Abstract

Abstract
Several real world prediction problems involve forecasting rare values of a target variable. When this variable is nominal, we have a problem of class imbalance that was thoroughly studied within machine learning. For regression tasks, where the target variable is continuous, few works exist addressing this type of problem. Still, important applications involve forecasting rare extreme values of a continuous target variable. This paper describes a contribution to this type of tasks. Namely, we propose to address such tasks by resampling approaches that change the distribution of the given data set to decrease the problem of imbalance between the rare target cases and the most frequent ones. We present two modifications of well-known resampling strategies for classification tasks: the under-sampling and the synthetic minority over-sampling technique (SMOTE) methods. These modifications allow the use of these strategies on regression tasks where the goal is to forecast rare extreme values of the target variable. In an extensive set of experiments, we provide empirical evidence for the superiority of our proposals for these particular regression tasks. The proposed resampling methods can be used with any existing regression algorithm, which means that they are general tools for addressing problems of forecasting rare extreme values of a continuous target variable.

Abstract
We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space-time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals' center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.

Abstract
Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear regression models for this type of data are necessarily more complex than a simple generalization of the classical model: the parameters cannot be negative; still the linear relation between the variables must be allowed to be either direct or inverse. In this work, we propose a new linear regression model for histogram-valued variables that solves this problem, named Distribution and Symmetric Distribution Regression Model. To determine the parameters of this model, it is necessary to solve a quadratic optimization problem, subject to non-negativity constraints on the unknowns; the error measure between the predicted and observed distributions uses the Mallows distance. As in classical analysis, the model is associated with a goodness-of-fit measure whose values range between 0 and 1. Using the proposed model, applications with real and simulated data are presented.

Abstract

Abstract