A Conformal Prediction Approach to Explore Functional Data
This work addresses outlier and cluster detection in functional data analysis, providing a distribution-free method with practical computational improvements, though it is incremental in adapting existing conformal techniques to this domain.
The paper tackles the problem of analyzing functional data by applying conformal prediction to compute prediction bands and clustering trees with guaranteed finite-sample coverage, using inductive conformal predictors and novel conformity scores to reduce computational costs, as demonstrated on real data examples.
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed finite sample behavior, under no distributional assumptions. The prediction sets are also informative in that they correspond to the high density region of the underlying process. While ordinary conformal prediction has high computational cost for functional data, we use the inductive conformal predictor, together with several novel choices of conformity scores, to simplify the computation. Our methods are illustrated on some real data examples.