Jianzhong Li

Bohan Lyu, Jianzhong Li

This paper introduces a new data analysis method for big data using a newly defined regression model named multiple model linear regression(MMLR), which separates input datasets into subsets and construct local linear regression models of them. The proposed data analysis method is shown to be more efficient and flexible than other regression based methods. This paper also proposes an approximate algorithm to construct MMLR models based on $(ε,δ)$-estimator, and gives mathematical proofs of the correctness and efficiency of MMLR algorithm, of which the time complexity is linear with respect to the size of input datasets. This paper also empirically implements the method on both synthetic and real-world datasets, the algorithm shows to have comparable performance to existing regression methods in many cases, while it takes almost the shortest time to provide a high prediction accuracy.

Xingxing Xiao, Jianzhong Li

Multi-criteria decision-making often requires finding a small representative set from the database. A recently proposed method is the regret minimization set (RMS) query. RMS returns a size $r$ subset $S$ of dataset $D$ that minimizes the regret-ratio (the difference between the score of top-1 in $S$ and the score of top-1 in $D$, for any possible utility function). RMS is not shift invariant, causing inconsistency in results. Further, existing work showed that the regret-ratio is often a made-up number and users may mistake its absolute value. Instead, users do understand the notion of rank. Thus it considered the problem of finding the minimal set $S$ with a rank-regret (the rank of top-1 tuple of $S$ in the sorted list of $D$) at most $k$, called the rank-regret representative (RRR) problem. Corresponding to RMS, we focus on the min-error version of RRR, called the rank-regret minimization (RRM) problem, which finds a size $r$ set to minimize the maximum rank-regret for all utility functions. Further, we generalize RRM and propose the restricted RRM (i.e., RRRM) problem to optimize the rank-regret for functions restricted in a given space. Previous studies on both RMS and RRR did not consider the restricted function space. The solution for RRRM usually has a lower regret level and can better serve the specific preferences of some users. Note that RRM and RRRM are shift invariant. In 2D space, we design a dynamic programming algorithm 2DRRM to return the optimal solution for RRM. In HD space, we propose an algorithm HDRRM that introduces a double approximation guarantee on rank-regret. Both 2DRRM and HDRRM are applicable for RRRM. Extensive experiments on the synthetic and real datasets verify the efficiency and effectiveness of our algorithms. In particular, HDRRM always has the best output quality in experiments.

Hengzhao Ma, Jianzhong Li

In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et al. have devised the distributed PCP framework for sub-quadratic time inapproximability. We show that the distributed PCP theorem can be generalized for proving arbitrary polynomial time inapproximability, but fails in the linear case. We prove the sub-linear PCP theorem by adapting from an MA-protocol for the Set Containment problem, and show how to use the theorem to prove both existing and new inapproximability results, exhibiting the power of the sub-linear PCP theorem. Considering the emerging research works on sub-linear time algorithms, the sub-linear PCP theorem is important in guiding the research in sub-linear time approximation algorithms.

Chunnan Wang, Hongzhi Wang, Tianyu Mu et al.

In many fields, a mass of algorithms with completely different hyperparameters have been developed to address the same type of problems. Choosing the algorithm and hyperparameter setting correctly can promote the overall performance greatly, but users often fail to do so due to the absence of knowledge. How to help users to effectively and quickly select the suitable algorithm and hyperparameter settings for the given task instance is an important research topic nowadays, which is known as the CASH problem. In this paper, we design the Auto-Model approach, which makes full use of known information in the related research paper and introduces hyperparameter optimization techniques, to solve the CASH problem effectively. Auto-Model tremendously reduces the cost of algorithm implementations and hyperparameter configuration space, and thus capable of dealing with the CASH problem efficiently and easily. To demonstrate the benefit of Auto-Model, we compare it with classical Auto-Weka approach. The experimental results show that our proposed approach can provide superior results and achieves better performance in a short time.

Xi Chen, Hongzhi Wang, Yanjie Wei et al.

Time series prediction with missing values is an important problem of time series analysis since complete data is usually hard to obtain in many real-world applications. To model the generation of time series, autoregressive (AR) model is a basic and widely used one, which assumes that each observation in the time series is a noisy linear combination of some previous observations along with a constant shift. To tackle the problem of prediction with missing values, a number of methods were proposed based on various data models. For real application scenarios, how do these methods perform over different types of time series with different levels of data missing remains to be investigated. In this paper, we focus on online methods for AR-model-based time series prediction with missing values. We adapted five mainstream methods to fit in such a scenario. We make detailed discussion on each of them by introducing their core ideas about how to estimate the AR coefficients and their different strategies to deal with missing values. We also present algorithmic implementations for better understanding. In order to comprehensively evaluate these methods and do the comparison, we conduct experiments with various configurations of relative parameters over both synthetic and real data. From the experimental results, we derived several noteworthy conclusions and shows that imputation is a simple but reliable strategy to handle missing values in online prediction tasks.

Zhixin Qi, Hongzhi Wang, Jianzhong Li et al.

Data quality issues have attracted widespread attention due to the negative impacts of dirty data on data mining and machine learning results. The relationship between data quality and the accuracy of results could be applied on the selection of the appropriate algorithm with the consideration of data quality and the determination of the data share to clean. However, rare research has focused on exploring such relationship. Motivated by this, this paper conducts an experimental comparison for the effects of missing, inconsistent and conflicting data on classification and clustering algorithms. Based on the experimental findings, we provide guidelines for algorithm selection and data cleaning.

Jialin Wan, Siyao Cheng, Shanshan Han et al.

Wireless communication systems, such as wireless sensor networks and RFIDs, are increasingly adopted to transfer potential highly sensitive information. Since the wireless medium has a sharing nature, adversaries have a chance to eavesdrop confidential information from the communication systems. Adding artificial noises caused by friendly jammers emerges as a feasible defensive technique against adversaries. This paper studies the schedule strategies of friendly jammers, which are randomly and redundantly deployed in a circumscribed geographical area and can be unrechargeable or rechargeable, to maximize the lifetime of the jammer networks and prevent the cracking of jamming effect made by the eavesdroppers, under the constraints of geographical area, energy consumption, transmission power, and threshold level. An approximation algorithm as baseline is first proposed using the integer linear programming model. To further reduce the computational complexity, a heuristic algorithm based on the greedy strategy that less consumption leads to longer lifetime is also proposed. Finally, extensive simulation results show that the proposed algorithms are effective and efficient.