arXiv subjects

Yancheng Yuan

Publications and source records attributed to Yancheng Yuan.

61 records · Page 4Linked to original sources

arXiv2021

A Dimension Reduction Technique for Large-scale Structured Sparse Optimization Problems with Application to Convex Clustering

In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with intrinsic structured sparsity. We establish the finite convergence property of the AS technique and the EAS technique with inexact solutions of the reduced subproblems. As an important application, we apply the AS technique and the EAS technique on the convex clustering model, which could accelerate the state-of-the-art algorithm SSNAL by more than 7 times and the algorithm ADMM by more than 14 times.

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arXiv2021

Learning Intents behind Interactions with Knowledge Graph for Recommendation

Knowledge graph (KG) plays an increasingly important role in recommender systems. A recent technical trend is to develop end-to-end models founded on graph neural networks (GNNs). However, existing GNN-based models are coarse-grained in relational modeling, failing to (1) identify user-item relation at a fine-grained level of intents, and (2) exploit relation dependencies to preserve the semantics of long-range connectivity. In this study, we explore intents behind a user-item interaction by using auxiliary item knowledge, and propose a new model, Knowledge Graph-based Intent Network (KGIN). Technically, we model each intent as an attentive combination of KG relations, encouraging the independence of different intents for better model capability and interpretability. Furthermore, we devise a new information aggregation scheme for GNN, which recursively integrates the relation sequences of long-range connectivity (i.e., relational paths). This scheme allows us to distill useful information about user intents and encode them into the representations of users and items. Experimental results on three benchmark datasets show that, KGIN achieves significant improvements over the state-of-the-art methods like KGAT, KGNN-LS, and CKAN. Further analyses show that KGIN offers interpretable explanations for predictions by identifying influential intents and relational paths. The implementations are available at https://github.com/huangtinglin/Knowledge_Graph_based_Intent_Network.

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arXiv2020

Adaptive Sieving with PPDNA: Generating Solution Paths of Exclusive Lasso Models

The exclusive lasso (also known as elitist lasso) regularization has become popular recently due to its superior performance on structured sparsity. Its complex nature poses difficulties for the computation of high-dimensional machine learning models involving such a regularizer. In this paper, we propose an adaptive sieving (AS) strategy for generating solution paths of machine learning models with the exclusive lasso regularizer, wherein a sequence of reduced problems with much smaller sizes need to be solved. In order to solve these reduced problems, we propose a highly efficient dual Newton method based proximal point algorithm (PPDNA). As important ingredients, we systematically study the proximal mapping of the weighted exclusive lasso regularizer and the corresponding generalized Jacobian. These results also make popular first-order algorithms for solving exclusive lasso models practical. Various numerical experiments for the exclusive lasso models have demonstrated the effectiveness of the AS strategy for generating solution paths and the superior performance of the PPDNA.

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arXiv2019

A dual Newton based preconditioned proximal point algorithm for exclusive lasso models

The exclusive lasso (also known as elitist lasso) regularization has become popular recently due to its superior performance on group sparsity. Compared to the group lasso regularization which enforces the competition on variables among different groups, the exclusive lasso regularization also enforces the competition within each group. In this paper, we propose a highly efficient dual Newton based preconditioned proximal point algorithm (PPDNA) to solve machine learning models involving the exclusive lasso regularizer. As an important ingredient, we provide a rigorous proof for deriving the closed-form solution to the proximal mapping of the weighted exclusive lasso regularizer. In addition, we derive the corresponding HS-Jacobian to the proximal mapping and analyze its structure --- which plays an essential role in the efficient computation of the PPA subproblem via applying a semismooth Newton method on its dual. Various numerical experiments in this paper demonstrate the superior performance of the proposed PPDNA against other state-of-the-art numerical algorithms.

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arXiv2019

SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)

SDPNAL+ is a {\sc Matlab} software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented Lagrangian method, here we designed it within an inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating direction method of multipliers/augmented Lagrangian method) framework for the purpose of deriving simpler stopping conditions and closing the gap between the practical implementation of the algorithm and the theoretical algorithm. The basic code is written in {\sc Matlab}, but some subroutines in C language are incorporated via Mex files. We also design a convenient interface for users to input their SDP models into the solver. Numerous problems arising from combinatorial optimization and binary integer quadratic programming problems have been tested to evaluate the performance of the solver. Extensive numerical experiments conducted in [Yang, Sun, and Toh, Mathematical Programming Computation, 7 (2015), pp. 331--366] show that the proposed method is quite efficient and robust, in that it is able to solve 98.9\% of the 745 test instances of SDP problems arising from various applications to the accuracy of $ 10^{-6}$ in the relative KKT residual.

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arXiv2018

Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the clustering path) has been proposed in Pelckmans et al. (2005), Lindsten et al. (2011) and Hocking et al. (2011). The perfect recovery properties of the convex clustering model with uniformly weighted all pairwise-differences regularization have been proved by Zhu et al. (2014) and Panahi et al. (2017). However, no theoretical guarantee has been established for the general weighted convex clustering model, where better empirical results have been observed. In the numerical optimization aspect, although algorithms like the alternating direction method of multipliers (ADMM) and the alternating minimization algorithm (AMA) have been proposed to solve the convex clustering model (Chi and Lange, 2015), it still remains very challenging to solve large-scale problems. In this paper, we establish sufficient conditions for the perfect recovery guarantee of the general weighted convex clustering model, which include and improve existing theoretical results as special cases. In addition, we develop a semismooth Newton based augmented Lagrangian method for solving large-scale convex clustering problems. Extensive numerical experiments on both simulated and real data demonstrate that our algorithm is highly efficient and robust for solving large-scale problems. Moreover, the numerical results also show the superior performance and scalability of our algorithm comparing to the existing first-order methods. In particular, our algorithm is able to solve a convex clustering problem with 200,000 points in $\mathbb{R}^3$ in about 6 minutes.

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arXiv2018

An Efficient Semismooth Newton Based Algorithm for Convex Clustering

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as clustering path), which is a convex relaxation of hierarchical clustering model, has been proposed in [7] and [5] Although numerical algorithms like ADMM and AMA are proposed to solve convex clustering model [2], it is known to be very challenging to solve large-scale problems. In this paper, we propose a semi-smooth Newton based augmented Lagrangian method for large-scale convex clustering problems. Extensive numerical experiments on both simulated and real data demonstrate that our algorithm is highly efficient and robust for solving large-scale problems. Moreover, the numerical results also show the superior performance and scalability of our algorithm compared to existing first-order methods.

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