机器学习 – 基本概念

Machine Learning Honor Code

We strongly encourage students to form study groups, and discuss the lecture videos (including in-video questions). We also encourage you to get together with friends to watch the videos together as a group. However, the answers that you submit for the review questions should be your own work. For the programming exercises, you are welcome to discuss them with other students, discuss specific algorithms, properties of algorithms, etc.; we ask only that you not look at any source code written by a different student, nor show your solution code to other students.

Guidelines for Posting Code in Discussion Forums

Scenario 1: Code to delete

Learner Question/Comment: “Here is the code I have so far, but it fails the grader. Please help me fix it.”

Why Delete?: The reason is that if there is a simple fix provided by a student, a quick copy and paste with a small edit will provide credit without individual effort.

Learner Question: A student substitutes words for the math operators, but includes the variable names (or substitutes the equivalent greek letters (θ for ‘theta’, etc). This student also provides a sentence-by-sentence, line by line, description of exactly what their code implements. “The first line of my script has the equation “hypothesis equals theta times X”, but I get the following error message…”.

Why Delete?: This should be deleted. “Spelling out” the code in English is the same as using the regular code.

Scenario 2: Code not to delete

Learner Question: How do I subset a matrix to eliminate the intercept?

Mentor Response: This probably would be okay, especially if the person posting makes an effort to not use familiar variable names, or to use a context which has nothing to do with the contexts in the assignments.

It is clearly ok to show examples of Octave code to demonstrate a technique. Even if the technique itself is directly applicable to a programming problem at hand. As long as what is typed cannot be “cut and pasted” into the program at hand.

E.g. how do I set column 1 of a matrix to zero? Try this in your Octave work area:

>> A = magic(3)

>> A(:,1) = 0

The above is always acceptable (in my understanding). Demonstrating techniques and learning the language/syntax are important Forum activities.

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.

Tom Mitchell provides a more modern definition: “A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.”

Example: playing checkers.

E = the experience of playing many games of checkers

T = the task of playing checkers.

P = the probability that the program will win the next game.

In general, any machine learning problem can be assigned to one of two broad classifications:

Supervised learning and Unsupervised learning.

Supervised Learning

In supervised learning, we are given a data set and already know what our correct output should look like, having the idea that there is a relationship between the input and the output.

Supervised learning problems are categorized into “regression” and “classification” problems. In a regression problem, we are trying to predict results within a continuous output, meaning that we are trying to map input variables to some continuous function. In a classification problem, we are instead trying to predict results in a discrete output. In other words, we are trying to map input variables into discrete categories.

Example 1:

Given data about the size of houses on the real estate market, try to predict their price. Price as a function of size is a continuous output, so this is a regression problem.

We could turn this example into a classification problem by instead making our output about whether the house “sells for more or less than the asking price.” Here we are classifying the houses based on price into two discrete categories.

Example 2:

(a) Regression – Given a picture of a person, we have to predict their age on the basis of the given picture

(b) Classification – Given a patient with a tumor, we have to predict whether the tumor is malignant or benign.

Unsupervised Learning

Unsupervised learning allows us to approach problems with little or no idea what our results should look like. We can derive structure from data where we don’t necessarily know the effect of the variables.

We can derive this structure by clustering the data based on relationships among the variables in the data.

With unsupervised learning there is no feedback based on the prediction results.

Example:

Clustering: Take a collection of 1,000,000 different genes, and find a way to automatically group these genes into groups that are somehow similar or related by different variables, such as lifespan, location, roles, and so on.

Non-clustering: The “Cocktail Party Algorithm”, allows you to find structure in a chaotic environment. (i.e. identifying individual voices and music from a mesh of sounds at a cocktail party).

Model Representation

To establish notation for future use, we’ll use x(i) to denote the “input” variables (living area in this example), also called input features, and y(i) to denote the “output” or target variable that we are trying to predict (price). A pair (x(i),y(i)) is called a training example, and the dataset that we’ll be using to learn—a list of m training examples (x(i),y(i));i=1,...,m—is called a training set. Note that the superscript “(i)” in the notation is simply an index into the training set, and has nothing to do with exponentiation. We will also use X to denote the space of input values, and Y to denote the space of output values. In this example, X = Y = ℝ.

To describe the supervised learning problem slightly more formally, our goal is, given a training set, to learn a function h : X → Y so that h(x) is a “good” predictor for the corresponding value of y. For historical reasons, this function h is called a hypothesis. Seen pictorially, the process is therefore like this:

When the target variable that we’re trying to predict is continuous, such as in our housing example, we call the learning problem a regression problem. When y can take on only a small number of discrete values (such as if, given the living area, we wanted to predict if a dwelling is a house or an apartment, say), we call it a classification problem.

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