6,393 research outputs found
Multiclass Learning with Simplex Coding
In this paper we discuss a novel framework for multiclass learning, defined
by a suitable coding/decoding strategy, namely the simplex coding, that allows
to generalize to multiple classes a relaxation approach commonly used in binary
classification. In this framework, a relaxation error analysis can be developed
avoiding constraints on the considered hypotheses class. Moreover, we show that
in this setting it is possible to derive the first provably consistent
regularized method with training/tuning complexity which is independent to the
number of classes. Tools from convex analysis are introduced that can be used
beyond the scope of this paper
Convex Calibration Dimension for Multiclass Loss Matrices
We study consistency properties of surrogate loss functions for general
multiclass learning problems, defined by a general multiclass loss matrix. We
extend the notion of classification calibration, which has been studied for
binary and multiclass 0-1 classification problems (and for certain other
specific learning problems), to the general multiclass setting, and derive
necessary and sufficient conditions for a surrogate loss to be calibrated with
respect to a loss matrix in this setting. We then introduce the notion of
convex calibration dimension of a multiclass loss matrix, which measures the
smallest `size' of a prediction space in which it is possible to design a
convex surrogate that is calibrated with respect to the loss matrix. We derive
both upper and lower bounds on this quantity, and use these results to analyze
various loss matrices. In particular, we apply our framework to study various
subset ranking losses, and use the convex calibration dimension as a tool to
show both the existence and non-existence of various types of convex calibrated
surrogates for these losses. Our results strengthen recent results of Duchi et
al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types
of convex calibrated surrogates in subset ranking. We anticipate the convex
calibration dimension may prove to be a useful tool in the study and design of
surrogate losses for general multiclass learning problems.Comment: Accepted to JMLR, pending editin
Inhibition in multiclass classification
The role of inhibition is investigated in a multiclass support vector machine formalism inspired by the brain structure of insects. The so-called mushroom bodies have a set of output neurons, or classification functions,
that compete with each other to encode a particular input. Strongly active output neurons depress or inhibit the remaining outputs without knowing which is correct or incorrect. Accordingly, we propose to use a
classification function that embodies unselective inhibition and train it in the large margin classifier framework. Inhibition leads to more robust classifiers in the sense that they perform better on larger areas of appropriate hyperparameters when assessed with leave-one-out strategies. We also show that the classifier with inhibition is a tight bound to probabilistic exponential models and is Bayes consistent for 3-class problems.
These properties make this approach useful for data sets with a limited number of labeled examples. For larger data sets, there is no significant comparative advantage to other multiclass SVM approaches
Inhibition in multiclass classification
The role of inhibition is investigated in a multiclass support vector machine formalism inspired by the brain structure of insects. The so-called mushroom bodies have a set of output neurons, or classification functions,
that compete with each other to encode a particular input. Strongly active output neurons depress or inhibit the remaining outputs without knowing which is correct or incorrect. Accordingly, we propose to use a
classification function that embodies unselective inhibition and train it in the large margin classifier framework. Inhibition leads to more robust classifiers in the sense that they perform better on larger areas of appropriate hyperparameters when assessed with leave-one-out strategies. We also show that the classifier with inhibition is a tight bound to probabilistic exponential models and is Bayes consistent for 3-class problems.
These properties make this approach useful for data sets with a limited number of labeled examples. For larger data sets, there is no significant comparative advantage to other multiclass SVM approaches
Class Proportion Estimation with Application to Multiclass Anomaly Rejection
This work addresses two classification problems that fall under the heading
of domain adaptation, wherein the distributions of training and testing
examples differ. The first problem studied is that of class proportion
estimation, which is the problem of estimating the class proportions in an
unlabeled testing data set given labeled examples of each class. Compared to
previous work on this problem, our approach has the novel feature that it does
not require labeled training data from one of the classes. This property allows
us to address the second domain adaptation problem, namely, multiclass anomaly
rejection. Here, the goal is to design a classifier that has the option of
assigning a "reject" label, indicating that the instance did not arise from a
class present in the training data. We establish consistent learning strategies
for both of these domain adaptation problems, which to our knowledge are the
first of their kind. We also implement the class proportion estimation
technique and demonstrate its performance on several benchmark data sets.Comment: Accepted to AISTATS 2014. 15 pages. 2 figure
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
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