I just began the new Coursera MOOC on probability , given by UPenn Dr. Santosh S. Venkatesh, and at the very first lecture, my interest was piqued by this intriguing idea, called the Chevalier de Méré's Paradox.. If I ask you which is more likely: Getting a "6" four times in four throws of a die Getting a "double 6" twenty-four times in twenty-four throws of a pair of dice You probably won't come…
There's something deeply fascinating in the fact that complexity can sometimes emerge from simple rules.. Here's a Langton's ant , which is always headed in one of four directions (up, down, left, right), which it changes before going a new step: By turning 90° right on a white pixel Or by turning 90° left on a black pixel This simple pattern leads to a surprinsingly chaotic behavior.. [Press the…
My previous machine learning posts: K-means vs Louvain Robustified Linear Regression Neural Network 101 Softmax Regression 101 Logistic Regression 101 Linear Regression 101 Suppose I give you this dataset of 2D points (with the added twist that the generating code has been obfuscated, to avoid making the answer too obvious), and ask you to group them into \(k\) meaningful clusters. Is there a way…
I'm currently reading Data Smart , a particularly good and entertaining book about machine learning and data science. The somewhat surprising twist in its approach is that it does almost entirely without code, and instead implements and illustrates everything in terms of spreadsheet operations. This has produced an interesting contradiction in me: the coding purist is somewhat put off by what he…
This post is part of a series, see also: Linear Regression 101 Logistic Regression 101 Softmax Regression 101 Neural Network 101 Let's revisit our toy linear regression problem , and in particular, look at what happens when the data contains a lot of outliers. In [1]: rcParams [ 'figure.figsize' ] = 12 , 8 domain = [ - 20 , 20 ] def dataset ( n , slope , intercept ): x = random . uniform ( domain…
As this seems to be becoming a series of related posts, see also: Linear Regression 101 Logistic Regression 101 Softmax Regression 101 Neural Network 101 A Cloud of Points As powerful as it is, a logistic regression model will only ever be able to solve linearly separable problems. No need to even try on problems like the one below (even though it's quite easy), because we saw that its \(\theta\)…
As this seems to be becoming a series of related posts, see also: Linear Regression 101 Logistic Regression 101 Softmax Regression 101 Neural Network 101 A Cloud of Points ¶ If logistic regression allows to solve binary classification problems, softmax regression, our third example of a generalized linear model, allows to solve multiclass ones. As before, we build an artificial dataset, this time…
As this seems to be becoming a series of related posts, see also: Linear Regression 101 Logistic Regression 101 Softmax Regression 101 Neural Network 101 A Cloud of Points ¶ We will next tackle the problem of binary supervised classification, using the logistic regression method. The artificial dataset we will use this time is built by sampling random 2D points in the plane, and assigning them a…
As it looks like I found myself a new job as a data scientist (freelancing time is over!), it's time to brush up on machine learning theory and practice. Let's start with the basics: linear regression. This seems to be becoming a series of related posts, see also: Linear Regression 101 Logistic Regression 101 Softmax Regression 101 Neural Network 101 A Cloud of Points ¶ Let's create an artificial…
A magic square of odd order can be efficiently constructed with a simple method brought from the travels of the French mathematician Simon de la Loubère to what was then Thailand (Siam), in the 17th century. I like to think of a time when you brought things like that from overseas trips, and not only a gazillion photos and some cheap souvenirs. The method is easier to undertand with a visual…