Li Xu

Wendong Bi, Xueqi Cheng, Bingbing Xu et al.

The data-hungry problem, characterized by insufficiency and low-quality of data, poses obstacles for deep learning models. Transfer learning has been a feasible way to transfer knowledge from high-quality external data of source domains to limited data of target domains, which follows a domain-level knowledge transfer to learn a shared posterior distribution. However, they are usually built on strong assumptions, e.g., the domain invariant posterior distribution, which is usually unsatisfied and may introduce noises, resulting in poor generalization ability on target domains. Inspired by Graph Neural Networks (GNNs) that aggregate information from neighboring nodes, we redefine the paradigm as learning a knowledge-enhanced posterior distribution for target domains, namely Knowledge Bridge Learning (KBL). KBL first learns the scope of knowledge transfer by constructing a Bridged-Graph that connects knowledgeable samples to each target sample and then performs sample-wise knowledge transfer via GNNs.KBL is free from strong assumptions and is robust to noises in the source data. Guided by KBL, we propose the Bridged-GNN} including an Adaptive Knowledge Retrieval module to build Bridged-Graph and a Graph Knowledge Transfer module. Comprehensive experiments on both un-relational and relational data-hungry scenarios demonstrate the significant improvements of Bridged-GNN compared with SOTA methods

Morteza Noshad, Li Xu, Alfred Hero

We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previous work on learning bounds on Bayes misclassification rate since it learns the {\it exact} Bayes error rate instead of a bound on error rate. We propose a benchmark learner based on an ensemble of $ε$-ball estimators and Chebyshev approximation. Under a smoothness assumption on the class densities we show that our estimator achieves an optimal (parametric) mean squared error (MSE) rate of $O(N^{-1})$, where $N$ is the number of samples. Experiments on both simulated and real datasets establish that our proposed benchmark learning algorithm produces estimates of the Bayes error that are more accurate than previous approaches for learning bounds on Bayes error probability.

Qilian Yu, Easton Li Xu, Shuguang Cui

Submodular maximization problems belong to the family of combinatorial optimization problems and enjoy wide applications. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a $d$-knapsack constraint, for which we propose a streaming algorithm that achieves a $\left(\frac{1}{1+2d}-ε\right)$-approximation of the optimal value, while it only needs one single pass through the dataset without storing all the data in the memory. In our experiments, we extensively evaluate the effectiveness of our proposed algorithm via two applications: news recommendation and scientific literature recommendation. It is observed that the proposed streaming algorithm achieves both execution speedup and memory saving by several orders of magnitude, compared with existing approaches.

Easton Li Xu, Xiaoning Qian, Tie Liu et al.

An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome. Our results can also be extended to the model that includes both individual effects and pairwise interactions via the help of an auxiliary covariate.