Supervise Learning Flashcards
What is the Hypothesis equation?
What are Supervised Learning problems?
“Regression” and “Classification” problems.
What is Supervised Learning?
Given a data set know what our correct output should look like, having the idea that there is a relationship between the input and the output.
What is Machine Learning?
Arthur Samuel described it as: “the field of study that gives computers the ability to learn without being explicitly programmed.”
What is Machine Learning?
Tom Mitchell: “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.
What we are trying to predict in a regression problem?
Results within a continuous output, meaning that we are trying to map input variables to some continuous function.
What we’re trying to predict in a classification problem?
Results in a discrete output, trying to map input variables into discrete categories.
What is 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, i.e., there is no teacher to correct you. It’s not just about clustering. For example, associative memory is unsupervised learning.
What is Cost Function?
A way to measure the accuracy of our hypothesis function. This takes an average (actually a fancier version of an average) of all the results of the hypothesis with inputs from x’s compared to the actual output y’s.
What is Gradient Descent?
It’s a way to automatically improve our hypothesis function. We put θ0 on the x axis and θ1 on the z axis, with the cost function on the vertical y axis. The points on our graph will be the result of the cost function using our hypothesis with those specific theta parameters. We will know that we have succeeded when our cost function is at the very bottom of the pits in our graph, i.e. when its value is the minimum. The way we do this is by taking the derivative (the line tangent to a function) of our cost function. The slope of the tangent is the derivative at that point and it will give us a direction to move towards. We make steps down that derivative by the parameter α, called the learning rate.
What is the Gradient Descent equation?
What is Gradient Descent for Linear Regression?
We can substitute our actual cost function and our actual hypothesis function and modify the equation to: (see the graph). Where m is the size of the training set, θ0 a constant that will be changing simultaneously with θ1 and x(i),y(i) are values of the given training set (data). Note that we have separated out the two cases for θj and that for θ1 we are multiplying x(i) at the end due to the derivative. The point of all this is that if we start with a guess for our hypothesis and then repeatedly
apply these gradient descent equations, our hypothesis will become more and more accurate.
What are Matrices?
Matrices are 2-dimensional arrays. In the graph, matrix has four rows and three columns, so it is a 4 x 3 matrix.
What are Vectors?
A vector is a matrix with one column and many rows:
What are Matrix Notations and Terms?
* Aij refers to the element in the ith row and jth column of matrix A.
* A vector with ‘n’ rows is referred to as an ‘n’-dimensional vector
* Vi refers to the element in the ith row of the vector.
* In general, all our vectors and matrices will be 1-indexed.
* Matrices are usually denoted by uppercase names while vectors are lowercase.
* “Scalar” means that an object is a single value, not a vector or matrix.
* ℝ refers to the set of scalar real numbers
* ℝ refers to the set of n-dimensional vectors of real numbers
How to Add and Subtract Matrices?
To add or subtract two matrices, their dimensions must be the same.
How to do Scalar Multiplication?
In scalar multiplication, we simply multiply every element by the scalar value:
How to do Matrix-Vector Multiplication?
We map the column of the vector onto each row of the matrix, multiplying each element and summing the result (see graph). The result is a vector. The vector must be the second term of the multiplication. The number of rows of the vector must equal the number of columns of the matrix. An n x m matrix multiplied by an m x 1 vector results in an n x 1 vector.
How to do Matrix-Matrix Multiplication?
We multiply two matrices by breaking it into several vector multiplications and concatenating the result (see graph). An m x n matrix multiplied by an n x o matrix results in an m x o matrix. In the above example, a 3 x 2 matrix times a 2 x 2 matrix resulted in a 3 x 2 matrix. To multiply two matrices, the number of columns of the first matrix must equal the number of rows of the second matrix.
What is Transposition of a Matrix?
The transposition of a matrix is like rotating the matrix once clockwise and then reversing it:
