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Category: Data Science

Imbalanced Data In R

Published 2017-10-09 by Kevin Feasel

Rathnadevi Manivannan explains how to deal with imbalanced data using R:

Imbalanced data refers to classification problems where one class outnumbers other class by a substantial proportion. Imbalanced classification occurs more frequently in binary classification than in multi-level classification. For example, extreme imbalanced data can be seen in banking or financial data where majority credit card uses are acceptable and very few credit card uses are fraudulent.

With an imbalanced dataset, the information required to make an accurate prediction about the minority class cannot be obtained using an algorithm. So, it is recommended to use balanced classification dataset.

Rathnadevi uses fraudulent transactions for his sample, but medical diagnoses is also a good example:  suppose 1 person in 10,000 has a particular disease.  You’re 99.99% right if you just say nobody has the disease, but that’s a rather unhelpful model.

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Sentiment Analysis In R

Published 2017-10-06 by Kevin Feasel

Rachel Tatman has a great tutorial introducing sentiment analysis in R:

By the end of this tutorial you will:

  • Understand what sentiment analysis is and how it works
  • Read text from a dataset & tokenize it
  • Use a sentiment lexicon to analyze the sentiment of texts
  • Visualize the sentiment of text

If you’re the hands-on type, you might want to head directly to the notebook for this tutorial. You can fork it and have your very own version of the code to run, modify and experiment with as we go along.

Check it out.  There’s a lot more to sentiment analysis—cleaning and tokenizing words, getting context right, etc.—but this is a very nice introduction.

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Fun With The Beta Distribution

Published 2017-09-27 by Kevin Feasel

John D. Cook shows how one chatoic equation just happens to follow a beta distribution:

Indeed the points do bounce all over the unit interval, though they more often bounce near one of the ends.

Does that distribution look familiar? You might recognize it from Bayesian statistics. It’s a beta distribution. It’s symmetric, so the two beta distribution parameters are equal. There’s a vertical asymptote on each end, so the parameters are less than 1. In fact, it’s a beta(1/2, 1/2) distribution. It comes up, for example, as the Jeffreys prior for Bernoulli trials.

The graph below adds the beta(1/2, 1/2) density to the histogram to show how well it fits.

It’s an interesting bit of math and statistics, and John provides some Python demo code at the end.

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Explaining Confidence Intervals

Published 2017-09-20 by Kevin Feasel

Mala Mahadevan explains what confidence intervals are:

Suppose I look at a sampling of 100 americans who are asked if they approve of the job the supreme court is doing. Let us say for simplicity’s sake that the only two answers possible are yes or no. Out of 100, say 40% say yes. As an ordinary person, you would think 40% of people just approve. But a deeper answer would be – the true proportion of americans who approve of the job the supreme court is doing is between x% and y%.

How confident I am that it is?  About z%. (the common math used is 95%).  That is an answer that is more reflective of the uncertainty related to questioning people and taking the answers to be what is truly reflective of an opinion. The x and y values make up what is called a ‘confidence interval’.

Read the whole thing.

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Introduction To Bayesian Statistics

Published 2017-09-15 by Kevin Feasel

Kennie Nybo Pontoppidan has just completed a course on Bayesian statistics:

Last month I finished a four-week course on Bayesian statistics. I have always wondered why people deemed it hard, and why I heard that the computations quickly became complicated. The course wasn’t that hard, and it gave a nice introduction to prior/posterior distributions and I many cases also how to interpret the parameters in the prior distribution as extra data points.

An interesting aspect of Bayesian statistics is that it is a mathematically rigorous model, with no magic numbers such as the 5% threshold for p-values. And I like the way it naturally caters sequential hypothesis testing with where the sample size of each iteration is not fixed in advance. Instead data are evaluated and used to update the model as they are collected.

Check out Kennie’s explanation as well as the course.  I also went through Bayes’ Theorem not too long ago, which is a good introduction to the topic if you’re unfamiliar with Bayes’s Law.

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Time-Varying Models

Published 2017-09-15 by Kevin Feasel

Lingrui Gan explains how to model for parameters whose effects change over time:

We can frame conversion prediction as a binary classification problem, with outcome “1” when the visitor converts, and outcome “0” when they do not. Suppose we build a model to predict conversion using site visitor features. Some examples of relevant features are: time of day, geographical features based on a visitor’s IP address, their device type, such as “iPhone”, and features extracted from paid ads the visitor interacted with online.

