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Jiangning Chen

Publications and source records attributed to Jiangning Chen.

8 recordsLinked to original sources
arXiv2026

Fragmentation and Cluster Prediction in One-Dimensional Finite-Range Normalized Alignment Dynamics

We study fragmentation in a one-dimensional finite-range normalized alignment system, where each agent relaxes its velocity toward the average velocity of agents within a fixed interaction radius. Because the communication graph depends on the agents' positions, edges can disappear as agents separate, leading to multiple asymptotic velocity clusters. We first consider spatially ordered initial data with velocities ordered in the same direction. In this expansive regime, we prove that velocity ordering is forward invariant, all pairwise separations are nondecreasing, and communication edges can only be deleted. Hence, the dynamics undergo finitely many topology changes. Between changes, the velocity dynamics form a linear system generated by a random-walk Laplacian. Using its group inverse, we derive an exact terminal-separation formula for every active edge and obtain a finite recursive procedure for determining the terminal communication graph and the asymptotic velocity of each cluster. For path graphs, this theory becomes explicit: a tridiagonal Green kernel gives a necessary-and-sufficient criterion for finite-time fragmentation and a sharp critical alignment strength separating fragmentation from mono-flocking. We also identify a class of non-monotone initial velocities that enters the expansive regime before the first topology change and derive Gaussian statistics for terminal separations under random initial velocities. For this class of ordered and safely entering initial data, our results provide a rigorous mechanism for the spontaneous group division observed in earlier numerical studies. The general switching problem for arbitrary initial configurations remains open. Reproducible computations validate the path threshold, first-fragmentation-time prediction, and finite-event recursion against independent direct integration of the switching dynamics.

math.DS↗
arXiv2024

Hybrid Reinforcement Learning Framework for Mixed-Variable Problems

Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable spaces effectively. To Address these challenges, we introduce a hybrid Reinforcement Learning (RL) framework that synergizes RL for discrete variable selection with Bayesian Optimization for continuous variable adjustment. This framework stands out by its strategic integration of RL and continuous optimization techniques, enabling it to dynamically adapt to the problem's mixed-variable nature. By employing RL for exploring discrete decision spaces and Bayesian Optimization to refine continuous parameters, our approach not only demonstrates flexibility but also enhances optimization performance. Our experiments on synthetic functions and real-world machine learning hyperparameter tuning tasks reveal that our method consistently outperforms traditional RL, random search, and standalone Bayesian optimization in terms of effectiveness and efficiency.

math.OC↗
arXiv2021

Personalized Entity Resolution with Dynamic Heterogeneous Knowledge Graph Representations

The growing popularity of Virtual Assistants poses new challenges for Entity Resolution, the task of linking mentions in text to their referent entities in a knowledge base. Specifically, in the shopping domain, customers tend to use implicit utterances (e.g., "organic milk") rather than explicit names, leading to a large number of candidate products. Meanwhile, for the same query, different customers may expect different results. For example, with "add milk to my cart", a customer may refer to a certain organic product, while some customers may want to re-order products they regularly purchase. To address these issues, we propose a new framework that leverages personalized features to improve the accuracy of product ranking. We first build a cross-source heterogeneous knowledge graph from customer purchase history and product knowledge graph to jointly learn customer and product embeddings. After that, we incorporate product, customer, and history representations into a neural reranking model to predict which candidate is most likely to be purchased for a specific customer. Experiments show that our model substantially improves the accuracy of the top ranked candidates by 24.6% compared to the state-of-the-art product search model.

cs.CL↗
arXiv2019

Convergence Rate of Krasulina Estimator

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points $X_1, X_2,..., X_n$ are vectors drawn i.i.d. from a distribution with mean zero and covariance $Σ$, where $Σ$ is unknown. Let $A_n = X_nX_n^T$, then $E[A_n] = Σ$. This paper consider the problem of finding the least eigenvalue and eigenvector of matrix $Σ$. A classical such estimator are due to Krasulina\cite{krasulina_method_1969}. We are going to state the convergence proof of Krasulina for the least eigenvalue and corresponding eigenvector, and then find their convergence rate.

stat.ML↗
arXiv2019

A cost-reducing partial labeling estimator in text classification problem

We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous training examples if they are unlikely fall into certain classes. We construct our new maximum likelihood estimators with self-correction property, and prove that under some conditions, our estimators converge faster. Also we discuss the advantages of applying one of our estimator to a fully supervised learning problem. The proposed method has potential applicability in many areas, such as crowdsourcing, natural language processing and medical image analysis.

stat.ML↗
arXiv2019

Naive Bayes with Correlation Factor for Text Classification Problem

Naive Bayes estimator is widely used in text classification problems. However, it doesn't perform well with small-size training dataset. We propose a new method based on Naive Bayes estimator to solve this problem. A correlation factor is introduced to incorporate the correlation among different classes. Experimental results show that our estimator achieves a better accuracy compared with traditional Naive Bayes in real world data.

cs.IR↗
arXiv2013

Self-Organization In 1-d Swarm Dynamics

Self-organization of a biologically motivated swarm into smaller subgroups of different velocities is found by solving a 1-dimensional adaptive-velocity swarm, in which the velocity of an agent is averaged over a finite local radius of influence. Using a mean field model in phase space, we find a dependence of this group-division phenomenon on the typical scales of the initial swarm in the position and velocity dimensions. Comparisons are made to previous swarm models in which the speed of an agent is either fixed or adjusted according to the degree of direction consensus among its local neighbors. Key words: self-organization of swarm, phase space, multi-agent system, dynamical system, group-division.

nlin.AO↗