Maximum probability estimators with a general loss function

1974 ◽  
pp. 30-39
Author(s):  
Lionel Weiss ◽  
Jacob Wolfowitz
Keyword(s):  
Loss Function ◽  
Maximum Probability ◽  
General Loss Function

scholarly journals MPCE: A Maximum Probability Based Cross Entropy Loss Function for Neural Network Classification

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 146331-146341 ◽  
Author(s):  
Yangfan Zhou ◽  
Xin Wang ◽  
Mingchuan Zhang ◽  
Junlong Zhu ◽  
Ruijuan Zheng ◽  
...  
Keyword(s):  
Neural Network ◽  
Loss Function ◽  
Cross Entropy ◽  
Maximum Probability ◽  
Entropy Loss ◽  
Neural Network Classification

scholarly journals Event-based backpropagation can compute exact gradients for spiking neural networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Timo C. Wunderlich ◽  
Christian Pehle
Keyword(s):  
Neural Networks ◽  
Loss Function ◽  
Spiking Neural Networks ◽  
Backpropagation Algorithm ◽  
General Loss Function ◽  
Gradient Based ◽  
Rigorous Study ◽  
Spiking Networks ◽  
Event Based ◽  
First Time

AbstractSpiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.

scholarly journals FCN-Based 3D Reconstruction with Multi-Source Photometric Stereo

2020 ◽  
Vol 10 (8) ◽  
pp. 2914
Author(s):  
Ruixin Wang ◽  
Xin Wang ◽  
Di He ◽  
Lei Wang ◽  
Ke Xu
Keyword(s):  
3D Reconstruction ◽  
Loss Function ◽  
Classical Method ◽  
Solution Process ◽  
Photometric Stereo ◽  
Good Effect ◽  
Reconstruction Method ◽  
Convolutional Network ◽  
General Loss Function ◽  
3D Information

As a classical method widely used in 3D reconstruction tasks, the multi-source Photometric Stereo can obtain more accurate 3D reconstruction results compared with the basic Photometric Stereo, but its complex calibration and solution process reduces the efficiency of this algorithm. In this paper, we propose a multi-source Photometric Stereo 3D reconstruction method based on the fully convolutional network (FCN). We first represent the 3D shape of the object as a depth value corresponding to each pixel as the optimized object. After training in an end-to-end manner, our network can efficiently obtain 3D information on the object surface. In addition, we added two regularization constraints to the general loss function, which can effectively help the network to optimize. Under the same light source configuration, our method can obtain a higher accuracy than the classic multi-source Photometric Stereo. At the same time, our new loss function can help the deep learning method to get a more realistic 3D reconstruction result. We have also used our own real dataset to experimentally verify our method. The experimental results show that our method has a good effect on solving the main problems faced by the classical method.

scholarly journals Gene-Based Multiclass Cancer Diagnosis with Class-Selective Rejections

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Nisrine Jrad ◽  
Edith Grall-Maës ◽  
Pierre Beauseroy
Keyword(s):  
Cancer Diagnosis ◽  
Loss Function ◽  
Microarray Data ◽  
Nearest Neighbor ◽  
Support Vector ◽  
Correct Decision ◽  
Gene Profiles ◽  
Vector Machines ◽  
General Loss Function ◽  
State Of Art

Supervised learning of microarray data is receiving much attention in recent years. Multiclass cancer diagnosis, based on selected gene profiles, are used as adjunct of clinical diagnosis. However, supervised diagnosis may hinder patient care, add expense or confound a result. To avoid this misleading, a multiclass cancer diagnosis with class-selective rejection is proposed. It rejects some patients from one, some, or all classes in order to ensure a higher reliability while reducing time and expense costs. Moreover, this classifier takes into account asymmetric penalties dependant on each class and on each wrong or partially correct decision. It is based onν-1-SVM coupled with its regularization path and minimizes a general loss function defined in the class-selective rejection scheme. The state of art multiclass algorithms can be considered as a particular case of the proposed algorithm where the number of decisions is given by the classes and the loss function is defined by the Bayesian risk. Two experiments are carried out in the Bayesian and the class selective rejection frameworks. Five genes selected datasets are used to assess the performance of the proposed method. Results are discussed and accuracies are compared with those computed by the Naive Bayes, Nearest Neighbor, Linear Perceptron, Multilayer Perceptron, and Support Vector Machines classifiers.

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