https://eli.thegreenplace.net/2016/the-softmax-function-and-its-derivative/  Eli Bendersky's website About Archives The Softmax function and its derivative  October 18, 2016 at 05:20 Tags Math , Machine Learning The softmax function takes an N-dimens…

DIFFERENCE BETWEEN SOFTMAX FUNCTION AND SIGMOID FUNCTION 二者主要的区别见于, softmax 用于多分类,sigmoid 则主要用于二分类: ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪F(Xi)=11+exp(−Xi)=exp(Xi)exp(Xi)+1F(Xi)=exp(Xi)∑kj=0exp(Xj),i=0,1,-,k import numpy as np import matplotlib.pyplot as plt def sigmoid(inputs…

sigmoid函数(也叫逻辑斯谛函数):  引用wiki百科的定义: A logistic function or logistic curve is a common “S” shape (sigmoid curve). 其实逻辑斯谛函数也就是经常说的sigmoid函数,它的几何形状也就是一条sigmoid曲线. logistic曲线如下:  同样,我们贴一下wiki百科对softmax函数的定义: softmax is a generalization of logistic functio…

#include <iostream> #include <vector> #include <cmath> #include <algorithm> #include <numeric> double myfunction(double num) { return exp(num); } template <typename T> void softmax(const typename::std::vector<T> &…

Back-propagation in a nerual network with a Softmax classifier, which uses the Softmax function: \[\hat y_i=\frac{\exp(o_i)}{\sum_j \exp(o_j)}\] This is used in a loss function of the form: \[\mathcal{L}=-\sum_j{y_j\log \hat y_j}\] where \(o\) is a v…

下溢(underflow):当接近零的数被四舍五入为零时发生下溢.许多函数在其参数为零而不是一个很小的正数时才会表现出质的不同.例如,我们通常要避免被零除或避免取零的对数. 上溢(overflow):当大量级的数被近似为∞或-∞时发生上溢.进一步的运算通常会导致这些无限值变为非数字. 必须对上溢和下溢进行数值稳定的一个例子是softmax函数(softmax function).softmax函数经常用于预测与Multinoulli分布相关联的概率,定义为: 考虑一下当所有xi都等于某个常数c时…

二分类:Logistic regression 多分类:Softmax分类函数 对于损失函数,我们求其最小值, 对于似然函数,我们求其最大值. Logistic是loss function,即: 在逻辑回归中,选择了 “对数似然损失函数”,L(Y,P(Y|X)) = -logP(Y|X). 对似然函数求最大值,其实就是对对数似然损失函数求最小值. Logistic regression, despite its name, is a linear model for classification…

转载请注明出处:http://www.cnblogs.com/BYRans/ 多分类问题 在一个多分类问题中,因变量y有k个取值,即.例如在邮件分类问题中,我们要把邮件分为垃圾邮件.个人邮件.工作邮件3类,目标值y是一个有3个取值的离散值.这是一个多分类问题,二分类模型在这里不太适用. 多分类问题符合多项分布.有许多算法可用于解决多分类问题,像决策树.朴素贝叶斯等.这篇文章主要讲解多分类算法中的Softmax回归(Softmax Regression) 推导思路为:首先证明多项分布属于指数分布族…

Softmax function Softmax 函数 \(y=[y_1,\cdots,y_m]\) 定义如下: \[y_i=\frac{exp(z_i)}{\sum\limits_{j=1}^m{exp(z_j)}}, i=1,2,\cdots,m\] 它具有很好的求导性质: \[\frac{\partial y_i}{\partial z_i}=y_i* (1-y_i)\] 其中,\(y\)的每一个维度 \(y_i\) 表明,属于第 \(i\) 类的概率.求导过程,请参考:Softmax v…

逻辑回归神经网络实现手写数字识别 如果更习惯看Jupyter的形式,请戳Gitthub_逻辑回归softmax神经网络实现手写数字识别.ipynb 1 - 导入模块 import numpy as np import matplotlib.pyplot as plt from PIL import Image from ld_mnist import load_digits %matplotlib inline 2 - 导入数据及数据预处理 mnist = load_digits() Extra…

目录 符号定义 对 softmax 求导 对 cross-entropy 求导 对 softmax 和 cross-entropy 一起求导 References 在论文中看到对 softmax 和 cross-entropy 的求导,一脸懵逼,故来整理整理. 以 softmax regression 为例来展示求导过程,softmax regression 可以看成一个不含隐含层的多分类神经网络,如 Fig. 1 所示. Fig. 1 Softmax Regression. softmax r…

Softmax Regression Chapter Basics generate random Tensors Three usual activation function in Neural Network Softmax funcion Softmax Regression Logistic Regression Softmax Regression Examples Basics generate random Tensors Three usual activation funct…

1.Logistic函数 在维基百科中,对logistic函数这样介绍道: A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: $$f(x)=\frac{L}{1+e^{-k(x-x0)}}$$ Logistic函数呈'S'型曲线,当x趋于-∞时函数趋于0,当x趋于+∞时函数趋于L. 2.Softmax函数 softmax函数定义如下: In mathem…

