3,269 research outputs found
Meta learning of bounds on the Bayes classifier error
Meta learning uses information from base learners (e.g. classifiers or
estimators) as well as information about the learning problem to improve upon
the performance of a single base learner. For example, the Bayes error rate of
a given feature space, if known, can be used to aid in choosing a classifier,
as well as in feature selection and model selection for the base classifiers
and the meta classifier. Recent work in the field of f-divergence functional
estimation has led to the development of simple and rapidly converging
estimators that can be used to estimate various bounds on the Bayes error. We
estimate multiple bounds on the Bayes error using an estimator that applies
meta learning to slowly converging plug-in estimators to obtain the parametric
convergence rate. We compare the estimated bounds empirically on simulated data
and then estimate the tighter bounds on features extracted from an image patch
analysis of sunspot continuum and magnetogram images.Comment: 6 pages, 3 figures, to appear in proceedings of 2015 IEEE Signal
Processing and SP Education Worksho
Occam's hammer: a link between randomized learning and multiple testing FDR control
We establish a generic theoretical tool to construct probabilistic bounds for
algorithms where the output is a subset of objects from an initial pool of
candidates (or more generally, a probability distribution on said pool). This
general device, dubbed "Occam's hammer'', acts as a meta layer when a
probabilistic bound is already known on the objects of the pool taken
individually, and aims at controlling the proportion of the objects in the set
output not satisfying their individual bound. In this regard, it can be seen as
a non-trivial generalization of the "union bound with a prior'' ("Occam's
razor''), a familiar tool in learning theory. We give applications of this
principle to randomized classifiers (providing an interesting alternative
approach to PAC-Bayes bounds) and multiple testing (where it allows to retrieve
exactly and extend the so-called Benjamini-Yekutieli testing procedure).Comment: 13 pages -- conference communication type forma
Altitude Training: Strong Bounds for Single-Layer Dropout
Dropout training, originally designed for deep neural networks, has been
successful on high-dimensional single-layer natural language tasks. This paper
proposes a theoretical explanation for this phenomenon: we show that, under a
generative Poisson topic model with long documents, dropout training improves
the exponent in the generalization bound for empirical risk minimization.
Dropout achieves this gain much like a marathon runner who practices at
altitude: once a classifier learns to perform reasonably well on training
examples that have been artificially corrupted by dropout, it will do very well
on the uncorrupted test set. We also show that, under similar conditions,
dropout preserves the Bayes decision boundary and should therefore induce
minimal bias in high dimensions.Comment: Advances in Neural Information Processing Systems (NIPS), 201
Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary -Mixing Processes
Pac-Bayes bounds are among the most accurate generalization bounds for
classifiers learned from independently and identically distributed (IID) data,
and it is particularly so for margin classifiers: there have been recent
contributions showing how practical these bounds can be either to perform model
selection (Ambroladze et al., 2007) or even to directly guide the learning of
linear classifiers (Germain et al., 2009). However, there are many practical
situations where the training data show some dependencies and where the
traditional IID assumption does not hold. Stating generalization bounds for
such frameworks is therefore of the utmost interest, both from theoretical and
practical standpoints. In this work, we propose the first - to the best of our
knowledge - Pac-Bayes generalization bounds for classifiers trained on data
exhibiting interdependencies. The approach undertaken to establish our results
is based on the decomposition of a so-called dependency graph that encodes the
dependencies within the data, in sets of independent data, thanks to graph
fractional covers. Our bounds are very general, since being able to find an
upper bound on the fractional chromatic number of the dependency graph is
sufficient to get new Pac-Bayes bounds for specific settings. We show how our
results can be used to derive bounds for ranking statistics (such as Auc) and
classifiers trained on data distributed according to a stationary {\ss}-mixing
process. In the way, we show how our approach seemlessly allows us to deal with
U-processes. As a side note, we also provide a Pac-Bayes generalization bound
for classifiers learned on data from stationary -mixing distributions.Comment: Long version of the AISTATS 09 paper:
http://jmlr.csail.mit.edu/proceedings/papers/v5/ralaivola09a/ralaivola09a.pd
Species abundance information improves sequence taxonomy classification accuracy.
Popular naive Bayes taxonomic classifiers for amplicon sequences assume that all species in the reference database are equally likely to be observed. We demonstrate that classification accuracy degrades linearly with the degree to which that assumption is violated, and in practice it is always violated. By incorporating environment-specific taxonomic abundance information, we demonstrate a significant increase in the species-level classification accuracy across common sample types. At the species level, overall average error rates decline from 25% to 14%, which is favourably comparable to the error rates that existing classifiers achieve at the genus level (16%). Our findings indicate that for most practical purposes, the assumption that reference species are equally likely to be observed is untenable. q2-clawback provides a straightforward alternative for samples from common environments
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