机器学习中的牛顿法和拟牛顿法

1. 训练神经网络的5大算法

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.

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神经网络中的正向传播与反向传播

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.

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基于方差的梯度下降算法

梯度下降算法简介

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.

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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 in the data structure. It has the following 5 properties:

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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 of the graph is incident to at least one vertex of the set. Now given a

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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 so that all the negative values appear before all of the non-negatives, and all the values in [0, K]

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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 integers of (K/2) digits long integers A and B. For example, after cutting Z = 167334,

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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. A unique binary tree can be determined by a given pair of postorder and inorder traversal sequences.

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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 exactly once. Similarly, an Eulerian circuit is an Eulerian path which starts and ends on the same vertex.

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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. Each time you may only fold two segments into loops and chain them into one

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