Machine Learning Posted Lectures as of Sep 28W11

Do you want a preview of what you'll learn when you take Stanford's FREE Machine Learning Class? Here are the posted lectures as of Sep 28, Wednesday, 2011. The class officially starts on Oct 10M11 but they have decided to have a few lectures posted in advance.

Machine Learning Preview:

I. INTRODUCTION

• Welcome
• What is Machine Learning?
• Supervised Learning
• Unsupervised Learning

II. LINEAR REGRESSION WITH ONE VARIABLE

• Model Representation
• Cost Function
• Cost Function - Intuition I
• Cost Function - Intuition II
• Gradient Descent
• Gradient Descent Intuition
• Gradient Descent For Linear Regression
• What's Next

III. LINEAR ALGEBRA REVIEW (OPTIONAL)

• Matrices and Vectors
• Addition and Scalar Multiplication
• Matrix Vector Multiplication
• Matrix Matrix Multiplication
• Matrix Multiplication Properties
• Inverse and Transpose

Intro to Databases Posted Lectures as of Sep 28W11

Do you want a preview of what you'll learn when you take Stanford's FREE Introduction to Databases class? Here are the posted lectures as of Sep 28, Wednesday, 2011. The class officially starts on Oct 10M11 but they have decided to have a few lectures and assignments posted in advanced.

Database Class Preview:

INTRODUCTION

• Introduction to the course (14 min)

RELATIONAL DATABASES

• The relational model (9 min)
• Querying relational databases (6 min)

XML DATA

• Well-formed XML (13 min)
• DTDs, IDs & IDREFs (18 min)
• XML Schema (13 min)

RELATIONAL ALGEBRA
Prerequisite: Relational Databases

• Select, project, join (18 min)
• Set operators, renaming, notation (20 min)

SQL
Prerequisite: Relational Databases; Recommended: Relational Algebra

• Introduction to SQL (5 min)
• Basic SELECT statement (10 min)
• Table variables and set operators (11 min)
• Subqueries in WHERE clause (20 min)
• Subqueries in FROM and SELECT (8 min)
• Aggregation (25 min)
• NULL values (6 min)
• Data modification statements (15 min)

FREE Machine Learning Class by Stanford now up! Enroll before start on Oct 10!

The Machine Learning class offered FREE by Stanford University is now OPEN. The class officially starts on October 10 but some video lectures and assignments are up. Enroll now before the class officially starts!

Enroll now at:

http://www.ml-class.org/

FREE "Intro to DataBases" class by Stanford now running! Enroll before Official start Oct 10

The Introduction to Databases class offered FREE by Stanford University is now OPEN. The class officially starts on October 10 but some video lectures and assignments are up. Enroll now before the class officially starts!

Enroll now at:

http://www.db-class.org/

Intuition for the Dot Product and the Cross Product

Often, we know how to solve things by formulas and we accept whatever was given to us. One thing we are forgetting is that these formulas actually mean something. The video below is a great example how to break in to learners that mathematical abstractions are more than just patterns..

Dot product intution:

One of the main point is how the dot product measures how much two vectors go in the same direction. Sal  did just dot.



 

Cross product intuition

The second topic of this video is how the cross product measures how much two vectors are perpendicular to each other. He also explained how the length of the cross product equals the area of the parallelogram the two vectors create.



One thing Sal could have added to this video is why we get negative values. Well, he might have had left that undiscussed for the viewer to think about.



Full video:

Cross and Dot Product intution

Easier Subtraction: Do all your borrowings first!

Are you having difficulties performing subtraction? Maybe you're just having trouble with the constant switching between borrowing and actually subtracting as thought traditionally in school. Why have they never taught us to do all the borrowing first so that all the actual subtraction is done in one fell swoop? In this video at KhanAcademy.org, Sal teaches a different approach and much more intuitive method to subtraction.


Full video:

Subtraction: Do all your borrowings first!

Lattice Multiplication: Easier multiplication fr: KhanAcademy.org

Lattice multiplication is a very neat way of multiplying non-single digit quantities. It eliminates the need of switching to and from multiplication and addition. In Lattice multiplication, all multiplication is done before the addition is done. The process is fairly simple:

1. Create a matrix with the number of columns equal to the number of digits of the first number and the number of rows equal to the number of digits of the second number. In the example above, there first and second number both have 2 digits, hence the 2 x 2 matrix.

2. Draw a diagonal in each cell starting from the upper right corner down to the lower left corner.

3. Each row correspond to a digit of the second number and Each column correspond to a digit of the first number. To get the value of each cell, simply multiply the corresponding column value times the column value then the first digit of the product is put on the upper left triangle while the second digit of the product is put on the lower right triangle. We are ensured that there are only 2 digits for any product since the only possible value for each column and each row only ranges from 0 to 9. This means that the maximum result of any product is 9 times 9 or 89. In cases that the product of the cell is only one digit, the product is put on the lower right triangle and zero is put on the upper left triangle. For example, Column 1, row 1 correspond to the digits 2 times 4 and the product is 8. 8 is put on the lower right triangle and zero is put on the upper right triangle.

4. The addition is done. Each diagonal represent a digit in the result. the lower right diagonal is the ones place, the diagonal just above the lower right corner represents the tens place, the diagonal just below the upper left corner represents the hundreds place, and the upper left corner represents the thousands place. To get the result, add the digits in the diagonal and carry over the first digit of the product to the next diagonal.
In the example, there is only one element in the diagonal so we know that the value in the ones place is 6. The digits in the tens diagonal are 8, 5, and 6 which have a sum of 19 that makes the value of the tens place as 9 and 1 is carried over to the hundreds diagonal. The hundreds diagonal have the digits 2, 8, 1, and the carried over 1 from the tens place resulting a sum of 12, this makes the value of hundreds to be 2 and 1 is carried over to the thousands place. The thousands place only have 0 and 1 carried over from the hundreds place which makes the value of the thousands place to be 1. This makes the product of 27 and 48 to be 1296.


Full video:
Lattice Multiplication at KhanAcademy.org

An explanation of why it works:
Why Lattice multiplication works

AI Class Pre Requisites Videos up!

AI Class has posted the recommended prerequisites videos from KhanAcademy that will help you polish up your math needed for the AI Class. Go check it out in the Other Resources link after you log-in on the my profile page. At the time of this posting, these are the topics posted:

Probability Prerequisites

Basic Probability
Probability (Part 6) [Conditional Probability]
Probability (Part 7) [Bayes' Rule]
Probability (Part 8) [More Bayes' Rule]
Introduction to Random Variables
Probability Density Functions
Expected Value: E(X)

Linear Algebra Prerequisites

Introduction to Matrices
Matrix Multiplication (Part 1)
Matrix Multiplication (Part 2)
Inverse Matrix (Part 1)
Inverting Matrices (Part 2)
Inverting Matrices (Part 3)
Matrices to Solve a System of Equations
Singular Matrices
Introduction to Vectors
Vector Dot Product and Vector Length
Defining the Angle Between Vectors
Cross Product Introduction
Matrix Vector Products
Linear Transformations as Matrix Vector Products
Linear Transformation Examples: Scaling and Reflections
Linear Transformation Examples: Rotations in R2
Introduction to Projections
Exploring the Solution Set of Ax = b
Transpose of a Matrix
3x3 Determinant
Introduction to Eigenvalues and Eigenvectors

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