Uncertain Regression Modeling Given the Observational Distributions

In regression theory, the distribution of the error terms occupies a critical position, particularly when switching the data environment from probability theory to uncertainty theory. On the probabilistic platform, the variance-covariance matrix for standard regression model is assumed by an identity matrix with a positive constant multiplier. On the uncertain measure foundation, for given observational distributions, the variance-covariance is an interval-valued matrix. In this paper, we derive the interval-valued variance for given uncertain normal distribution. Further, we derive the interval-valued auto variance matrix for the observational error terms being the members of an uncertain canonical process. This new model may be regarded as an extension to the uncertain canonical process regression models, but its interval-valued variance-covariance matrix is also intrinsic to the uncertain canonical process, which results in an interval-valued weighted regression model

An incremental dual nu-support vector regression algorithm

© 2018, Springer International Publishing AG, part of Springer Nature. Support vector regression (SVR) has been a hot research topic for several years as it is an effective regression learning algorithm. Early studies on SVR mostly focus on solving large-scale problems. Nowadays, an increasing number of researchers are focusing on incremental SVR algorithms. However, these incremental SVR algorithms cannot handle uncertain data, which are very common in real life because the data in the training example must be precise. Therefore, to handle the incremental regression problem with uncertain data, an incremental dual nu-support vector regression algorithm (dual-v-SVR) is proposed. In the algorithm, a dual-v-SVR formulation is designed to handle the uncertain data at first, then we design two special adjustments to enable the dual-v-SVR model to learn incrementally: incremental adjustment and decremental adjustment. Finally, the experiment results demonstrate that the incremental dual-v-SVR algorithm is an efficient incremental algorithm which is not only capable of solving the incremental regression problem with uncertain data, it is also faster than batch or other incremental SVR algorithms

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications

The use of function points to find cost analogies

Finding effective techniques for the early estimation of project effort remains an important — and frustratingly elusive — research objective for the software development community. We have conducted an empirical study of 21 real time projects for a major software developer. The study collected a range of counts and measures derived from specification documents, including a derivative of Function Points intended for highly constrained systems. Notwithstanding the fact that the projects were drawn from a comparatively stable environment, traditional approaches for building prediction systems, (for example, regression analysis) failed to yield a useful predictive model. By contrast, estimation based upon the automated search for analogous projects produced more accurate estimates. How much this is a characteristic of this particular dataset and how much these findings might be more generally replicated is uncertain. Nevertheless, these results should act as encouragement for follow up research on a much under utilised estimation technique

Use of an Active Learning Strategy Based on Gaussian Process Regression for the Uncertainty Quantification of Electronic Devices

This paper presents a preliminary version of an Active Learning (AL) scheme for the sample selection aimed at the development of a surrogate model for the uncertainty quantification based on the Gaussian Process regression. The proposed AL strategy iteratively searches for new candidate points to be included within the training set by trying to minimize the relative posterior standard deviation provided by the Gaussian Process regression surrogate. The above scheme has been applied for the construction of a surrogate model for the statistical analysis of the efficiency of a switching buck converter as a function of 7 uncertain parameters. The performance of the surrogate model constructed via the proposed active learning method are compared with the ones provided by an equivalent model built via a latin hypercube sampling. The results of a Monte Carlo simulation with the computational model are used as reference