9,846 research outputs found
Pathwise stability of likelihood estimators for diffusions via rough paths
We consider the classical estimation problem of an unknown drift parameter
within classes of nondegenerate diffusion processes. Using rough path theory
(in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE)
with regard to its pathwise stability properties as well as robustness toward
misspecification in volatility and even the very nature of the noise. Two
numerical examples demonstrate the practical relevance of our results.Comment: Published at http://dx.doi.org/10.1214/15-AAP1143 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
M\"obius Invariants of Shapes and Images
Identifying when different images are of the same object despite changes
caused by imaging technologies, or processes such as growth, has many
applications in fields such as computer vision and biological image analysis.
One approach to this problem is to identify the group of possible
transformations of the object and to find invariants to the action of that
group, meaning that the object has the same values of the invariants despite
the action of the group. In this paper we study the invariants of planar shapes
and images under the M\"obius group , which arises
in the conformal camera model of vision and may also correspond to neurological
aspects of vision, such as grouping of lines and circles. We survey properties
of invariants that are important in applications, and the known M\"obius
invariants, and then develop an algorithm by which shapes can be recognised
that is M\"obius- and reparametrization-invariant, numerically stable, and
robust to noise. We demonstrate the efficacy of this new invariant approach on
sets of curves, and then develop a M\"obius-invariant signature of grey-scale
images
Robust automated detection of microstructural white matter degeneration in Alzheimer’s disease using machine learning classification of multicenter DTI data
Diffusion tensor imaging (DTI) based assessment of white matter fiber tract integrity can support the diagnosis of Alzheimer’s disease (AD). The use of DTI as a biomarker, however, depends on its applicability in a multicenter setting accounting for effects of different MRI scanners. We applied multivariate machine learning (ML) to a large multicenter sample from the recently created framework of the European DTI study on Dementia (EDSD). We hypothesized that ML approaches may amend effects of multicenter acquisition. We included a sample of 137 patients with clinically probable AD (MMSE 20.6±5.3) and 143 healthy elderly controls, scanned in nine different scanners. For diagnostic classification we used the DTI indices fractional anisotropy (FA) and mean diffusivity (MD) and, for comparison, gray matter and white matter density maps from anatomical MRI. Data were classified using a Support Vector Machine (SVM) and a Naïve Bayes (NB) classifier. We used two cross-validation approaches, (i) test and training samples randomly drawn from the entire data set (pooled cross-validation) and (ii) data from each scanner as test set, and the data from the remaining scanners as training set (scanner-specific cross-validation). In the pooled cross-validation, SVM achieved an accuracy of 80% for FA and 83% for MD. Accuracies for NB were significantly lower, ranging between 68% and 75%. Removing variance components arising from scanners using principal component analysis did not significantly change the classification results for both classifiers. For the scanner-specific cross-validation, the classification accuracy was reduced for both SVM and NB. After mean correction, classification accuracy reached a level comparable to the results obtained from the pooled cross-validation. Our findings support the notion that machine learning classification allows robust classification of DTI data sets arising from multiple scanners, even if a new data set comes from a scanner that was not part of the training sample
Fuzzy Fibers: Uncertainty in dMRI Tractography
Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI)
allows for noninvasive reconstruction of fiber bundles in the human brain. In
this chapter, we discuss sources of error and uncertainty in this technique,
and review strategies that afford a more reliable interpretation of the
results. This includes methods for computing and rendering probabilistic
tractograms, which estimate precision in the face of measurement noise and
artifacts. However, we also address aspects that have received less attention
so far, such as model selection, partial voluming, and the impact of
parameters, both in preprocessing and in fiber tracking itself. We conclude by
giving impulses for future research
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