29,492 research outputs found
Statistical Inference using the Morse-Smale Complex
The Morse-Smale complex of a function decomposes the sample space into
cells where is increasing or decreasing. When applied to nonparametric
density estimation and regression, it provides a way to represent, visualize,
and compare multivariate functions. In this paper, we present some statistical
results on estimating Morse-Smale complexes. This allows us to derive new
results for two existing methods: mode clustering and Morse-Smale regression.
We also develop two new methods based on the Morse-Smale complex: a
visualization technique for multivariate functions and a two-sample,
multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic
Adaptation to lowest density regions with application to support recovery
A scheme for locally adaptive bandwidth selection is proposed which
sensitively shrinks the bandwidth of a kernel estimator at lowest density
regions such as the support boundary which are unknown to the statistician. In
case of a H\"{o}lder continuous density, this locally minimax-optimal bandwidth
is shown to be smaller than the usual rate, even in case of homogeneous
smoothness. Some new type of risk bound with respect to a density-dependent
standardized loss of this estimator is established. This bound is fully
nonasymptotic and allows to deduce convergence rates at lowest density regions
that can be substantially faster than . It is complemented by a
weighted minimax lower bound which splits into two regimes depending on the
value of the density. The new estimator adapts into the second regime, and it
is shown that simultaneous adaptation into the fastest regime is not possible
in principle as long as the H\"{o}lder exponent is unknown. Consequences on
plug-in rules for support recovery are worked out in detail. In contrast to
those with classical density estimators, the plug-in rules based on the new
construction are minimax-optimal, up to some logarithmic factor.Comment: Published at http://dx.doi.org/10.1214/15-AOS1366 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Anomaly Detection and Removal Using Non-Stationary Gaussian Processes
This paper proposes a novel Gaussian process approach to fault removal in
time-series data. Fault removal does not delete the faulty signal data but,
instead, massages the fault from the data. We assume that only one fault occurs
at any one time and model the signal by two separate non-parametric Gaussian
process models for both the physical phenomenon and the fault. In order to
facilitate fault removal we introduce the Markov Region Link kernel for
handling non-stationary Gaussian processes. This kernel is piece-wise
stationary but guarantees that functions generated by it and their derivatives
(when required) are everywhere continuous. We apply this kernel to the removal
of drift and bias errors in faulty sensor data and also to the recovery of EOG
artifact corrupted EEG signals.Comment: 9 pages, 14 figure
Fast and Accurate Algorithm for Eye Localization for Gaze Tracking in Low Resolution Images
Iris centre localization in low-resolution visible images is a challenging
problem in computer vision community due to noise, shadows, occlusions, pose
variations, eye blinks, etc. This paper proposes an efficient method for
determining iris centre in low-resolution images in the visible spectrum. Even
low-cost consumer-grade webcams can be used for gaze tracking without any
additional hardware. A two-stage algorithm is proposed for iris centre
localization. The proposed method uses geometrical characteristics of the eye.
In the first stage, a fast convolution based approach is used for obtaining the
coarse location of iris centre (IC). The IC location is further refined in the
second stage using boundary tracing and ellipse fitting. The algorithm has been
evaluated in public databases like BioID, Gi4E and is found to outperform the
state of the art methods.Comment: 12 pages, 10 figures, IET Computer Vision, 201
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