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Working with Sessionized Data 2: Variable Selection

In our previous post in this series, we introduced sessionization, or converting log data into a form that’s suitable for analysis. We looked at basic considerations, like dealing with time, choosing an appropriate dataset for training models, and choosing appropriate (and achievable) business goals. In that previous example, we sessionized the data by considering all possible aggregations (window widths) of the data as features. Such naive sessionization can quickly lead to very wide data sets, with potentially more features than you have datums (and collinear features, as well). In this post, we will use the same example, but try to select our features more intelligently.

4203801748 f760c22c47 zIllustration: Boris Artzybasheff
photo: James Vaughan, some rights reserved

The Example Problem

Recall that you have a mobile app with both free (A) and paid (B) actions; if a customer’s tasks involve too many paid actions, they will abandon the app. Your goal is to detect when a customer is in a state when they are likely to abandon, and offer them (perhaps through an in-app ad) a more economical alternative, for example a “Pro User” subscription that allows them to do what they are currently doing at a lower rate. You don’t want to be too aggressive about showing customers this ad, because showing it to someone who doesn’t need the subscription service is likely to antagonize them (and convince them to stop using your app).

You want to build a model that predicts whether a customer will abandon the app (“exit”) within seven days. Your training set is a set of 648 customers who were present on a specific reference day (“day 0”); their activity on day 0 and the ten days previous to that (days 1 through 10), and how many days until each customer exited (Inf for customers who never exit), counting from day 0. For each day, you constructed all possible windows within those ten days, and counted the relative rates of A events and B events in each window. This gives you 132 features per row. You also have a hold-out set of 660 customers, with the same structure. You can download the wide data set used for these examples as an .rData file here. The explanation of the variable names is in the previous post in this series.

In the previous installment, we built a regularized (ridge) logistic regression model over all 132 features. This model didn’t perform too badly, but in general there is more danger of overfitting when working with very wide data sets; in addition, it is quite expensive to analyze a large number of variables with standard implementations of logistic regression. In this installment, we will look for potentially more robust and less expensive ways of analyzing this data.

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