4,381 research outputs found
Conformal Rule-Based Multi-label Classification
We advocate the use of conformal prediction (CP) to enhance rule-based
multi-label classification (MLC). In particular, we highlight the mutual
benefit of CP and rule learning: Rules have the ability to provide natural
(non-)conformity scores, which are required by CP, while CP suggests a way to
calibrate the assessment of candidate rules, thereby supporting better
predictions and more elaborate decision making. We illustrate the potential
usefulness of calibrated conformity scores in a case study on lazy multi-label
rule learning
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
Least Ambiguous Set-Valued Classifiers with Bounded Error Levels
In most classification tasks there are observations that are ambiguous and
therefore difficult to correctly label. Set-valued classifiers output sets of
plausible labels rather than a single label, thereby giving a more appropriate
and informative treatment to the labeling of ambiguous instances. We introduce
a framework for multiclass set-valued classification, where the classifiers
guarantee user-defined levels of coverage or confidence (the probability that
the true label is contained in the set) while minimizing the ambiguity (the
expected size of the output). We first derive oracle classifiers assuming the
true distribution to be known. We show that the oracle classifiers are obtained
from level sets of the functions that define the conditional probability of
each class. Then we develop estimators with good asymptotic and finite sample
properties. The proposed estimators build on existing single-label classifiers.
The optimal classifier can sometimes output the empty set, but we provide two
solutions to fix this issue that are suitable for various practical needs.Comment: Final version to be published in the Journal of the American
Statistical Association at
https://www.tandfonline.com/doi/abs/10.1080/01621459.2017.1395341?journalCode=uasa2
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
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
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
An Algebraic Classification of Exceptional EFTs
We classify four-dimensional effective field theories (EFTs) with enhanced
soft limits, which arise due to non-linearly realised symmetries on the
Goldstone modes of such theories. We present an algorithm for deriving all
possible algebras that can be non-linearly realised on a set of Goldstone modes
with canonical propagators, linearly realised Poincar\'{e} symmetries and
interactions at weak coupling. We then perform a full classification of the
cases with multiple scalars or multiple spin- fermions as the Goldstone
modes. In each case there are only a small number of algebras consistent with
field-dependent transformation rules, leading to the class of exceptional EFTs
including the scalar sector of Dirac-Born-Infeld, Special Galileon and
Volkov-Akulov theories. We also discuss the coupling of a gauge vector
to the exceptional scalar theories, showing that there is a Special Galileon
version of the full Dirac-Born-Infeld theory. This paper is part I in a series
of two papers, with the second providing an algebraic classification of
supersymmetric theories
Branes: from free fields to general backgrounds
Motivated by recent developments in string theory, we study the structure of
boundary conditions in arbitrary conformal field theories. A boundary condition
is specified by two types of data: first, a consistent collection of reflection
coefficients for bulk fields on the disk; and second, a choice of an
automorphism of the fusion rules that preserves conformal weights.
Non-trivial automorphisms correspond to D-brane configurations for
arbitrary conformal field theories. The choice of the fusion rule automorphism
amounts to fixing the dimension and certain global topological
features of the D-brane world volume and the background gauge field on it. We
present evidence that for fixed choice of the boundary conditions are
classified as the irreducible representations of some commutative associative
algebra, a generalization of the fusion rule algebra. Each of these irreducible
representations corresponds to a choice of the moduli for the world volume of
the D-brane and the moduli of the flat connection on it.Comment: 56 pages, LaTeX2e. Typos corrected; two references adde
Lectures on conformal field theory and Kac-Moody algebras
This is an introduction to the basic ideas and to a few further selected
topics in conformal quantum field theory and in the theory of Kac-Moody
algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate
Course on Conformal Field Theory and Integrable Models (Budapest, August
1996), to appear in Springer Lecture Notes in Physic
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