773 research outputs found
A general setting for symmetric distributions and their relationship to general distributions
A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.PostprintPeer reviewe
HMMs for Anomaly Detection in Autonomous Robots
Detection of anomalies and faults is a key element for long-term robot autonomy, because, together with subsequent diagnosis and recovery, allows to reach the required levels of robustness and persistency. In this paper, we propose an approach for detecting anomalous behaviors in autonomous robots starting from data collected during their routine operations. The main idea is to model the nominal (expected) behavior of a robot system using Hidden Markov Models (HMMs) and to evaluate how far the observed behavior is from the nominal one using variants of the Hellinger distance adopted for our purposes. We present a method for online anomaly detection that computes the Hellinger distance between the probability distribution of observations made in a sliding window and the corresponding nominal emission probability distribution. We also present a method for o!ine anomaly detection that computes a variant of the Hellinger distance between two HMMs representing nominal and observed behaviors. The use of the Hellinger distance positively impacts on both detection performance and interpretability of detected anomalies, as shown by results of experiments performed in two real-world application domains, namely, water monitoring with aquatic drones and socially assistive robots for elders living at home. In particular, our approach improves by 6% the area under the ROC curve of standard online anomaly detection methods. The capabilities of our o!ine method to discriminate anomalous behaviors in real-world applications are statistically proved
Adversarial Data Augmentation for HMM-based Anomaly Detection
In this work, we concentrate on the detection of anomalous behaviors in systems operating in the physical world and for which it is usually not possible to have a complete set of all possible anomalies in advance. We present a data augmentation and retraining approach based on adversarial learning for improving anomaly detection. In particular, we first define a method for gener- ating adversarial examples for anomaly detectors based on Hidden Markov Models (HMMs). Then, we present a data augmentation and retraining technique that uses these adversarial examples to improve anomaly detection performance. Finally, we evaluate our adversarial data augmentation and retraining approach on four datasets showing that it achieves a statistically significant perfor- mance improvement and enhances the robustness to adversarial attacks. Key differences from the state-of-the-art on adversarial data augmentation are the focus on multivariate time series (as opposed to images), the context of one-class classification (in contrast to standard multi-class classification), and the use of HMMs (in contrast to neural networks)
Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies
Two non-integer parameters are defined for MAX statistics, which are maxima
of simpler test statistics. The first parameter, , is the
fractional number of tests, representing the equivalent numbers of independent
tests in MAX. If the tests are dependent, . The second
parameter is the fractional degrees of freedom of the chi-square
distribution that fits the MAX null distribution. These two
parameters, and , can be independently defined, and can be
non-integer even if is an integer. We illustrate these two parameters
using the example of MAX2 and MAX3 statistics in genetic case-control studies.
We speculate that is related to the amount of ambiguity of the model
inferred by the test. In the case-control genetic association, tests with low
(e.g. ) are able to provide definitive information about the disease
model, as versus tests with high (e.g. ) that are completely uncertain
about the disease model. Similar to Heisenberg's uncertain principle, the
ability to infer disease model and the ability to detect significant
association may not be simultaneously optimized, and seems to measure the
level of their balance
Integral Geometry of Linearly Combined Gaussian and Student-t, and Skew Student's t Random Fields
International audienceThe integral geometry of random fields has been investigated since the 1980s, and the analytic formulae of the Minkowski functionals (also called Lipschitz-Killing curvatures, shortly denoted LKCs) of their excursion sets on a compact subset S in the n-dimensional Euclidean space have been reported in the specialized literature for Gaussian and student-t random fields. Very recently, explicit analytical formulae of the Minkowski functionals of their excursion sets in the bi-dimensional case (n = 2) have been defined on more sophisticated random fields, namely: the Linearly Combined Gaussian and Student-t, and the Skew Student-t random fields. This paper presents the theoretical background, and gives the explicit analytic formulae of the three Minkowski functionals. Simulation results are also presented both for illustration and validation, together with a real application example on an worn engineered surface
Fast calibrated additive quantile regression
We propose a novel framework for fitting additive quantile regression models,
which provides well calibrated inference about the conditional quantiles and
fast automatic estimation of the smoothing parameters, for model structures as
diverse as those usable with distributional GAMs, while maintaining equivalent
numerical efficiency and stability. The proposed methods are at once
statistically rigorous and computationally efficient, because they are based on
the general belief updating framework of Bissiri et al. (2016) to loss based
inference, but compute by adapting the stable fitting methods of Wood et al.
(2016). We show how the pinball loss is statistically suboptimal relative to a
novel smooth generalisation, which also gives access to fast estimation
methods. Further, we provide a novel calibration method for efficiently
selecting the 'learning rate' balancing the loss with the smoothing priors
during inference, thereby obtaining reliable quantile uncertainty estimates.
Our work was motivated by a probabilistic electricity load forecasting
application, used here to demonstrate the proposed approach. The methods
described here are implemented by the qgam R package, available on the
Comprehensive R Archive Network (CRAN)
The Bivariate Normal Copula
We collect well known and less known facts about the bivariate normal
distribution and translate them into copula language. In addition, we prove a
very general formula for the bivariate normal copula, we compute Gini's gamma,
and we provide improved bounds and approximations on the diagonal.Comment: 24 page
Distributed Generation and Resilience in Power Grids
We study the effects of the allocation of distributed generation on the
resilience of power grids. We find that an unconstrained allocation and growth
of the distributed generation can drive a power grid beyond its design
parameters. In order to overcome such a problem, we propose a topological
algorithm derived from the field of Complex Networks to allocate distributed
generation sources in an existing power grid.Comment: proceedings of Critis 2012 http://critis12.hig.no
- …