Name
Abstract | ||
|---|---|---|
In some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances $x \in \mathcal{X}$ contain a β proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level γ≈1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/978-3-642-35101-3_51 | Australasian Conference on Artificial Intelligence |
Keywords | Field | DocType |
new interval regression method,conventional interval approximation method,simultaneous tolerance interval,problem simultaneous interval regression,linear regression,regression method,regression problem,tolerance interval,k-nearest neighbor,simultaneous interval regression problem,benchmark regression data set | Regression analysis,Polynomial regression,Prediction interval,Tolerance interval,Statistics,Confidence interval,Credible interval,Mathematics,Segmented regression,Linear regression | Conference |
Citations | PageRank | References |
3 | 0.79 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Ghasemi Hamed | 1 | 28 | 3.29 |
| Mathieu Serrurier | 2 | 267 | 26.94 |
| Nicolas Durand | 3 | 3 | 0.79 |