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

Collective flow in 2.76 A TeV and 5.02 A TeV Pb+Pb collisions

In this paper, we study and predict flow observables in 2.76 A TeV and 5.02 A TeV Pb +Pb collisions, using the iEBE-VISHNU hybrid model with TRENto and AMPT initial conditions and with different forms of the QGP transport coefficients. With properly chosen and tuned parameter sets, our model calculations can nicely describe various flow observables in 2.76 A TeV Pb +Pb collisions, as well as the measured flow harmonics of all charged hadrons in 5.02 A TeV Pb +Pb collisions. We also predict other flow observables, including $v_n(p_T)$ of identified particles, event-by-event $v_n$ distributions, event-plane correlations, (Normalized) Symmetric Cumulants, non-linear response coefficients and $p_T$-dependent factorization ratios, in 5.02 A TeV Pb+Pb collisions. We find many of these observables remain approximately the same values as the ones in 2.76 A TeV Pb+Pb collisions. Our theoretical studies and predictions could shed light to the experimental investigations in the near future.Comment: 17 pages, 11 figure