1,245 research outputs found
From conformal to probabilistic prediction
This paper proposes a new method of probabilistic prediction, which is based
on conformal prediction. The method is applied to the standard USPS data set
and gives encouraging results.Comment: 12 pages, 2 table
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
Criteria of efficiency for conformal prediction
We study optimal conformity measures for various criteria of efficiency of
classification in an idealised setting. This leads to an important class of
criteria of efficiency that we call probabilistic; it turns out that the most
standard criteria of efficiency used in literature on conformal prediction are
not probabilistic unless the problem of classification is binary. We consider
both unconditional and label-conditional conformal prediction.Comment: 31 page
Hedging predictions in machine learning
Recent advances in machine learning make it possible to design efficient
prediction algorithms for data sets with huge numbers of parameters. This paper
describes a new technique for "hedging" the predictions output by many such
algorithms, including support vector machines, kernel ridge regression, kernel
nearest neighbours, and by many other state-of-the-art methods. The hedged
predictions for the labels of new objects include quantitative measures of
their own accuracy and reliability. These measures are provably valid under the
assumption of randomness, traditional in machine learning: the objects and
their labels are assumed to be generated independently from the same
probability distribution. In particular, it becomes possible to control (up to
statistical fluctuations) the number of erroneous predictions by selecting a
suitable confidence level. Validity being achieved automatically, the remaining
goal of hedged prediction is efficiency: taking full account of the new
objects' features and other available information to produce as accurate
predictions as possible. This can be done successfully using the powerful
machinery of modern machine learning.Comment: 24 pages; 9 figures; 2 tables; a version of this paper (with
discussion and rejoinder) is to appear in "The Computer Journal
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
Extended Gravity Cosmography
Cosmography can be considered as a sort of a model-independent approach to
tackle the dark energy/modified gravity problem. In this review, the success
and the shortcomings of the CDM model, based on General Relativity and
standard model of particles, are discussed in view of the most recent
observational constraints. The motivations for considering extensions and
modifications of General Relativity are taken into account, with particular
attention to and theories of gravity where dynamics is
represented by curvature or torsion field respectively. The features of
models are explored in metric and Palatini formalisms. We discuss the
connection between gravity and scalar-tensor theories highlighting the
role of conformal transformations in the Einstein and Jordan frames.
Cosmological dynamics of models is investigated through the
corresponding viability criteria. Afterwards, the equivalent formulation of
General Relativity (Teleparallel Equivalent General Relativity) in terms of
torsion and its extension to gravity is considered. Finally, the
cosmographic method is adopted to break the degeneracy among dark energy
models. A novel approach, built upon rational Pad\'e and Chebyshev polynomials,
is proposed to overcome limits of standard cosmography based on Taylor
expansion. The approach provides accurate model-independent approximations of
the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain
integration of cosmic data, are presented to bound coefficients of the
cosmographic series. These techniques are thus applied to reconstruct
and functions and to frame the late-time expansion history of the
universe with no \emph{a priori} assumptions on its equation of state. A
comparison between the CDM cosmological model with and
models is reported.Comment: 82 pages, 35 figures. Accepted for publication in IJMP
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