1,780 research outputs found
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
Sparse Conformal Predictors
Conformal predictors, introduced by Vovk et al. (2005), serve to build
prediction intervals by exploiting a notion of conformity of the new data point
with previously observed data. In the present paper, we propose a novel method
for constructing prediction intervals for the response variable in multivariate
linear models. The main emphasis is on sparse linear models, where only few of
the covariates have significant influence on the response variable even if
their number is very large. Our approach is based on combining the principle of
conformal prediction with the penalized least squares estimator
(LASSO). The resulting confidence set depends on a parameter and
has a coverage probability larger than or equal to . The numerical
experiments reported in the paper show that the length of the confidence set is
small. Furthermore, as a by-product of the proposed approach, we provide a
data-driven procedure for choosing the LASSO penalty. The selection power of
the method is illustrated on simulated data
ELM regime classification by conformal prediction on an information manifold
Characterization and control of plasma instabilities known as edge-localized modes (ELMs) is crucial for the operation of fusion reactors. Recently, machine learning methods have demonstrated good potential in making useful inferences from stochastic fusion data sets. However, traditional classification methods do not offer an inherent estimate of the goodness of their prediction. In this paper, a distance-based conformal predictor classifier integrated with a geometric-probabilistic framework is presented. The first benefit of the approach lies in its comprehensive treatment of highly stochastic fusion data sets, by modeling the measurements with probability distributions in a metric space. This enables calculation of a natural distance measure between probability distributions: the Rao geodesic distance. Second, the predictions are accompanied by estimates of their accuracy and reliability. The method is applied to the classification of regimes characterized by different types of ELMs based on the measurements of global parameters and their error bars. This yields promising success rates and outperforms state-of-the-art automatic techniques for recognizing ELM signatures. The estimates of goodness of the predictions increase the confidence of classification by ELM experts, while allowing more reliable decisions regarding plasma control and at the same time increasing the robustness of the control system
Detecting adversarial manipulation using inductive Venn-ABERS predictors
Inductive Venn-ABERS predictors (IVAPs) are a type of probabilistic predictors with the theoretical guarantee that their predictions are perfectly calibrated. In this paper, we propose to exploit this calibration property for the detection of adversarial examples in binary classification tasks. By rejecting predictions if the uncertainty of the IVAP is too high, we obtain an algorithm that is both accurate on the original test set and resistant to adversarial examples. This robustness is observed on adversarials for the underlying model as well as adversarials that were generated by taking the IVAP into account. The method appears to offer competitive robustness compared to the state-of-the-art in adversarial defense yet it is computationally much more tractable
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