# Confidence and prediction intervals for semiparametric mixed-effect least squares support vector machine

In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. Least squares support vector machines (LS-SVM) are least squares versions of support vector machines (SVM), which are a set of related supervised learning methods that analyze data and recognize patterns, and which are used for classification and regression analysis. In this version one finds the solution by solving a set of linear equations instead of a convex quadratic programming (QP) problem for classical SVMs. Least squares SVM classifiers, were proposed by Suykens and Vandewalle. In statistics a semiparametric model is a model that has parametric and nonparametric components. A model is a collection of distributions: indexed by a parameter . A parametric model is one in which the indexing parameter is a finite-dimensional vector (in -dimensional Euclidean space for some integer), i.e. the set of possible values for is a subset of, or . In this case we say that is finite-dimensional. In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result (the estimate) are distinguished. There are point and interval estimators. The point estimators yield single-valued results, although this includes the possibility of single vector-valued results and results that can be expressed as a single function. Cluster analysis or clustering is the task of assigning a set of objects into groups (called clusters) so that the objects in the same cluster are more similar (in some sense or another) to each other than to those in other clusters. Clustering is a main task of explorative data mining, and a common technique for statistical data analysis used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics. Source.