26,232 research outputs found
Surrogate regret bounds for generalized classification performance metrics
We consider optimization of generalized performance metrics for binary
classification by means of surrogate losses. We focus on a class of metrics,
which are linear-fractional functions of the false positive and false negative
rates (examples of which include -measure, Jaccard similarity
coefficient, AM measure, and many others). Our analysis concerns the following
two-step procedure. First, a real-valued function is learned by minimizing
a surrogate loss for binary classification on the training sample. It is
assumed that the surrogate loss is a strongly proper composite loss function
(examples of which include logistic loss, squared-error loss, exponential loss,
etc.). Then, given , a threshold is tuned on a separate
validation sample, by direct optimization of the target performance metric. We
show that the regret of the resulting classifier (obtained from thresholding
on ) measured with respect to the target metric is
upperbounded by the regret of measured with respect to the surrogate loss.
We also extend our results to cover multilabel classification and provide
regret bounds for micro- and macro-averaging measures. Our findings are further
analyzed in a computational study on both synthetic and real data sets.Comment: 22 page
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
Multiclass problems are often decomposed into multiple binary problems that
are solved by individual binary classifiers whose results are integrated into a
final answer. Various methods, including all-pairs (APs), one-versus-all (OVA),
and error correcting output code (ECOC), have been studied, to decompose
multiclass problems into binary problems. However, little study has been made
to optimally aggregate binary problems to determine a final answer to the
multiclass problem. In this paper we present a convex optimization method for
an optimal aggregation of binary classifiers to estimate class membership
probabilities in multiclass problems. We model the class membership probability
as a softmax function which takes a conic combination of discrepancies induced
by individual binary classifiers, as an input. With this model, we formulate
the regularized maximum likelihood estimation as a convex optimization problem,
which is solved by the primal-dual interior point method. Connections of our
method to large margin classifiers are presented, showing that the large margin
formulation can be considered as a limiting case of our convex formulation.
Numerical experiments on synthetic and real-world data sets demonstrate that
our method outperforms existing aggregation methods as well as direct methods,
in terms of the classification accuracy and the quality of class membership
probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on
Data Mining (SDM 2014
Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models
Learning accurate probabilistic models from data is crucial in many practical
tasks in data mining. In this paper we present a new non-parametric calibration
method called \textit{ensemble of near isotonic regression} (ENIR). The method
can be considered as an extension of BBQ, a recently proposed calibration
method, as well as the commonly used calibration method based on isotonic
regression. ENIR is designed to address the key limitation of isotonic
regression which is the monotonicity assumption of the predictions. Similar to
BBQ, the method post-processes the output of a binary classifier to obtain
calibrated probabilities. Thus it can be combined with many existing
classification models. We demonstrate the performance of ENIR on synthetic and
real datasets for the commonly used binary classification models. Experimental
results show that the method outperforms several common binary classifier
calibration methods. In particular on the real data, ENIR commonly performs
statistically significantly better than the other methods, and never worse. It
is able to improve the calibration power of classifiers, while retaining their
discrimination power. The method is also computationally tractable for large
scale datasets, as it is time, where is the number of
samples
Gibbs Max-margin Topic Models with Data Augmentation
Max-margin learning is a powerful approach to building classifiers and
structured output predictors. Recent work on max-margin supervised topic models
has successfully integrated it with Bayesian topic models to discover
discriminative latent semantic structures and make accurate predictions for
unseen testing data. However, the resulting learning problems are usually hard
to solve because of the non-smoothness of the margin loss. Existing approaches
to building max-margin supervised topic models rely on an iterative procedure
to solve multiple latent SVM subproblems with additional mean-field assumptions
on the desired posterior distributions. This paper presents an alternative
approach by defining a new max-margin loss. Namely, we present Gibbs max-margin
supervised topic models, a latent variable Gibbs classifier to discover hidden
topic representations for various tasks, including classification, regression
and multi-task learning. Gibbs max-margin supervised topic models minimize an
expected margin loss, which is an upper bound of the existing margin loss
derived from an expected prediction rule. By introducing augmented variables
and integrating out the Dirichlet variables analytically by conjugacy, we
develop simple Gibbs sampling algorithms with no restricting assumptions and no
need to solve SVM subproblems. Furthermore, each step of the
"augment-and-collapse" Gibbs sampling algorithms has an analytical conditional
distribution, from which samples can be easily drawn. Experimental results
demonstrate significant improvements on time efficiency. The classification
performance is also significantly improved over competitors on binary,
multi-class and multi-label classification tasks.Comment: 35 page
Differential geometric regularization for supervised learning of classifiers
We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to an estimator of the class probability P(y|\vec x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.http://proceedings.mlr.press/v48/baia16.pdfPublished versio
Supervised Collective Classification for Crowdsourcing
Crowdsourcing utilizes the wisdom of crowds for collective classification via
information (e.g., labels of an item) provided by labelers. Current
crowdsourcing algorithms are mainly unsupervised methods that are unaware of
the quality of crowdsourced data. In this paper, we propose a supervised
collective classification algorithm that aims to identify reliable labelers
from the training data (e.g., items with known labels). The reliability (i.e.,
weighting factor) of each labeler is determined via a saddle point algorithm.
The results on several crowdsourced data show that supervised methods can
achieve better classification accuracy than unsupervised methods, and our
proposed method outperforms other algorithms.Comment: to appear in IEEE Global Communications Conference (GLOBECOM)
Workshop on Networking and Collaboration Issues for the Internet of
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