4,038 research outputs found
Fast rates for support vector machines using Gaussian kernels
For binary classification we establish learning rates up to the order of
for support vector machines (SVMs) with hinge loss and Gaussian RBF
kernels. These rates are in terms of two assumptions on the considered
distributions: Tsybakov's noise assumption to establish a small estimation
error, and a new geometric noise condition which is used to bound the
approximation error. Unlike previously proposed concepts for bounding the
approximation error, the geometric noise assumption does not employ any
smoothness assumption.Comment: Published at http://dx.doi.org/10.1214/009053606000001226 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Model Selection for Support Vector Machine Classification
We address the problem of model selection for Support Vector Machine (SVM)
classification. For fixed functional form of the kernel, model selection
amounts to tuning kernel parameters and the slack penalty coefficient . We
begin by reviewing a recently developed probabilistic framework for SVM
classification. An extension to the case of SVMs with quadratic slack penalties
is given and a simple approximation for the evidence is derived, which can be
used as a criterion for model selection. We also derive the exact gradients of
the evidence in terms of posterior averages and describe how they can be
estimated numerically using Hybrid Monte Carlo techniques. Though
computationally demanding, the resulting gradient ascent algorithm is a useful
baseline tool for probabilistic SVM model selection, since it can locate maxima
of the exact (unapproximated) evidence. We then perform extensive experiments
on several benchmark data sets. The aim of these experiments is to compare the
performance of probabilistic model selection criteria with alternatives based
on estimates of the test error, namely the so-called ``span estimate'' and
Wahba's Generalized Approximate Cross-Validation (GACV) error. We find that all
the ``simple'' model criteria (Laplace evidence approximations, and the Span
and GACV error estimates) exhibit multiple local optima with respect to the
hyperparameters. While some of these give performance that is competitive with
results from other approaches in the literature, a significant fraction lead to
rather higher test errors. The results for the evidence gradient ascent method
show that also the exact evidence exhibits local optima, but these give test
errors which are much less variable and also consistently lower than for the
simpler model selection criteria
Automatic Environmental Sound Recognition: Performance versus Computational Cost
In the context of the Internet of Things (IoT), sound sensing applications
are required to run on embedded platforms where notions of product pricing and
form factor impose hard constraints on the available computing power. Whereas
Automatic Environmental Sound Recognition (AESR) algorithms are most often
developed with limited consideration for computational cost, this article seeks
which AESR algorithm can make the most of a limited amount of computing power
by comparing the sound classification performance em as a function of its
computational cost. Results suggest that Deep Neural Networks yield the best
ratio of sound classification accuracy across a range of computational costs,
while Gaussian Mixture Models offer a reasonable accuracy at a consistently
small cost, and Support Vector Machines stand between both in terms of
compromise between accuracy and computational cost
Classification of Human Ventricular Arrhythmia in High Dimensional Representation Spaces
We studied classification of human ECGs labelled as normal sinus rhythm,
ventricular fibrillation and ventricular tachycardia by means of support vector
machines in different representation spaces, using different observation
lengths. ECG waveform segments of duration 0.5-4 s, their Fourier magnitude
spectra, and lower dimensional projections of Fourier magnitude spectra were
used for classification. All considered representations were of much higher
dimension than in published studies. Classification accuracy improved with
segment duration up to 2 s, with 4 s providing little improvement. We found
that it is possible to discriminate between ventricular tachycardia and
ventricular fibrillation by the present approach with much shorter runs of ECG
(2 s, minimum 86% sensitivity per class) than previously imagined. Ensembles of
classifiers acting on 1 s segments taken over 5 s observation windows gave best
results, with sensitivities of detection for all classes exceeding 93%.Comment: 9 pages, 2 tables, 5 figure
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Application of Machine Learning Methods to the Open-Loop Control of a Freeform Fabrication System
Freeform fabrication of complete functional devices requires the fabrication system to achieve well-controlled
deposition of many materials with widely varying material properties. In a research setting, material preparation
processes are not highly refined, causing batch property variation, and cost and time may prohibit accurate
quantification of the relevant material properties, such as viscosity, elasticity, etc. for each batch. Closed-loop
control based on the deposited material road is problematic due to the difficulty in non-contact measurement of the
road geometry, so a labor-intensive calibration and open-loop control method is typically used. In the present work,
k-Nearest Neighbor and Support Vector Machine (SVM) machine learning algorithms are applied to the problem of
generating open-loop control parameters which produce desired deposited material road geometry from a description
of a given material and tool configuration comprising a set of qualitative and quantitative attributes. Training data
for the algorithms is generated in the course of ordinary use of the SFF system as the results of manual calibration of
control parameters. Given the large instance space and the small training data set compiled thus far, the
performance is quite promising, although still insufficient to allow complete automation of the calibration process.
The SVM-based approach produces tolerable results when tested with materials not in the training data set. When
control parameters produced by the learning algorithms are used as a starting point for manual calibration,
significant operator time savings and material waste reduction may be achieved.Mechanical Engineerin
Scalable and Interpretable One-class SVMs with Deep Learning and Random Fourier features
One-class support vector machine (OC-SVM) for a long time has been one of the
most effective anomaly detection methods and extensively adopted in both
research as well as industrial applications. The biggest issue for OC-SVM is
yet the capability to operate with large and high-dimensional datasets due to
optimization complexity. Those problems might be mitigated via dimensionality
reduction techniques such as manifold learning or autoencoder. However,
previous work often treats representation learning and anomaly prediction
separately. In this paper, we propose autoencoder based one-class support
vector machine (AE-1SVM) that brings OC-SVM, with the aid of random Fourier
features to approximate the radial basis kernel, into deep learning context by
combining it with a representation learning architecture and jointly exploit
stochastic gradient descent to obtain end-to-end training. Interestingly, this
also opens up the possible use of gradient-based attribution methods to explain
the decision making for anomaly detection, which has ever been challenging as a
result of the implicit mappings between the input space and the kernel space.
To the best of our knowledge, this is the first work to study the
interpretability of deep learning in anomaly detection. We evaluate our method
on a wide range of unsupervised anomaly detection tasks in which our end-to-end
training architecture achieves a performance significantly better than the
previous work using separate training.Comment: Accepted at European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases (ECML-PKDD) 201
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