Conformal Prediction: a Unified Review of Theory and New Challenges

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.Comment: arXiv admin note: text overlap with arXiv:0706.3188, arXiv:1604.04173, arXiv:1709.06233, arXiv:1203.5422 by other author

Hierarchical independent component analysis: A multi-resolution non-orthogonal data-driven basis

A new method named Hierarchical Independent Component Analysis is presented, particularly suited for dealing with two problems regarding the analysis of high-dimensional and complex data: dimensional reduction and multi-resolution analysis. It takes into account the Blind Source Separation framework, where the purpose is the research of a basis for a dimensional reduced space to represent data, whose basis elements represent physical features of the phenomenon under study. In this case orthogonal basis could be not suitable, since the orthogonality introduces an artificial constraint not related to the phenomenological properties of the analyzed problem. For this reason this new approach is introduced. It is obtained through the integration between Treelets and Independent Component Analysis, and it is able to provide a multi-scale non-orthogonal data-driven basis. Furthermore a strategy to perform dimensional reduction with a non orthogonal basis is presented and the theoretical properties of Hierarchical Independent Component Analysis are analyzed. Finally HICA algorithm is tested both on synthetic data and on a real dataset regarding electroencephalographic traces

Fuzzy C-Means Clustering of Signal Functional Principal Components for Post-Processing Dynamic Scenarios of a Nuclear Power Plant Digital Instrumentation and Control System

International audienceThis paper addresses the issue of the classification of accident scenarios generated in a dynamic safety and reliability analyses of a Nuclear Power Plant (NPP) equipped with a Digital Instrumentation and Control system (I&C). More specifically, the classification of the final state reached by the system at the end of an accident scenario is performed by Fuzzy C-Means clustering the Functional Principal Components (FPCs) of selected relevant process variables. The approach allows capturing the characteristics of the process evolution determined by the occurrence, timing, and magnitudes of the fault events. An illustrative case study is considered, regarding the fault scenarios of the digital I&C system of the Lead Bismuth Eutectic eXperimental Accelerator Driven System (LBE-XADS). The results obtained are compared with those of the Kth Nearest Neighbor (KNN), and Classification and Regression Tree (CART) classifiers