Statistical depth functions and depth-based robustness diagnosis

2005 ◽  
Author(s):  
Wing-sze Lok
Keyword(s):  
Statistical Depth ◽  
Depth Functions ◽  
Statistical Depth Functions

scholarly journals Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions

2021 ◽  
Vol 48 (2) ◽  
Author(s):  
Olusola S. Makinde ◽  
Keyword(s):  
Affine Invariant ◽  
Classification Methods ◽  
Statistical Depth ◽  
Depth Functions ◽  
Maximal Depth ◽  
Depth Classification ◽  
Multivariate Outcomes ◽  
Statistical Depth Functions ◽  
Spatial Depth

Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.

scholarly journals Comparison-based centrality measures

2021 ◽  
Author(s):  
Luca Rendsburg ◽  
Damien Garreau
Keyword(s):  
Machine Learning ◽  
Learning Community ◽  
Outlier Detection ◽  
Centrality Measures ◽  
Human Intelligence ◽  
Ordinal Information ◽  
Statistical Depth ◽  
Depth Functions ◽  
Statistical Depth Functions ◽  
Synthetic Datasets

AbstractRecently, learning only from ordinal information of the type “item x is closer to item y than to item z” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.

scholarly journals Robust multivariate estimation based on statistical depth filters

Test ◽  
2021 ◽  
Author(s):  
Giovanni Saraceno ◽  
Claudio Agostinelli
Keyword(s):  
Missing Values ◽  
Statistical Data ◽  
Data Depth ◽  
Data Set ◽  
Statistical Depth ◽  
Depth Functions ◽  
Gross Error ◽  
Special Cases ◽  
Model Cell ◽  
Multivariate Estimation

AbstractIn the classical contamination models, such as the gross-error (Huber and Tukey contamination model or case-wise contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. (Ann Stat 37(1):311–331, 2009) show the limits of this approach for a larger number of variables and introduced the independent contamination model (cell-wise contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here, we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g., Agostinelli et al. (TEST 24(3):441–461, 2015b) and Leung et al. (Comput Stat Data Anal 111:59–76, 2017), are special cases. We illustrate our method by using the half-space depth.

scholarly journals Neural Rate and Timing Cues for Detection and Discrimination of Amplitude-Modulated Tones in the Awake Rabbit Inferior Colliculus

2007 ◽  
Vol 97 (1) ◽  
pp. 522-539 ◽  
Author(s):  
Paul C. Nelson ◽  
Laurel H. Carney
Keyword(s):  
Inferior Colliculus ◽  
Dynamic Range ◽  
Modulation Depth ◽  
Average Rate ◽  
Modulation Frequency ◽  
Detection Threshold ◽  
Depth Functions ◽  
Depth Discrimination ◽  
High Modulation ◽  
Envelope Processing

Neural responses to amplitude-modulated (AM) tones in the unanesthetized rabbit inferior colliculus (IC) were studied in an effort to establish explicit relationships between physiological and psychophysical measures of temporal envelope processing. Specifically, responses to variations in modulation depth ( m) at the cell’s best modulation frequency, with and without modulation maskers, were quantified in terms of average rate and synchronization to the envelope over the entire perceptual dynamic range of depths. Statistically significant variations in the metrics were used to define neural AM detection and discrimination thresholds. Synchrony emerged at modulation depths comparable with psychophysical AM detection sensitivities in some neurons, whereas the lowest rate-based neural thresholds could not account for psychoacoustical thresholds. The majority of rate thresholds (85%) were −10 dB or higher (in 20 log m), and 16% of the population exhibited no systematic dependence of average rate on m. Neural thresholds for AM detection did not decrease systematically at higher SPLs (as observed psychophysically): thresholds remained constant or increased with level for most cells tested at multiple sound-pressure levels (SPLs). At depths higher than the rate-based detection threshold, some rate modulation-depth functions were sufficiently steep with respect to the across-trial variability of the rate to predict depth discrimination thresholds as low as 1 dB (comparable with the psychophysics). Synchrony, on the other hand, did not vary systematically with m in many cells at high modulation depths. A simple computational model was extended to reproduce several features of the modulation frequency and depth dependence of both transient and sustained pure-tone responders.

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