B1527
Title: Conditional conformal depth measures algorithm for uncertainty quantification in complex regression models
Authors: Marcos Matabuena - Harvard University (Spain)
Rahul Ghosal - University of South Carolina (United States)
Pavlo Mozharovskyi - LTCI, Telecom Paris, Institut Polytechnique de Paris (France) [presenting]
Oscar Hernan Madrid Padilla - UCLA (United States)
Jukka-Pekka Onnela - Harvard University (United States)
Abstract: Depth measures have gained popularity in the statistical literature for defining level sets in the context of multivariate and more complex data structures such as functional data objects and graphs. However, their application in regression modelling for providing prediction regions is currently limited. A novel conditional depth measure is proposed based on conditional kernel mean embeddings to address this research gap. The new measure has the potential to introduce prediction regions in regression models for complex statistical responses and predictors that take values in separable Hilbert spaces. To enhance the practicality of our approach, a conformal inference algorithm is incorporated into the conditional depth measure. The algorithm has the potential to offer non-asymptotic guarantees for constructing prediction regions. Moreover, conditional and unconditional consistency results are introduced for the derived prediction regions. In order to evaluate the performance of the approach across different scenarios with finite samples, an extensive simulation study is conducted. Various response types are encompassed, including Euclidean as well as complex statistical data types such as graphs and probability distributions. Through these simulations, the versatility and robustness of the method are demonstrated on finite samples.
