Saturday, September 7, 2013

To Bayes or not to Bayes

Why is this argument important? For a long time, the argument of the frequentist approach was that the the data generating mechanism had a distribution where the parameters that described the distribution were fixed. While this made sense initially (why would that parameter change in any case) and all you would do would be to estimate that parameter based on the data that you observe. However Bayesian inference came into the world much later and postulated (I am not sure who did it specifically) that I should be using any prior information that I have about the parameter estimate and not necessarily let it be driven purely by data.

While this in theory sounded quite radical initially, there have been significant contributions that have enabled this idea to be used successfully in very practical applications. Specifically, Bayesian regression is quite useful to build updating models by using continuous data collection mechanism as opposed to waiting till models deteriorate to the point of having to be rebuild. This can incorporate a good test and learn setup from a data input perspective. These models have very practical applications in credit scoring, churn analysis and customer acquisition.

The machine learning world took to Bayes theorem a lot more seriously than the statistical crowd. Algorithms which assumed prior knowledge and then were updated based on fresh data seemed to make a lot more sense. Spam filtering is one of the biggest application of this theorem. A general rule to define spam based on many emails can be a baseline, and the model can then be updated based on user characteristics and performance. This allows the spam filter to be very customized to the user.

Judea Pearl is one of the pioneers in looking at Bayesian Inference from a fresh new perspective. Graph theory has been in mathematics for quite a long time. However the usage of Bayesian theory enabled a fresh new perspective in this domain and Bayesian Networks is the result of this marriage. The network structure allows one to incorporate a lot more variables in the model and measure causal relationships which previously was only available in the time series domain (Will write on this later!).

The bottom line that I see is that the frequentist approach is outdated and we need to develop that perspective when looking at new models. This should be the way we think of incorporating models in the real world.

No comments:

Post a Comment