2,634 research outputs found
Non-Parametric Calibration of Probabilistic Regression
The task of calibration is to retrospectively adjust the outputs from a
machine learning model to provide better probability estimates on the target
variable. While calibration has been investigated thoroughly in classification,
it has not yet been well-established for regression tasks. This paper considers
the problem of calibrating a probabilistic regression model to improve the
estimated probability densities over the real-valued targets. We propose to
calibrate a regression model through the cumulative probability density, which
can be derived from calibrating a multi-class classifier. We provide three
non-parametric approaches to solve the problem, two of which provide empirical
estimates and the third providing smooth density estimates. The proposed
approaches are experimentally evaluated to show their ability to improve the
performance of regression models on the predictive likelihood
Fast & Confident Probabilistic Categorization
We describe NRC's submission to the Anomaly Detection/Text Mining competition organised at the Text Mining Workshop 2007. This submission relies on a straightforward implementation of the probabilistic categoriser described in (Gaussier et al., ECIR'02). This categoriser is adapted to handle multiple labelling and a piecewise-linear confidence estimation layer is added to provide an estimate of the labelling confidence. This technique achieves a score of 1.689 on the test data
Solving for multi-class using orthogonal coding matrices
A common method of generalizing binary to multi-class classification is the
error correcting code (ECC). ECCs may be optimized in a number of ways, for
instance by making them orthogonal. Here we test two types of orthogonal ECCs
on seven different datasets using three types of binary classifier and compare
them with three other multi-class methods: 1 vs. 1, one-versus-the-rest and
random ECCs. The first type of orthogonal ECC, in which the codes contain no
zeros, admits a fast and simple method of solving for the probabilities.
Orthogonal ECCs are always more accurate than random ECCs as predicted by
recent literature. Improvments in uncertainty coefficient (U.C.) range between
0.4--17.5% (0.004--0.139, absolute), while improvements in Brier score between
0.7--10.7%. Unfortunately, orthogonal ECCs are rarely more accurate than 1 vs.
1. Disparities are worst when the methods are paired with logistic regression,
with orthogonal ECCs never beating 1 vs. 1. When the methods are paired with
SVM, the losses are less significant, peaking at 1.5%, relative, 0.011 absolute
in uncertainty coefficient and 6.5% in Brier scores. Orthogonal ECCs are always
the fastest of the five multi-class methods when paired with linear
classifiers. When paired with a piecewise linear classifier, whose
classification speed does not depend on the number of training samples,
classifications using orthogonal ECCs were always more accurate than the the
remaining three methods and also faster than 1 vs. 1. Losses against 1 vs. 1
here were higher, peaking at 1.9% (0.017, absolute), in U.C. and 39% in Brier
score. Gains in speed ranged between 1.1% and over 100%. Whether the speed
increase is worth the penalty in accuracy will depend on the application
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