Beyond LASSO: Other Loss Functions

2018 ◽  
pp. 134-151
Author(s):  
MISSING-VALUE MISSING-VALUE
Keyword(s):  
Loss Functions

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.

A CLASS OF LORENZ CURVES BASED ON LINEAR EXPONENTIAL LOSS FUNCTIONS

2002 ◽  
Vol 31 (6) ◽  
pp. 925-942 ◽  
Author(s):  
José María Sarabia ◽  
Marta Pascual
Keyword(s):  
Loss Functions ◽  
Lorenz Curves

scholarly journals Study on Radar Echo-Filling in an Occlusion Area by a Deep Learning Algorithm

2021 ◽  
Vol 13 (9) ◽  
pp. 1779
Author(s):  
Xiaoyan Yin ◽  
Zhiqun Hu ◽  
Jiafeng Zheng ◽  
Boyong Li ◽  
Yuanyuan Zuo
Keyword(s):  
Deep Learning ◽  
Loss Function ◽  
Learning Algorithm ◽  
Weather Radar ◽  
Loss Functions ◽  
Training Dataset ◽  
Echo Intensity ◽  
Common Mean ◽  
Deep Learning Algorithm ◽  
Radar Beam

Radar beam blockage is an important error source that affects the quality of weather radar data. An echo-filling network (EFnet) is proposed based on a deep learning algorithm to correct the echo intensity under the occlusion area in the Nanjing S-band new-generation weather radar (CINRAD/SA). The training dataset is constructed by the labels, which are the echo intensity at the 0.5° elevation in the unblocked area, and by the input features, which are the intensity in the cube including multiple elevations and gates corresponding to the location of bottom labels. Two loss functions are applied to compile the network: one is the common mean square error (MSE), and the other is a self-defined loss function that increases the weight of strong echoes. Considering that the radar beam broadens with distance and height, the 0.5° elevation scan is divided into six range bands every 25 km to train different models. The models are evaluated by three indicators: explained variance (EVar), mean absolute error (MAE), and correlation coefficient (CC). Two cases are demonstrated to compare the effect of the echo-filling model by different loss functions. The results suggest that EFnet can effectively correct the echo reflectivity and improve the data quality in the occlusion area, and there are better results for strong echoes when the self-defined loss function is used.

scholarly journals Testing Segmentation Popular Loss and Variations in Three Multiclass Medical Imaging Problems

2021 ◽  
Vol 7 (2) ◽  
pp. 16
Author(s):  
Pedro Furtado
Keyword(s):  
False Negative ◽  
Magnetic Resonance Images ◽  
Medical Image Segmentation ◽  
Cross Entropy ◽  
Loss Functions ◽  
Optic Disk ◽  
False Negatives ◽  
Convolutional Network ◽  
Percentage Points ◽  
Class Background

Image structures are segmented automatically using deep learning (DL) for analysis and processing. The three most popular base loss functions are cross entropy (crossE), intersect-over-the-union (IoU), and dice. Which should be used, is it useful to consider simple variations, such as modifying formula coefficients? How do characteristics of different image structures influence scores? Taking three different medical image segmentation problems (segmentation of organs in magnetic resonance images (MRI), liver in computer tomography images (CT) and diabetic retinopathy lesions in eye fundus images (EFI)), we quantify loss functions and variations, as well as segmentation scores of different targets. We first describe the limitations of metrics, since loss is a metric, then we describe and test alternatives. Experimentally, we observed that DeeplabV3 outperforms UNet and fully convolutional network (FCN) in all datasets. Dice scored 1 to 6 percentage points (pp) higher than cross entropy over all datasets, IoU improved 0 to 3 pp. Varying formula coefficients improved scores, but the best choices depend on the dataset: compared to crossE, different false positive vs. false negative weights improved MRI by 12 pp, and assigning zero weight to background improved EFI by 6 pp. Multiclass segmentation scored higher than n-uniclass segmentation in MRI by 8 pp. EFI lesions score low compared to more constant structures (e.g., optic disk or even organs), but loss modifications improve those scores significantly 6 to 9 pp. Our conclusions are that dice is best, it is worth assigning 0 weight to class background and to test different weights on false positives and false negatives.

A Densely Connected Network Based on U-Net for Medical Image Segmentation

2021 ◽  
Vol 17 (3) ◽  
pp. 1-14
Author(s):  
Zhenzhen Yang ◽  
Pengfei Xu ◽  
Yongpeng Yang ◽  
Bing-Kun Bao
Keyword(s):  
Feature Extraction ◽  
Image Segmentation ◽  
Loss Function ◽  
Network Architecture ◽  
Medical Image ◽  
Medical Image Segmentation ◽  
Cross Entropy ◽  
Loss Functions ◽  
Feature Maps ◽  
Different Levels

The U-Net has become the most popular structure in medical image segmentation in recent years. Although its performance for medical image segmentation is outstanding, a large number of experiments demonstrate that the classical U-Net network architecture seems to be insufficient when the size of segmentation targets changes and the imbalance happens between target and background in different forms of segmentation. To improve the U-Net network architecture, we develop a new architecture named densely connected U-Net (DenseUNet) network in this article. The proposed DenseUNet network adopts a dense block to improve the feature extraction capability and employs a multi-feature fuse block fusing feature maps of different levels to increase the accuracy of feature extraction. In addition, in view of the advantages of the cross entropy and the dice loss functions, a new loss function for the DenseUNet network is proposed to deal with the imbalance between target and background. Finally, we test the proposed DenseUNet network and compared it with the multi-resolutional U-Net (MultiResUNet) and the classic U-Net networks on three different datasets. The experimental results show that the DenseUNet network has significantly performances compared with the MultiResUNet and the classic U-Net networks.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

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