机器学习中的牛顿法和拟牛顿法

在神经网络中, 处理学习进程的程序称为训练算法. 有许多这样的训练算法, 并有不同的特点和效用.

在训练神经网络中, 算法的目的就是求出极值点, 在此之中, 有5大算法.

1. 梯度下降法

梯度下降法式最简单的训练算法, 它需要计算出梯度向量, 根据梯度向量以及当前的点和学习率计算出当前步长, 以此来向极值点更近一步, 经过多次迭代, 最终到达极值点.

2. 牛顿法

神经网络中的正向传播与反向传播

1. 概述

我们知道, 一个简单的神经网络可以是这样的, 分为多个层, 输入层、隐藏层和输出层. 在层与层之间, 有权重 $w_{ij}^k$ , 表示第k层的第i个节点到下一层的第j个节点的权重. 再每一层, 都会有个激活函数, 用于归一化, 也可以说是计算该层节点的输出.

所谓正向传播, 就是依据这一过程由输入层一直延续到输出层.

基于方差的梯度下降算法

梯度下降算法是寻找函数极小值点的迭代优化算法. 必须基于当前点的梯度(或近似梯度)方向的反方向进行规定步长距离进行迭代搜索, 以达到接近极小值的算法. 假如按梯度相同方向迭代搜索, 就会接近极大值, 称为梯度上升法.

该简介译自: Gradient descent from wikipedia

PAT(A) 1135. Is It A Red-Black Tree (30)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1135

1135. Is It A Red-Black Tree (30)


There is a kind of balanced binary search tree named red-black tree

PAT(A) 1134. Vertex Cover (25)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1134

1134. Vertex Cover (25)


A vertex cover of a graph is a set of vertices such that each edge

PAT(A) 1133. Splitting A Linked List (25)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1133

1133. Splitting A Linked List (25)


Given a singly linked list, you are supposed to rearrange its elements

PAT(A) 1132. Cut Integer (20)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1132

1132. Cut Integer (20)


Cutting an integer means to cut a K digits long integer Z into two

PAT(A) 1127. ZigZagging on a Tree (30)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1127

1127. ZigZagging on a Tree (30)


Suppose that all the keys in a binary tree are distinct positive integers

PAT(A) 1126. Eulerian Path (25)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1126

1126. Eulerian Path (25)


In graph theory, an Eulerian path is a path in a graph which visits every edge

PAT(A) 1125. Chain the Ropes (25)

原题目:

原题链接:https://www.patest.cn/contests/pat-a-practise/1125

1125. Chain the Ropes (25)


Given some segments of rope, you are supposed to chain them into one rope.

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