本文讨论的关键词:Logistic Regression(逻辑回归).Neural Networks(神经网络) 之前在学习LR和NN的时候,一直对它们独立学习思考,就简单当做是机器学习中的两个不同的models,从来没有放在一起观察过,最近通过阅读网络资料,才发现,原来LR和NN之间是有一定的联系的,了解它们之间的联系后,可以更好地理解 Logistic Regression(逻辑回归)和Neural Networks(神经网络) Logistic Regression:典型的二值分类器,用来…

多分类问题 在一个多分类问题中,因变量y有k个取值,即.例如在邮件分类问题中,我们要把邮件分为垃圾邮件.个人邮件.工作邮件3类,目标值y是一个有3个取值的离散值.这是一个多分类问题,二分类模型在这里不太适用. 多分类问题符合多项分布.有许多算法可用于解决多分类问题,像决策树.朴素贝叶斯等.这篇文章主要讲解多分类算法中的Softmax回归(Softmax Regression)  推导思路为:首先证明多项分布属于指数分布族,这样就可以使用广义线性模型来拟合这个多项分布,由广义线性模型推导出的目标函…

原文地址:https://segmentfault.com/a/1190000010039529?utm_source=tag-newest softmax函数将任意n维的实值向量转换为取值范围在(0,1)之间的n维实值向量,并且总和为1. 例如:向量softmax([1.0, 2.0, 3.0]) ------> [0.09003057, 0.24472847, 0.66524096] 性质: 因为softmax是单调递增函数,因此不改变原始数据的大小顺序. 将原始输入映射到(0,1)区间,并…

Hacker's guide to Neural Networks Hi there, I'm a CS PhD student at Stanford. I've worked on Deep Learning for a few years as part of my research and among several of my related pet projects is ConvNetJS - a Javascript library for training Neural Net…

When a golf player is first learning to play golf, they usually spend most of their time developing a basic swing. Only gradually do they develop other shots, learning to chip, draw and fade the ball, building on and modifying their basic swing. In a…

Hi there, I'm a CS PhD student at Stanford. I've worked on Deep Learning for a few years as part of my research and among several of my related pet projects is ConvNetJS - a Javascript library for training Neural Networks. Javascript allows one to ni…

一.Training of a Single-Layer Neural Network 1 Delta Rule Consider a single-layer neural network, as shown in Figure 2-11. In the figure, d i is the correct output of the output node i. Long story short, the delta rule adjusts the weight as the follow…

Linear Regression The Normal Equation Computational Complexity 线性回归模型与MSE. the normal equation: a closed-form solution to find the value of θ that minimize the cost function. generate some linear-looking data to test this equation. inv() to compute t…

Python Basics with numpy (optional)Welcome to your first (Optional) programming exercise of the deep learning specialization. In this assignment you will: - Learn how to use numpy. - Implement some basic core deep learning functions such as the softm…

Training (deep) Neural Networks Part: 1 Nowadays training deep learning models have become extremely easy with high-quality libraries such as Torch and Theano. These libraries are really helpful for rapidly prototyping deep learning models even witho…

sklearn实战-乳腺癌细胞数据挖掘(博客主亲自录制视频教程) https://study.163.com/course/introduction.htm?courseId=1005269003&utm_campaign=commission&utm_source=cp-400000000398149&utm_medium=share 参考资料 https://www.cnblogs.com/webRobot/p/9034079.html 逻辑回归重点: 1.sigmoid函数(…

CS231n的课后作业非常的好,这里记录一下自己对作业一些笔记. 一.第一个是KNN的代码,这里的trick是计算距离的三种方法,核心的话还是python和machine learning中非常实用的向量化操作,可以大大的提高计算速度. import numpy as np class KNearestNeighbor(object):#首先是定义一个处理KNN的类 """ a kNN classifier with L2 distance """…

import numpy as np from cs231n.classifiers.linear_svm import * from cs231n.classifiers.softmax import * class LinearClassifier(object): def __init__(self): self.W = None def train(self, X, y, learning_rate=1e-3, reg=1e-5, num_iters=100, batch_size=20…

Lecture note 5: word2vec + manage experiments Word2vec Most of you are probably already familiar with word embedding and understand the importance of a model like word2vec. For those who aren't, Stanford CS 224N's lecture on word vectors is a great r…

About this Course This course will teach you the "magic" of getting deep learning to work well. Rather than the deep learning process being a black box, you will understand what drives performance, and be able to more systematically get good res…

人类通过模仿自然界中的生物,已经发明了很多东西,比如飞机,就是模仿鸟翼,但最终,这些东西会和原来的东西有些许差异,artificial neural networks (ANNs)就是模仿动物大脑的神经网络. ANNs是Deep Learning的基本组成部分,它有很多用处: ANNs are at the very core of Deep Learning. They are versatile, powerful, and scala‐ ble, making them ideal to…

Welcome to your first assignment. This exercise gives you a brief introduction to Python. Even if you've used Python before, this will help familiarize you with functions we'll need. Instructions: You will be using Python 3. Avoid using for-loops and…