SVM and Kernels

Optimization Objective

Ps:
向量机（Vector Machine）：简称VM。向量算机的简称。

The Support Vector Machine (SVM) is yet another type of supervised machine learning algorithm. It is sometimes cleaner and more powerful.

Recall that in logistic regression, we use the following rules:

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Advice for Applying Machine Learning

Deciding What to Try Next

Errors in your predictions can be troubleshooted by:

• Getting more training examples
• Trying smaller sets of features
• Trying additional features
• Trying polynomial features
• Increasing or decreasing λ

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Neural Networks

Cost Function

Let’s first define a few variables that we will need to use:

• L = total number of layers in the network
• s_l = number of units (not counting bias unit) in layer l
• K = number of output units/classes

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Neural Networks

Model Representation I

Let’s examine how we will represent a hypothesis function using neural networks. At a very simple level, neurons are basically computational units that take inputs (dendrites) as electrical inputs (called “spikes”) that are channeled to outputs (axons). In our model, our dendrites are like the input features x₁…x_n and the output is the result of our hypothesis function. In this model our x₀ input node is sometimes called the “bias unit.” It is always equal to 1. In neural networks, we use the same logistic function as in classification, 1/(1+e^ΘTx),yet we sometimes call it a sigmoid (logistic) activation function. In this situation, our “theta” parameters are sometimes called “weights”.

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Classification

To attempt classification, one method is to use linear regression and map all predictions greater than 0.5 as a 1 and all less than 0.5 as a 0.

However, this method doesn’t work well because classification is not actually a linear function.
The classification problem is just like the regression problem, except that the values y we now want to predict take on only a small number of discrete values. For now, we will focus on the binary classification problem in which y can take on only two values, 0 and 1. (Most of what we say here will also generalize to the multiple-class case.) For instance, if we are trying to build a spam classifier for email, then x⁽ⁱ⁾ may be some features of a piece of email, and y may be 1 if it is a piece of spam mail, and 0 otherwise. Hence, y∈{0,1}. 0 is also called the negative class, and 1 the positive class, and they are sometimes also denoted by the symbols “-” and “+.” Given x⁽ⁱ⁾ , the corresponding y⁽ⁱ⁾ is also called the label for the training example.

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Multiple Features

Linear regression with multiple variables is also known as “multivariate linear regression”.

We now introduce notation for equations where we can have any number of input variables.

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这个系列是我跟着斯坦福的coursera中的机器学习做的笔记，本打算做个翻译来着，等翻译了一大半后发现有很多地方翻译的不是很能准确的表示含义，一怒之下就给删了...有些东西看英文原版反而更容易懂，不是吗？

What is Machine Learning?

Two definitions of Machine Learning are offered. Arthur Samuel described it as: “the field of study that gives computers the ability to learn without being explicitly programmed.” This is an older, informal definition.

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