26,972 research outputs found
A U-statistic estimator for the variance of resampling-based error estimators
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Therefore, several standard theorems on properties of U-statistics apply.
In particular, it has minimal variance among all unbiased estimators and is asymptotically normally distributed. Moreover, there is an unbiased estimator for this minimal variance if the total sample size is at least the double learning set size plus two. In this case, we exhibit such an estimator which is another U-statistic. It enjoys, again, various optimality properties and yields an asymptotically exact hypothesis test of the equality of error rates when two learning algorithms are compared. Our statements apply to any deterministic learning algorithms under weak non-degeneracy assumptions.
In an application to tuning parameter choice in lasso regression on a gene expression data set, the test does not reject the null hypothesis of equal rates between two different parameters
Consistency of plug-in confidence sets for classification in semi-supervised learning
Confident prediction is highly relevant in machine learning; for example, in
applications such as medical diagnoses, wrong prediction can be fatal. For
classification, there already exist procedures that allow to not classify data
when the confidence in their prediction is weak. This approach is known as
classification with reject option. In the present paper, we provide new
methodology for this approach. Predicting a new instance via a confidence set,
we ensure an exact control of the probability of classification. Moreover, we
show that this methodology is easily implementable and entails attractive
theoretical and numerical properties
Generalized Kernel-based Visual Tracking
In this work we generalize the plain MS trackers and attempt to overcome
standard mean shift trackers' two limitations.
It is well known that modeling and maintaining a representation of a target
object is an important component of a successful visual tracker.
However, little work has been done on building a robust template model for
kernel-based MS tracking. In contrast to building a template from a single
frame, we train a robust object representation model from a large amount of
data. Tracking is viewed as a binary classification problem, and a
discriminative classification rule is learned to distinguish between the object
and background. We adopt a support vector machine (SVM) for training. The
tracker is then implemented by maximizing the classification score. An
iterative optimization scheme very similar to MS is derived for this purpose.Comment: 12 page
Supervised Learning in Multilayer Spiking Neural Networks
The current article introduces a supervised learning algorithm for multilayer
spiking neural networks. The algorithm presented here overcomes some
limitations of existing learning algorithms as it can be applied to neurons
firing multiple spikes and it can in principle be applied to any linearisable
neuron model. The algorithm is applied successfully to various benchmarks, such
as the XOR problem and the Iris data set, as well as complex classifications
problems. The simulations also show the flexibility of this supervised learning
algorithm which permits different encodings of the spike timing patterns,
including precise spike trains encoding.Comment: 38 pages, 4 figure
Bandwidth choice for nonparametric classification
It is shown that, for kernel-based classification with univariate
distributions and two populations, optimal bandwidth choice has a dichotomous
character. If the two densities cross at just one point, where their curvatures
have the same signs, then minimum Bayes risk is achieved using bandwidths which
are an order of magnitude larger than those which minimize pointwise estimation
error. On the other hand, if the curvature signs are different, or if there are
multiple crossing points, then bandwidths of conventional size are generally
appropriate. The range of different modes of behavior is narrower in
multivariate settings. There, the optimal size of bandwidth is generally the
same as that which is appropriate for pointwise density estimation. These
properties motivate empirical rules for bandwidth choice.Comment: Published at http://dx.doi.org/10.1214/009053604000000959 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …