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

Stress-energy tensor correlations across regular black holes horizons

Hawking radiation can be regarded as a spontaneous and continuous creation of virtual particle-antiparticle pairs outside the event horizon of a black hole where strong tidal forces prevent the annihilation: the particle escapes to infinity contributing to the Hawking flux, while its corresponding antiparticle partner enters the event horizon and ultimately reaches the singularity. The aim of this paper is to investigate the energy density correlations between the Hawking particles and their partners across the event horizon of two models of non-singular black holes by calculating the two-point correlation function of the density operator of a massless scalar field. This analysis is motivated by the fact that in acoustic black holes particle-partner correlations are signalled by the presence of a peak in the equal time density-density correlator. Performing the calculation in a Schwarzschild black hole it was shown in [1] that the peak does not appear, mainly because of the singularity. It is then interesting to consider what happens when the singularity is not present. In the Hayward and Simpson-Visser non-singular black holes we show that the density-density correlator remains finite when the partner particle approaches the hypersurface that replaces the singularity, opening the possibility that partner-particle correlations can propagate towards other regions of spacetime instead of being lost in a singularity.Comment: Version accepted for publication in PR

Bayesian functional emulation of CO2 emissions on future climate change scenarios

We propose a statistical emulator for a climate-economy deterministic integrated assessmentmodel ensemble, based on a functional regression framework. Inference on the unknown parameters is carried out through a mixed effects hierarchical model using a fully Bayesian framework with a prior distribution on the vector of all parameters. We also suggest an autoregressive parameterization of the covariance matrix of the error, with matching marginal prior. In this way, we allow for a functional framework for the discretized output of the simulators that allows their time continuous evaluation

Turbulence studies in TCV using the Correlation ECE diagnostic

In this thesis work, the flexibility of the Tokamak à Configuration Variable (TCV) is exploited to study the influence of plasma parameters on turbulent fluctuations. The correlation electron cyclotron emission (CECE) diagnostic is used to measure low amplitude, large bandwidth radiative temperature fluctuations, associated with the anomalous transport terms that constitute the largest contribution to heat and particle loss in tokamak plasmas. In a series of L-mode limited plasmas, fluctuations are characterized over a large range of plasma parameters, obtained varying collisionality, Te/Ti and plasma triangularity. The influence of negative triangularity on confinement and fluctuations is also investigated. Temperature fluctuations profiles have been measured in low density, ohmic, positive and negative triangularity discharges, with matched current and density profiles. Strong suppression of fluctuations is observed in negative triangularity discharges from the plasma edge to the plasma mid radius. This is despite triangularity quickly decreasing when moving away from the edge. The existence of a region of low stiffness at the plasma edge is postulated to be responsible for this. Negative triangularity is confirmed having beneficial effects on confinement and reducing fluctuations amplitude in regimes with high Te/Ti. The neutral beam injector (NBI) has been used on positive and negative triangularity discharges in order to study the effect of negative triangularity on plasmas where Te/Ti~1. This condition is of particular interest since future reactor-like tokamaks are expected to work with thermalized electrons and ions. A pair of discharges with positive and negative triangularity has been realized, where matched temperature profiles are attained with ~385 kW and ~145 kW of NBI power respectively for the two shapes. This is evidence of negative triangularity improving plasma confinement also in conditions of low Te/Ti. In these discharges, CECE measurements find suppressed fluctuations in the negative triangularity discharges. Linear, flux tube, gyrokinetic simulations show that, in the same plasmas, the dominant turbulent regime is a mix of ion temperature gradient (ITG) instabilities and trapped electron modes (TEM). This is different with respect to all previous works in TCV, in which no ion heating had been available and only pure TEM regimes were observed. The results of the linear simulations indicate that, also in this mixed turbolence regime, negative triangularity has a stabilizing effect on instabilities, more visible for radial positions closer to the plasma edge, where the magnitude of triangularity is higher. A database of fluctuations measurements has been constructed from a series of discharges with positive and negative triangularity covering a large range of plasma conditions, particularly focusing on the effects of different combinations of collisionality and the Te/Ti ratio. Collisionality is found to be the main parameter to control the relative suppression of fluctutations in negative triangularity plasmas. No direct effect of Te/Ti on the fluctuation amplitudes is observed in the explored parameter range. Measurements taken in positive and negative triangularity plasmas, with comparable conditions and matched normalized temperature scale lengths still show reduced fluctuation levels for negative triangularity, suggesting influence on the threshold gradients for the onset of fluctuations

A fingerprint of a heterogeneous data set

In this paper, we describe the fingerprint method, a technique to classify bags of mixed-type measurements. The method was designed to solve a real-world industrial problem: classifying industrial plants (individuals at a higher level of organisation) starting from the measurements collected from their production lines (individuals at a lower level of organisation). In this specific application, the categorical information attached to the numerical measurements induced simple mixture-like structures on the global multivariate distributions associated with different classes. The fingerprint method is designed to compare the mixture components of a given test bag with the corresponding mixture components associated with the different classes, identifying the most similar generating distribution. When compared to other classification algorithms applied to several synthetic data sets and the original industrial data set, the proposed classifier showed remarkable improvements in performance

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named as S-LASSO, is proposed for the coefficient function of a functional linear regression model where values of the response function, at a given domain point, depends on the full trajectory of the covariate function. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating regions where the coefficient function is zero, and to smoothly estimate non-zero values of the coefficient function. The sparsity of the estimator is ensured by a functional LASSO penalty whereas the smoothness is provided by two roughness penalties. The resulting estimator is proved to be estimation and pointwise sign consistent. Via an extensive Monte Carlo simulation study, the estimation and predictive performance of the S-LASSO estimator are shown to be better than (or at worst comparable with) competing estimators already presented in the literature before. Practical advantages of the S-LASSO estimator are illustrated through the analysis of the well known \textit{Canadian weather} and \textit{Swedish mortality dat

Conformal Prediction Bands for Two-Dimensional Functional Time Series

Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Se