Archive for the ‘Statistics’ Category
I found a good article discussing the difference between the Frequentist and Bayesian approach to Inference.
Predicting whether a loan will default or not is a tricky task. It may involve many variables, incomplete information and is a task that involves time as a component. Loans may also perform for a while before they default. Some loans may even be late, but recover back to the regular payment schedule. It’s an interesting application for statistics.
The LendingClub website, a service offering peer-to-peer lending, offers an interesting data set: historical data of loan performance as well as data for new loans. I’ve been playing around a bit with the data and built a model to predict whether a loan is a good investment. The LendingClub data is available for download. A data dictionary can be found on the website also.
First we need to define the outcome we want to predict. A loan can be in several states, some being “current”, others being “defaulted”, “late” or even on a “performing payment plan”. Conservatively, I defined all loans that were not “paid off” as bad. Loans that are “current” were excluded as they still can default in the future. Loans that are “late” are considered bad, because the borrower run into problems. The model I’m trying to built is basically for a conservative investor looking for loans that will simply be paid back without a hitch. With the usual statistical techniques a model can be built and the performance can be measured by 10-fold cross-validation or evaluating the model on a hold-out set. The real result of a prediction will of course only be available after about 3 years when a loan is fully paid off. As measure to optimize I chose the AUC metric. A 10-fold cross-validation estimates the performance of my model at 0.698 which is not too bad. The predictions implicitly make a few assumptions. The first one being that future performance of loans will be similar to historical performance of similar loans. I’m assuming a stationary distribution and the IID assumption – which is not completely true in reality, but hopefully close enough Also, inflation expectations were not taken into account, but I’m limiting my model to 36 month loans to make that more manageable.
I won’t go into the details of how I encoded the variables and what variables I’m using. I discovered that I can extract information out of the textual variables in the loans. The “Loan Description”, a free text field where potential borrowers can leave comments or answer questions, is quite predictive. The difficult part is using that information in practice. A loan is in “funding state” for two weeks were investors can ask questions and invest in the loan. Many loans get fully funded before the two week period is over, some without any question or comment on the loan. New information may become available in the Loan Description field that may change the classification. That means, however, that the prediction may change over time – positively or negatively – after an investment decision has been. Not ideal, but the variables are quite powerful so I’m still looking for a good solution.
I made the ratings for the LendingClub loans my program produces public. I will update them occasionally (i.e., whenever I feel like it). If you have some suggestions on how to use the textual variables, leave a comment.
Interesting blog post on Differential Privacy. I wasn’t aware of this specific privacy model.
A really interesting paper on A/B testing and experiments in online environments just got accepted to KDD 2012:
- Don’t make changes to your application if your average customers lifetime value will decline. Understand the change, consider alternative hypothesis, watch several metrics. Ensure that your findings align with the long term strategy so that long term growth is not sacrificed for short term financial gain. Example: one time Bing had a bug, which served poor search results, so distinct queries went up 10% and CTR on advertisements went up 30%.
- Ensure that your statistic results are trustworthy. Incorrect results may cause bad ideas to be deployed; good ideas may be ruled out by mistake.
- An upwards trend in a newly launched feature does not imply that users like the feature more. (delayed effect & primacy effect).
- Often running an experiment longer does not provide extra statistical power. Pick a duration and stick to it. Do not stop tests early (unless you use algorithms to tell you when you have statistical confidence enough to be able to stop your test)
- Re-run your experiment again if you get surprising results. Investigating the underlying reasons is often worth it.
- Watch for Carryover Effect… Run A/A experiments. If you use bucketing techniques to assign participants to experiments rerun the exerpiment with a larger test group and with local randomization.
The RAND corporation just published an interesting paper exploring the benefits of using risk prediction to reduce the screening required at airports. You might have noticed various attempts to establish some kind of fast-lane or trusted traveler program. Obvious this is a very sensitive topic and probably hard to get right. Screening certain groups of the population more than others (“profiling”) is generally frowned upon and also not a good idea in general (see “Strong profiling is not mathematically optimal for discovering rare malfeasors on rare event detection“), but what hasn’t been examined much is identifying people that can be considered more “safe” than others. The paper explores that idea and shows that even under the assumption that the bad guys will try and subvert this program that there can be benefits to implementing this solution. The paper is a bit sparse on mathematical details. Certainly an interesting idea, though.
I’m not sure what to think of it. For one, insurance is not about fairness; it’s about risk. An insurance company should be able to use whatever reliable information for determining the true risk to help price policies. From what I’ve read it seems that young men cost ~50% more to insure than young women. This might not be true on an individual level, but it is true across the entire pool people. On the other hand, if all reliable information could be used, then health insurance would naturally be more expensive for people with, e.g., known genetic disorders if it were purely about risk. That wouldn’t be fair either. Legislating what can and cannot be used in what circumstances will be a hard trade off. In the intermediate term this ruling will probably lead to models that are using all sorts of things to work around this ruling in order to get an adequate risk score.
I found an interesting article on how to communicate risks and probabilities to the public.
Kaggle has a new and interesting competition on building a chess rating algorithm that performs better than the official Elo rating system currently in use. Entrants build their own rating systems based on the results of more than 65,000 historical chess games and then test their algorithms by predicting the results on a holdout set of 7,800 games.
Looks like an interesting problem. The only other thing that comes to my mind literature-wise is that Microsoft built and published their TrueSkill(tm) Ranking System for the XBox in order to match players with similar skills in online games. In the original paper at NIPS, the authors had shown that TrueSkill outperformed Elo.