Analytic approximation of the interval of Bayes actions derived from a class of loss functions

Test ◽  
1999 ◽  
Vol 8 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Christophe Abraham ◽  
Jean-Pierre Daurès
Keyword(s):  
Loss Functions ◽  
Analytic Approximation ◽  
Class Of Loss Functions

scholarly journals On the discrepancy principle and generalised maximum likelihood for regularisation

1995 ◽  
Vol 52 (3) ◽  
pp. 399-424 ◽  
Author(s):  
Mark A. Lukas
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Properties ◽  
Noisy Data ◽  
Loss Functions ◽  
Discrepancy Principle ◽  
Random Errors ◽  
Asymptotically Optimal ◽  
Large N ◽  
Class Of Loss Functions ◽  
Input Error

Let fnλ be the regularised solution of a general, linear operator equation, K f0 = g, from discrete, noisy data yi = g(xi ) + εi, i = 1, …, n, where εi are uncorrelated random errors with variance σ2. In this paper, we consider the two well–known methods – the discrepancy principle and generalised maximum likelihood (GML), for choosing the crucial regularisation parameter λ. We investigate the asymptotic properties as n → ∞ of the “expected” estimates λD and λM corresponding to these two methods respectively. It is shown that if f0 is sufficiently smooth, then λD is weakly asymptotically optimal (ao) with respect to the risk and an L2 norm on the output error. However, λD oversmooths for all sufficiently large n and also for all sufficiently small σ2. If f0 is not too smooth relative to the regularisation space W, then λD can also be weakly ao with respect to a whole class of loss functions involving stronger norms on the input error. For the GML method, we show that if f0 is smooth relative to W (for example f0 ∈ Wθ, 2, θ > m, if W = Wm, 2), then λM is asymptotically sub-optimal and undersmoothing with respect to all of the loss functions above.

scholarly journals A class of loss functions of catenary form

1973 ◽  
Vol 7 (3) ◽  
pp. 189-195
Author(s):  
D. E. Raeside ◽  
R. J. Owen
Keyword(s):  
Loss Functions ◽  
Class Of Loss Functions

An Intrusion Detection Model Based on Non-Negative Matrix Factorization

2011 ◽  
Vol 148-149 ◽  
pp. 895-899 ◽  
Author(s):  
Shan Xiong Chen ◽  
Sheng Wu ◽  
Yi Cao ◽  
Dong Sheng Tang
Keyword(s):  
Intrusion Detection ◽  
Wide Class ◽  
Matrix Factorization ◽  
Loss Functions ◽  
Detection Model ◽  
Model Based ◽  
Error Measures ◽  
Class Of Loss Functions ◽  
Non Negative Matrix Factorization

In this paper ,we discus a wide class of loss functions for non-negative matrix factorization (NMF) and derive flexible and improved NMF algorithms based alpha-divergences for error measures, which generalize or combine several different criteria in order to extract intrusion signal.

ON THE UNIVERSAL CLUSTERING UNDER A BROAD CLASS OF LOSS FUNCTIONS

2006 ◽  
Vol 16 (05) ◽  
pp. 329-339
Author(s):  
VLADIMIR NIKULIN
Keyword(s):  
Euclidean Space ◽  
Power Loss ◽  
Broad Class ◽  
Loss Functions ◽  
Number Of Clusters ◽  
Proposed Model ◽  
Probabilistic Space ◽  
Synthetic Datasets ◽  
Class Of Loss Functions

Determination of the number of significant clusters in the sample represents a very important problem. It is expected that the outcome of clustering under a broad class of loss functions will be more stable if the correct number of clusters is used. In order to illustrate the model of universal clustering we consider 1) family of power loss functions in probabilistic space; 2) family of exponential loss functions in Euclidean space. The proposed model is general, and proved to be effective in application to the synthetic datasets.

Valence electron spectroscopy of inhomogeneous media

1992 ◽  
Vol 50 (2) ◽  
pp. 1150-1151
Author(s):  
A. Howie ◽  
D.W. McComb
Keyword(s):  
Specific Gravity ◽  
Loss Function ◽  
Electron Spectroscopy ◽  
Valence Electron ◽  
Peak Height ◽  
Loss Functions ◽  
Loss Peak ◽  
High Energies ◽  
Valence Electron Density ◽  
Electron Microscopist

The bulk loss function Im(-l/ε (ω)), a well established tool for the interpretation of valence loss spectra, is being progressively adapted to the wide variety of inhomogeneous samples of interest to the electron microscopist. Proportionality between n, the local valence electron density, and ε-1 (Sellmeyer's equation) has sometimes been assumed but may not be valid even in homogeneous samples. Figs. 1 and 2 show the experimentally measured bulk loss functions for three pure silicates of different specific gravity ρ - quartz (ρ = 2.66), coesite (ρ = 2.93) and a zeolite (ρ = 1.79). Clearly, despite the substantial differences in density, the shift of the prominent loss peak is very small and far less than that predicted by scaling e for quartz with Sellmeyer's equation or even the somewhat smaller shift given by the Clausius-Mossotti (CM) relation which assumes proportionality between n (or ρ in this case) and (ε - 1)/(ε + 2). Both theories overestimate the rise in the peak height for coesite and underestimate the increase at high energies.

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