A panel regression method for quantifying the convergence of house prices

The convergence among house prices has attracted much attention from researchers. Previous research mainly utilised a time-series regression method to investigate convergences of house prices, which may ignore the heterogeneity of houses across cities. This research developed a panel regression method, by which the heterogeneity of house prices can be captured. Seemingly unrelated regression estimators were also adapted to deal with the contemporary correlations across cities. Investigation of the convergence among house prices in the Australian capital cities was carried out by using the developed panel regression method. Results suggested that house prices converge in Sydney, Adelaide and Hobart but diverge in Darwin.

Robust-diagnostic regression : a prelude for inducing reliable knowledge from regression

Regression lies heart in statistics, it is the one of the most important branch of multivariate techniques available for extracting knowledge in almost every field of study and research. Nowadays, it has drawn a huge interest to perform the tasks with different fields like machine learning, pattern recognition and data mining. Investigating outlier (exceptional) is a century long problem to the data analyst and researchers. Blind application of data could have dangerous consequences and leading to discovery of meaningless patterns and carrying to the imperfect knowledge. As a result of digital revolution and the growth of the Internet and Intranet data continues to be accumulated at an exponential rate and thereby importance of detecting outliers and study their costs and benefits as a tool for reliable knowledge discovery claims perfect attention. Investigating outliers in regression has been paid great value for the last few decades within two frames of thoughts in the name of robust regression and regression diagnostics. Robust regression first wants to fit a regression to the majority of the data and then to discover outliers as those points that possess large residuals from the robust output whereas in regression diagnostics one first finds the outliers, delete/correct them and then fit the regular data by classical (usual) methods. At the beginning there seems to be much confusion but now the researchers reach to the consensus, robustness and diagnostics are two complementary approaches to the analysis of data and any one is not good enough. In this chapter, we discuss both of them under the unique spectrum of regression diagnostics. Chapter expresses the necessity and views of regression diagnostics as well as presents several contemporary methods through numerical examples in linear regression within each aforesaid category together with current challenges and possible future research directions. Our aim is to make the chapter self-explained maintaining its general accessibility.

Computing of high breakdown regression estimators without sorting on graphics processing units

We present an approach to computing high-breakdown regression estimators in parallel on graphics processing units (GPU).We show that sorting the residuals is not necessary, and it can be substituted by calculating the median. We present and compare various methods to calculate the median and order statistics on GPUs. We introduce an alternative method based on the optimization of a convex function, and showits numerical superiority when calculating the order statistics of very large arrays on GPUs.

A hybrid neural network model for noisy data regression

A hybrid neural network model, based on the fusion of fuzzy adaptive resonance theory (FA ART) and the general regression neural network (GRNN), is proposed in this paper. Both FA and the GRNN are incremental learning systems and are very fast in network training. The proposed hybrid model, denoted as GRNNFA, is able to retain these advantages and, at the same time, to reduce the computational requirements in calculating and storing information of the kernels. A clustering version of the GRNN is designed with data compression by FA for noise removal. An adaptive gradient-based kernel width optimization algorithm has also been devised. Convergence of the gradient descent algorithm can be accelerated by the geometric incremental growth of the updating factor. A series of experiments with four benchmark datasets have been conducted to assess and compare effectiveness of GRNNFA with other approaches. The GRNNFA model is also employed in a novel application task for predicting the evacuation time of patrons at typical karaoke centers in Hong Kong in the event of fire. The results positively demonstrate the applicability of GRNNFA in noisy data regression problems.

Fusion of GRNN and FA for online noisy data regression

A new online neural-network-based regression model for noisy data is proposed in this paper. It is a hybrid system combining the Fuzzy ART (FA) and General Regression Neural Network (GRNN) models. Both the FA and GRNN models are fast incremental learning systems. The proposed hybrid model, denoted as GRNNFA-online, retains the online learning properties of both models. The kernel centers of the GRNN are obtained by compressing the training samples using the FA model. The width of each kernel is then estimated by the K-nearest-neighbors (kNN) method. A heuristic is proposed to tune the value of Kof the kNN dynamically based on the concept of gradient-descent. The performance of the GRNNFA-online model was evaluated using two benchmark datasets, i.e., OZONE and Friedman#1. The experimental results demonstrated the convergence of the prediction errors. Bootstrapping was employed to assess the performance statistically. The final prediction errors are analyzed and compared with those from other systems.Bootstrapping was employed to assess the performance statistically. The final prediction errors are analyzed and compared with those from other systems.

Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell's derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.

Modeling of a stereo vision system using a genetic algorithm based fuzzy linear regression

In this paper a fuzzy linear regression (FLR) model integrated with a genetic algorithm (GA) is proposed. The proposed GA-FLR model is applied to modeling of a stereo vision system. A set of empirical data from stereo vision object measurement is collected based on the full factorial design technique. Three regression models, namely ordinary least-squares regression (OLS), FLR, and GA-FLR, are developed, and with their performances compared. The results show that the proposed GA-FLR model performs better than OLS and FLR in modeling of a stereo vision system.

Derivative-free optimization and neural networks for robust regression

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.

Rapid determination of protein contents in microencapsulated fish oil supplements by ATR-FTIR spectroscopy and partial least square regression (PLSR) analysis

Following the recent success in quantitative analysis of essential fatty acid compositions in a commercial microencapsulated fish oil (?EFO) supplement, we extended the application of portable attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopic technique and partial least square regression (PLSR) analysis for rapid determination of total protein contents-the other major component in most commercial ?EFO powders. In contrast to the traditional chromatographic methodology used in a routine amino acid analysis (AAA), the ATR-FTIR spectra of the ?EFO powder can be acquired directly from its original powder form with no requirement of any sample preparation, making the technique exceptionally fast, noninvasive, and environmentally friendly as well as being cost effective and hence eminently suitable for routine use by industry. By optimizing the spectral region of interest and number of latent factors through the developed PLSR strategy, a good linear calibration model was produced as indicated by an excellent value of coefficient of determination R2 = 0.9975, using standard ?EFO powders with total protein contents in the range of 140-450 mg/g. The prediction of the protein contents acquired from an independent validation set through the optimized PLSR model was highly accurate as evidenced through (1) a good linear fitting (R2 = 0.9759) in the plot of predicted versus reference values, which were obtained from a standard AAA method, (2) lowest root mean square error of prediction (11.64 mg/g), and (3) high residual predictive deviation (6.83) ranked in very good level of predictive quality indicating high robustness and good predictive performance of the achieved PLSR calibration model. The study therefore demonstrated the potential application of the portable ATR-FTIR technique when used together with PLSR analysis for rapid online monitoring of the two major components (i.e., oil and protein contents) in finished ?EFO powders in the actual manufacturing setting.