18,181 research outputs found
Making Risk Minimization Tolerant to Label Noise
In many applications, the training data, from which one needs to learn a
classifier, is corrupted with label noise. Many standard algorithms such as SVM
perform poorly in presence of label noise. In this paper we investigate the
robustness of risk minimization to label noise. We prove a sufficient condition
on a loss function for the risk minimization under that loss to be tolerant to
uniform label noise. We show that the loss, sigmoid loss, ramp loss and
probit loss satisfy this condition though none of the standard convex loss
functions satisfy it. We also prove that, by choosing a sufficiently large
value of a parameter in the loss function, the sigmoid loss, ramp loss and
probit loss can be made tolerant to non-uniform label noise also if we can
assume the classes to be separable under noise-free data distribution. Through
extensive empirical studies, we show that risk minimization under the
loss, the sigmoid loss and the ramp loss has much better robustness to label
noise when compared to the SVM algorithm
Fast calibrated additive quantile regression
We propose a novel framework for fitting additive quantile regression models,
which provides well calibrated inference about the conditional quantiles and
fast automatic estimation of the smoothing parameters, for model structures as
diverse as those usable with distributional GAMs, while maintaining equivalent
numerical efficiency and stability. The proposed methods are at once
statistically rigorous and computationally efficient, because they are based on
the general belief updating framework of Bissiri et al. (2016) to loss based
inference, but compute by adapting the stable fitting methods of Wood et al.
(2016). We show how the pinball loss is statistically suboptimal relative to a
novel smooth generalisation, which also gives access to fast estimation
methods. Further, we provide a novel calibration method for efficiently
selecting the 'learning rate' balancing the loss with the smoothing priors
during inference, thereby obtaining reliable quantile uncertainty estimates.
Our work was motivated by a probabilistic electricity load forecasting
application, used here to demonstrate the proposed approach. The methods
described here are implemented by the qgam R package, available on the
Comprehensive R Archive Network (CRAN)
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
Selective machine learning of doubly robust functionals
While model selection is a well-studied topic in parametric and nonparametric
regression or density estimation, selection of possibly high-dimensional
nuisance parameters in semiparametric problems is far less developed. In this
paper, we propose a selective machine learning framework for making inferences
about a finite-dimensional functional defined on a semiparametric model, when
the latter admits a doubly robust estimating function and several candidate
machine learning algorithms are available for estimating the nuisance
parameters. We introduce two new selection criteria for bias reduction in
estimating the functional of interest, each based on a novel definition of
pseudo-risk for the functional that embodies the double robustness property and
thus is used to select the pair of learners that is nearest to fulfilling this
property. We establish an oracle property for a multi-fold cross-validation
version of the new selection criteria which states that our empirical criteria
perform nearly as well as an oracle with a priori knowledge of the pseudo-risk
for each pair of candidate learners. We also describe a smooth approximation to
the selection criteria which allows for valid post-selection inference.
Finally, we apply the approach to model selection of a semiparametric estimator
of average treatment effect given an ensemble of candidate machine learners to
account for confounding in an observational study
Choosing the Right Spatial Weighting Matrix in a Quantile Regression Model
This paper proposes computationally tractable methods for selecting the appropriate spatial weighting matrix in the context of a spatial quantile regression model. This selection is a notoriously difficult problem even in linear spatial models and is even more difficult in a quantile regression setup. The proposal is illustrated by an empirical example and manages to produce tractable models. One important feature of the proposed methodology is that by allowing different degrees and forms of spatial dependence across quantiles it further relaxes the usual quantile restriction attributable to the linear quantile regression. In this way we can obtain a more robust, with regard to potential functional misspecification, model, but nevertheless preserve the parametric rate of convergence and the established inferential apparatus associated with the linear quantile regression approach
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