrays for centralized coded caching

In caching system, it is desirable to design a coded caching scheme with the transmission load $R$ and subpacketization $F$ as small as possible, in order to improve efficiency of transmission in the peak traffic times and to decrease implementation complexity. Yan et al. reformulated the centralized coded caching scheme as designing a corresponding $F\times K$ array called placement delivery array (PDA), where $F$ is the subpacketization and $K$ is the number of users. Motivated by several constructions of PDAs, we introduce a framework for constructing PDAs, where each row is indexed by a row vector of some matrix called row index matrix and each column's index is labelled by an element of a direct product set. Using this framework, a new scheme is obtained, which can be regarded as a generalization of some previously known schemes. When $K$ is equal to ${m\choose t}q^t$ for positive integers $m$, $t$ with $t<m$ and $q\geq 2$, we show that the row index matrix must be an orthogonal array if all the users have the same memory size. Furthermore, the row index matrix must be a covering array if the coded gain is ${m\choose t}$, which is the maximal coded gain under our framework. Consequently the lower bounds on the transmission load and subpacketization of the schemes are derived under our framework. Finally, using orthogonal arrays as the row index matrix, we obtain two more explicit classes of schemes which have significantly advantages on the subpacketization while the transmission load is equal or close to that of the schemes constructed by Shangguan et al. (IEEE Trans. Inf. Theory, 64, 5755-5766, 2018) for the same number of users and memory size.

cs.IT↗

arXiv2020

New coded caching schemes from placement delivery arrays

Coded caching schemes with low subpacketization and small transmission rate are desirable in practice due to the requirement of low implementation complexity and efficiency of the transmission. Placement delivery arrays (PDA in short) can be used to generate coded caching schemes. However, many known coded caching schemes have large memory ratios. In this paper, we realize that some schemes with low subpacketization generated by PDAs do not fully use the users' caching content to create multicasting opportunities and thus propose to overcome this drawback. As an application, we obtain two new schemes with low subpacketizations, which have significantly advantages on the memory ratio and transmission rate compared with the original scheme.

cs.IT↗

arXiv2017

On the Placement Delivery Array Design for Coded Caching Scheme in D2D Networks

The coded caching scheme is an efficient technique as a solution to reduce the wireless network burden during the peak times in a Device-to-Device (D2D in short) communications. In a coded caching scheme, each file block should be divided into $F$ packets. It is meaningful to design a coded caching scheme with the rate and $F$ as small as possible, especially in the practice for D2D network. In this paper we first characterize coded caching scheme for D2D network by a simple array called D2D placement delivery array (DPDA in shot). Consequently some coded caching scheme for D2D network can be discussed by means of an appropriate DPDA. Secondly we derive the lower bounds on the rate and $F$ of a DPDA. According these two lower bounds, we show that the previously known determined scheme proposed by Ji et al., (IEEE Trans. Inform. Theory, 62(2): 849-869,2016) reaches our lower bound on the rate, but does not meet the lower bound on $F$ for some parameters. Finally for these parameters, we construct three classes of DPDAs which meet our two lower bounds. Based on these DPDAs, three classes of coded caching scheme with low rate and lower $F$ are obtained for D2D network.

cs.IT↗