Category: Python

Tim Sweester and Aaron Bradley announce Diamond, a Python library which solves certain kinds of generalized linear models.  In a two-part series, they explain more.  Part 1 covers the mathematical principles behind it:

Many computational problems in data science and statistics can be cast as convex problems. There are many advantages to doing so:

• Convex problems have a unique global solution, i.e. there is one best answer
• There are well-known, efficient, and reliable algorithms for finding it

One ubiquitous example of a convex problem in data science is finding the coefficients of an L2L2-regularized logistic regression model using maximum likelihood. In this post, we’ll talk about some basic algorithms for convex optimization, and discuss our attempts to make them scale up to the size of our models. Unlike many applications, the “scale” challenge we faced was not the number of observations, but the number of features in our datasets. First, let’s review the model we want to fit.

Part 2 looks at one interesting use case:

In this example, GLMMs allow you to pool information across different brands, while still learning individual effects for each brand. It breaks the problem into sets of fixed and random effects. The fixed effects are similar to what you would find in a traditional logistic regression model, while the random effects allow the regression relationship to vary for each brand. One of the advantages of GLMMs is that they learn how different brands are from each other. Brands that are very similar to the overall average will have small random effect estimates. Because of the regularization of these models, brands with few observations will also have small random effect estimates, and be treated more like the overall average. In contrast, for brands that are very different from the average, with lots of data to support that, GLMMs will learn large random effect estimates.

Check it out.  Part 2 also contains a link to the GitHub repo if you want to try it on your own.

Mark Needham shows how easy it is to create a random forest model in Python using scikit-learn:

As I mentioned in a blog post a couple of weeks ago, I’ve been playing around with the Kaggle House Prices competition and the most recent thing I tried was training a random forest regressor.

Unfortunately, although it gave me better results locally it got a worse score on the unseen data, which I figured meant I’d overfitted the model.

I wasn’t really sure how to work out if that theory was true or not, but by chance, I was reading Chris Albon’s blog and found a post where he explains how to inspect the importance of every feature in a random forest. Just what I needed!

There’s a nagging voice in my head saying “Principal Component Analysis” as I read this post.

Kevin Jacobs has a walkthrough of how to use Pandas and scikit-learn to perform fraud detection against a sample set of credit card transactions:

Apparently, the data consists of 28 variables (V1, …, V28), an “Amount” field a “Class” field and the “Time” field. We do not know the exact meanings of the variables (due to privacy concerns). The Class field takes values 0 (when the transaction is not fraudulent) and value 1 (when a transaction is fraudulent). The data is unbalanced: the number of non-fraudulent transactions (where Class equals 0) is way more than the number of fraudulent transactions (where Class equals 1). Furthermore, there is a Time field. Further inspection shows that these are integers, starting from 0.

There is a small trick for getting more information than only the raw records. We can use the following code:

print(df.describe())

This code will give a statistically summary of all the columns. It shows for example that the Amount field ranges between 0.00 and 25691.16. Thus, there are no negative transactions in the data.

The Kaggle competition data set is available, so you can follow along.

Gopi Subramanian discusses one of my favorite regression concepts, heteroskedasticity:

With variance score of 0.43 linear regression did not do a good job overall. When the x values are close to 0, linear regression is giving a good estimate of y, but we near end of x values the predicted y is far way from the actual values and hence becomes completely meaningless.

Here is where Quantile Regression comes to rescue. I have used the python package statsmodels 0.8.0 for Quantile Regression.

Let us begin with finding the regression coefficients for the conditioned median, 0.5 quantile.

The article doesn’t render the code very well at all, but Gopi does have the example code on Github, so you can follow along that way.