1,080 research outputs found
On the Consistency of Ordinal Regression Methods
Many of the ordinal regression models that have been proposed in the
literature can be seen as methods that minimize a convex surrogate of the
zero-one, absolute, or squared loss functions. A key property that allows to
study the statistical implications of such approximations is that of Fisher
consistency. Fisher consistency is a desirable property for surrogate loss
functions and implies that in the population setting, i.e., if the probability
distribution that generates the data were available, then optimization of the
surrogate would yield the best possible model. In this paper we will
characterize the Fisher consistency of a rich family of surrogate loss
functions used in the context of ordinal regression, including support vector
ordinal regression, ORBoosting and least absolute deviation. We will see that,
for a family of surrogate loss functions that subsumes support vector ordinal
regression and ORBoosting, consistency can be fully characterized by the
derivative of a real-valued function at zero, as happens for convex
margin-based surrogates in binary classification. We also derive excess risk
bounds for a surrogate of the absolute error that generalize existing risk
bounds for binary classification. Finally, our analysis suggests a novel
surrogate of the squared error loss. We compare this novel surrogate with
competing approaches on 9 different datasets. Our method shows to be highly
competitive in practice, outperforming the least squares loss on 7 out of 9
datasets.Comment: Journal of Machine Learning Research 18 (2017
Improving Deep Regression with Ordinal Entropy
In computer vision, it is often observed that formulating regression problems
as a classification task often yields better performance. We investigate this
curious phenomenon and provide a derivation to show that classification, with
the cross-entropy loss, outperforms regression with a mean squared error loss
in its ability to learn high-entropy feature representations. Based on the
analysis, we propose an ordinal entropy loss to encourage higher-entropy
feature spaces while maintaining ordinal relationships to improve the
performance of regression tasks. Experiments on synthetic and real-world
regression tasks demonstrate the importance and benefits of increasing entropy
for regression.Comment: Accepted to ICLR 2023. Project page:
https://github.com/needylove/OrdinalEntrop
Applied statistics: A review
The main phases of applied statistical work are discussed in general terms.
The account starts with the clarification of objectives and proceeds through
study design, measurement and analysis to interpretation. An attempt is made to
extract some general notions.Comment: Published at http://dx.doi.org/10.1214/07-AOAS113 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales
Econometric analyses in the happiness literature typically use subjective
well-being (SWB) data to compare the mean of observed or latent happiness
across samples. Recent critiques show that comparing the mean of ordinal data
is only valid under strong assumptions that are usually rejected by SWB data.
This leads to an open question whether much of the empirical studies in the
economics of happiness literature have been futile. In order to salvage some of
the prior results and avoid future issues, we suggest regression analysis of
SWB (and other ordinal data) should focus on the median rather than the mean.
Median comparisons using parametric models such as the ordered probit and logit
can be readily carried out using familiar statistical softwares like STATA. We
also show a previously assumed impractical task of estimating a semiparametric
median ordered-response model is also possible by using a novel constrained
mixed integer optimization technique. We use GSS data to show the famous
Easterlin Paradox from the happiness literature holds for the US independent of
any parametric assumption
Time series ordinal classification via shapelets
Nominal time series classification has been widely developed over the last years. However, to the best of our knowledge, ordinal classification of time series is an unexplored field, and this paper proposes a first approach in the context of the shapelet transform (ST). For those time series dataset where there is a natural order between the labels and the number of classes is higher than 2, nominal classifiers are not capable of achieving the best results, because the models impose the same cost of misclassification to all the errors, regardless the difference between the predicted and the ground-truth. In this sense, we consider four different evaluation metrics to do so, three of them of an ordinal nature. The first one is the widely known Information Gain (IG), proved to be very competitive for ST methods, whereas the remaining three measures try to boost the order information by refining the quality measure. These three measures are a reformulation of the Fisher score, the Spearman's correlation coefficient (ρ), and finally, the Pearson's correlation coefficient (R 2 ). An empirical evaluation is carried out, considering 7 ordinal datasets from the UEA & UCR time series classification repository, 4 classifiers (2 of them of nominal nature, whereas the other 2 are of ordinal nature) and 2 performance measures (correct classification rate, CCR, and average mean absolute error, AMAE). The results show that, for both performance metrics, the ST quality metric based on R 2 is able to obtain the best results, specially for AMAE, for which the differences are statistically significant in favour of R 2
The Dynamics of Food Deprivation and Overall Health: Evidence from the Canadian National Population Health Survey
The paper explores whether the responses to food deprivation questions on the longitudinal Canadian National Population Health Survey help explain the links between socio-economic status and health. Transitions in food deprivation status are correlated with changes in health status. While health transitions are correlated with changes in food deprivation status, there is little evidence that change in food deprivation status leads changes in health status but some evidence that change in health status leads change in food deprivation status.Food insecurity; Granger causality; NPHS
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