A static classification model, such as logistic regression, assumes the influence of all features is stable over time, in other words, the coefficients in the model are constants. For many applications, this assumption is reasonable—we wouldn’t expect huge variations in the effect of a visitor’s device type. In other situations, we may want to allow for coefficients that change over time—as we better optimize our paid ad channel, we expect features extracted from ad interactions to be more influential in our prediction model.

Read on for more.

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Analyzing Clickstream Data With Markov Chains

Published 2017-09-14 by Kevin Feasel

Eleni Markou shows one method of analyzing clickstream data:

We chose to use the third-order Markov Chain on the above-produced data, as:

  • The number of parameters needed for the chain’s representation remains manageable. As the order increases, the parameters necessary for the representation increase exponentially and thus managing them requires significant computational power.
  • As a rule of thumb, we would like at least half of the clickstreams to consist of as many clicks as the order of the Markov Chain that should be fitted. There is no point in selecting a third-order chain if the majority of the clickstream consists of two states and so there is no state three steps behind to take into consideration.

Fitting the Markov Chain model gives us transition probabilities matrices and the lambda parameters of the chain for each one of the three lags, along with the start and end probabilities.

This particular analysis is trying to understand which page (if any) a user will go to next when on a particular page.  Eleni uses additional techniques like k-means clustering to segment out particular groups of users.  Very interesting analysis.

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Basics Of Survival Analysis

Published 2017-09-14 by Kevin Feasel

Subhasree Chatterjee explains the basics of survival analysis:

Survival analysis is a set of methods to analyze the ‘time to occurrence’ of an event. The response is often referred to as a failure time, survival time, or event time. These methods are widely used in clinical experiments to analyze the ‘time to death’, but nowadays these methods are being used to predict the ‘when’ and ‘why’ of customer churn or employee turnover as well.

The dependent variables for the analysis are generally two functions:

Read the whole thing.  H/T R-Bloggers

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Understanding Neural Networks: Perceptrons

Published 2017-09-13 by Kevin Feasel

Akash Sethi explains what a perceptron is:

In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector.
Linear classifier defined that the training data should be classified into corresponding categories i.e. if we are applying classification for the 2 categories then all the training data must be lie in these two categories.
Binary classifier defines that there should be only 2 categories for classification.
Hence, The basic Perceptron algorithm is used for binary classification and all the training example should lie in these categories. The basic unit in the Neuron is called the Perceptron.

Click through to learn more about perceptrons.

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Uses Of kd-trees

Published 2017-09-13 by Kevin Feasel

Sandipan Dey explains what a kd-tree is and how it works:

The prime advantage of a 2d-tree over a BST is that it supports efficient implementation of range search and nearest-neighbor search. Each node corresponds to an axis-aligned rectangle, which encloses all of the points in its subtree. The root corresponds to the entire plane [(−∞, −∞), (+∞, +∞ )]; the left and right children of the root correspond to the two rectangles split by the x-coordinate of the point at the root; and so forth.

  • Range search: To find all points contained in a given query rectangle, start at the root and recursively search for points in both subtrees using the following pruning rule: if the query rectangle does not intersect the rectangle corresponding to a node, there is no need to explore that node (or its subtrees). That is, search a subtree only if it might contain a point contained in the query rectangle.

  • Nearest-neighbor search: To find a closest point to a given query point, start at the root and recursively search in both subtrees using the following pruning rule: if the closest point discovered so far is closer than the distance between the query point and the rectangle corresponding to a node, there is no need to explore that node (or its subtrees). That is, search a node only if it might contain a point that is closer than the best one found so far. The effectiveness of the pruning rule depends on quickly finding a nearby point. To do this, organize the recursive method so that when there are two possible subtrees to go down, you choose first the subtree that is on the same side of the splitting line as the query point; the closest point found while exploring the first subtree may enable pruning of the second subtree.

  • k-nearest neighbors search: This method returns the k points that are closest to the query point (in any order); return all n points in the data structure if n ≤ k. It must do this in an efficient manner, i.e. using the technique from kd-tree nearest neighbor search, not from brute force.

Sandipan implements a fairly classic problem in this space:  the behavior of a group of flocking birds.

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