12,639 research outputs found
Robust nearest-neighbor methods for classifying high-dimensional data
We suggest a robust nearest-neighbor approach to classifying high-dimensional
data. The method enhances sensitivity by employing a threshold and truncates to
a sequence of zeros and ones in order to reduce the deleterious impact of
heavy-tailed data. Empirical rules are suggested for choosing the threshold.
They require the bare minimum of data; only one data vector is needed from each
population. Theoretical and numerical aspects of performance are explored,
paying particular attention to the impacts of correlation and heterogeneity
among data components. On the theoretical side, it is shown that our truncated,
thresholded, nearest-neighbor classifier enjoys the same classification
boundary as more conventional, nonrobust approaches, which require finite
moments in order to achieve good performance. In particular, the greater
robustness of our approach does not come at the price of reduced effectiveness.
Moreover, when both training sample sizes equal 1, our new method can have
performance equal to that of optimal classifiers that require independent and
identically distributed data with known marginal distributions; yet, our
classifier does not itself need conditions of this type.Comment: Published in at http://dx.doi.org/10.1214/08-AOS591 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Classification with the nearest neighbor rule in general finite dimensional spaces: necessary and sufficient conditions
Given an -sample of random vectors whose
joint law is unknown, the long-standing problem of supervised classification
aims to \textit{optimally} predict the label of a given a new observation
. In this context, the nearest neighbor rule is a popular flexible and
intuitive method in non-parametric situations.
Even if this algorithm is commonly used in the machine learning and
statistics communities, less is known about its prediction ability in general
finite dimensional spaces, especially when the support of the density of the
observations is . This paper is devoted to the study of the
statistical properties of the nearest neighbor rule in various situations. In
particular, attention is paid to the marginal law of , as well as the
smoothness and margin properties of the \textit{regression function} . We identify two necessary and sufficient conditions to
obtain uniform consistency rates of classification and to derive sharp
estimates in the case of the nearest neighbor rule. Some numerical experiments
are proposed at the end of the paper to help illustrate the discussion.Comment: 53 Pages, 3 figure
Context-aware Captions from Context-agnostic Supervision
We introduce an inference technique to produce discriminative context-aware
image captions (captions that describe differences between images or visual
concepts) using only generic context-agnostic training data (captions that
describe a concept or an image in isolation). For example, given images and
captions of "siamese cat" and "tiger cat", we generate language that describes
the "siamese cat" in a way that distinguishes it from "tiger cat". Our key
novelty is that we show how to do joint inference over a language model that is
context-agnostic and a listener which distinguishes closely-related concepts.
We first apply our technique to a justification task, namely to describe why an
image contains a particular fine-grained category as opposed to another
closely-related category of the CUB-200-2011 dataset. We then study
discriminative image captioning to generate language that uniquely refers to
one of two semantically-similar images in the COCO dataset. Evaluations with
discriminative ground truth for justification and human studies for
discriminative image captioning reveal that our approach outperforms baseline
generative and speaker-listener approaches for discrimination.Comment: Accepted to CVPR 2017 (Spotlight
Efficient Localization of Discontinuities in Complex Computational Simulations
Surrogate models for computational simulations are input-output
approximations that allow computationally intensive analyses, such as
uncertainty propagation and inference, to be performed efficiently. When a
simulation output does not depend smoothly on its inputs, the error and
convergence rate of many approximation methods deteriorate substantially. This
paper details a method for efficiently localizing discontinuities in the input
parameter domain, so that the model output can be approximated as a piecewise
smooth function. The approach comprises an initialization phase, which uses
polynomial annihilation to assign function values to different regions and thus
seed an automated labeling procedure, followed by a refinement phase that
adaptively updates a kernel support vector machine representation of the
separating surface via active learning. The overall approach avoids structured
grids and exploits any available simplicity in the geometry of the separating
surface, thus reducing the number of model evaluations required to localize the
discontinuity. The method is illustrated on examples of up to eleven
dimensions, including algebraic models and ODE/PDE systems, and demonstrates
improved scaling and efficiency over other discontinuity localization
approaches
Efficient Classification for Metric Data
Recent advances in large-margin classification of data residing in general
metric spaces (rather than Hilbert spaces) enable classification under various
natural metrics, such as string edit and earthmover distance. A general
framework developed for this purpose by von Luxburg and Bousquet [JMLR, 2004]
left open the questions of computational efficiency and of providing direct
bounds on generalization error.
We design a new algorithm for classification in general metric spaces, whose
runtime and accuracy depend on the doubling dimension of the data points, and
can thus achieve superior classification performance in many common scenarios.
The algorithmic core of our approach is an approximate (rather than exact)
solution to the classical problems of Lipschitz extension and of Nearest
Neighbor Search. The algorithm's generalization performance is guaranteed via
the fat-shattering dimension of Lipschitz classifiers, and we present
experimental evidence of its superiority to some common kernel methods. As a
by-product, we offer a new perspective on the nearest neighbor classifier,
which yields significantly sharper risk asymptotics than the classic analysis
of Cover and Hart [IEEE Trans. Info. Theory, 1967].Comment: This is the full version of an extended abstract that appeared in
Proceedings of the 23rd COLT, 201
Survey of data mining approaches to user modeling for adaptive hypermedia
The ability of an adaptive hypermedia system to create tailored environments depends mainly on the amount and accuracy of information stored in each user model. Some of the difficulties that user modeling faces are the amount of data available to create user models, the adequacy of the data, the noise within that data, and the necessity of capturing the imprecise nature of human behavior. Data mining and machine learning techniques have the ability to handle large amounts of data and to process uncertainty. These characteristics make these techniques suitable for automatic generation of user models that simulate human decision making. This paper surveys different data mining techniques that can be used to efficiently and accurately capture user behavior. The paper also presents guidelines that show which techniques may be used more efficiently according to the task implemented by the applicatio
On Classification with Bags, Groups and Sets
Many classification problems can be difficult to formulate directly in terms
of the traditional supervised setting, where both training and test samples are
individual feature vectors. There are cases in which samples are better
described by sets of feature vectors, that labels are only available for sets
rather than individual samples, or, if individual labels are available, that
these are not independent. To better deal with such problems, several
extensions of supervised learning have been proposed, where either training
and/or test objects are sets of feature vectors. However, having been proposed
rather independently of each other, their mutual similarities and differences
have hitherto not been mapped out. In this work, we provide an overview of such
learning scenarios, propose a taxonomy to illustrate the relationships between
them, and discuss directions for further research in these areas
Supervised Classification: Quite a Brief Overview
The original problem of supervised classification considers the task of
automatically assigning objects to their respective classes on the basis of
numerical measurements derived from these objects. Classifiers are the tools
that implement the actual functional mapping from these measurements---also
called features or inputs---to the so-called class label---or output. The
fields of pattern recognition and machine learning study ways of constructing
such classifiers. The main idea behind supervised methods is that of learning
from examples: given a number of example input-output relations, to what extent
can the general mapping be learned that takes any new and unseen feature vector
to its correct class? This chapter provides a basic introduction to the
underlying ideas of how to come to a supervised classification problem. In
addition, it provides an overview of some specific classification techniques,
delves into the issues of object representation and classifier evaluation, and
(very) briefly covers some variations on the basic supervised classification
task that may also be of interest to the practitioner
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