Removing Serial Correlation

Vincent Granville has an easy trick for removing serial correlation from a data set:

Here is a simple trick that can solve a lot of problems.

You can not trust a linear or logistic regression performed on data if the error term (residuals) are auto-correlated. There are different approaches to de-correlate the observations, but they usually involve introducing a new matrix to take care of the resulting bias. See for instance here.  

Click through for the alternative.

Cross-Validation in a Picture

Stephanie Glen shows us cross-validation in one picture:

Cross Validation explained in one simple picture. The method shown here is k-fold cross validation, where data is split into k folds (in this example, 5 folds). Blue balls represent training data; 1/k (i.e. 1/5) balls are held back for model testing.

Monte Carlo cross validation works the same way, except that the balls would be chosen with replacement. In other words, it would be possible for a ball to appear in more than one sample.

You’ll have to click through for the picture.

Linear Programming in Python

Francisco Alvarez shows us an example of linear programming in Python:

The first two constraints, x1 ≥ 0 and x2 ≥ 0 are called nonnegativity constraints. The other constraints are then called the main constraints. The function to be maximized (or minimized) is called the objective function. Here, the objective function is x1 + x2.

Two classes of problems, called here the standard maximum problem and the standard minimum problem, play a special role. In these problems, all variables are constrained to be nonnegative, and all main constraints are inequalities.

That post spurred me on to look up LINGO and see that it’s actually still around.

Exploratory Data Analysis with inspectdf

Laura Ellis continues a dive into Exploratory Data Analysis, this time using the inspectdf package:

I like this package because it’s got a lot of functionality and it’s incredibly straightforward to use. In short, it allows you to understand and visualize column types, sizes, values, value imbalance & distributions as well as correlations. Better yet, you can run each of these features for an individual data frame, or compare the differences between two data frames.

I liked the inspectdf package so much that in this blog, I’m going to extend my previous EDA tutorial with an overview of the package.

There are some interesting functions which make EDA easier, so check it out.

Non-Linear Classifiers with Support Vector Machines

Rahul Khanna continues a series on support vector machines:

In this blog post, we will look at a detailed explanation of how to use SVM for complex decision boundaries and build Non-Linear Classifiers using SVM. The primary method for doing this is by using Kernels.

In linear SVM we find margin maximizing hyperplane with features Xi’s . Similarly, in Logistic regression, we also try to find the hyperplane which minimizes logistic loss with features Xi’s. Most often when we use both these techniques the results are the same. But linear SVM or for the same reason a logistic regression would fail where there is a need to have complex or non-linear decision boundaries. These types of boundaries are then achieved by SVM using Kernels. So let us understand how SVM creates non-linear boundaries using Kernels

Read on to see how it works.

Vectors for Programmers

John Mount has a couple of videos available:

We have just released two new free video lectures on vectors from a programmer’s point of view. I am experimenting with what ideas do programmers find interesting about vectors, what concepts do they consider safe starting points, and how to condense and present the material.

Click through for the links, one with Python examples and the other with R examples.

Defining TF-IDF

Bruno Stecanella explains the concept behind TF-IDF:

TF-IDF was invented for document search and information retrieval. It works by increasing proportionally to the number of times a word appears in a document, but is offset by the number of documents that contain the word. So, words that are common in every document, such as this, what, and if, rank low even though they may appear many times, since they don’t mean much to that document in particular.

However, if the word Bug appears many times in a document, while not appearing many times in others, it probably means that it’s very relevant. For example, if what we’re doing is trying to find out which topics some NPS responses belong to, the word Bug would probably end up being tied to the topic Reliability, since most responses containing that word would be about that topic.

This makes the technique useful for natural language processing, especially in classification problems.

Sentiment Analysis with Python

Bruno Stecanella shows us how to use MonkeyLearn to perform sentiment analysis in Python:

Sentiment analysis is a set of Natural Language Processing (NLP) techniques that takes a text (in more academic circles, a document) written in natural language and extracts the opinions present in the text.

In a more practical sense, our objective here is to take a text and produce a label (or labels) that summarizes the sentiment of this text, e.g. positiveneutral, and negative.

For example, if we were dealing with hotel reviews, we would want the sentence ‘The staff were lovely‘ to be labeled as Positive, and the sentence ‘The shared bathroom was absolutely disgusting‘ labeled as Negative.

Click through for a demo.

Repeated Cross-Validation in R

Ludvig Olsen walks us through a couple of nice R packages:

The benefits of using groupdata2 to create the folds are 1) that it allows us to balance the ratios of our output classes (or simply a categorical column, if we are working with linear regression instead of classification), and 2) that it allows us to keep all observations with a specific ID (e.g. participant/user ID) in the same fold to avoid leakage between the folds.

The benefit of cvms is that it trains all the models and outputs a tibble (data frame) with results, predictions, model coefficients, and other sweet stuff, which is easy to add to a report or do further analyses on. It even allows us to cross-validate multiple model formulas at once to quickly compare them and select the best model.

Ludvig also gives us some examples of how both packages can help you out. H/T R-Bloggers

Exploratory Data Analysis on Categorical Variables

Giorgio Garziano continues digging into earthquake data:

To understand relationship or dependencies among categorical variables, we take advantage of various types of tables and graphical methods. Also stratifying variables can be encompassed in order to highlight if the relationship between two primary variables is the same or different for all levels of the stratifying variable under consideration.

The contingency table are said to be of one-way flavor when involving just one categorical variable. They are said two-way when involving two categorical variables, and so on (N-way).

Read on for various techniques for data analysis against categorical variables.

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