Tuesday, August 06, 2013

Reverse Deduction ... It is Elementary My Dear Readers

I have started re-reading classics over the past six months. The last time I read books such as David Copperfield and Jekyll & Hyde, was during my school days. During that time these represented more of a fantasy or science fiction. Today, after almost 3 decades of living, these same books now take a more philosophical tint. I have recently finished reading the complete works related to Sherlock Holmes. So expect a few articles influenced by Sherlock Holmes and Sir Doyle.

As an analytical person, the first curiosity was on how Holmes can solve the seemingly complex crimes. I managed to string together the theory based on the hints thrown by Holmes during his discussions with Watson. To the statistician in me, this theory connected very well. Today's post is on how Holmes solves his crimes and its relevance to modern day business.

A typical approach to analytics is to identify a particular event ... say customer attrition. The analytics consultant will go about collecting data elements that he believes may be influencing customer attrition. Then he starts building the predictive model to identify the data elements that are more significant to customer attrition. Once identified, the next step is to contextualize the significance of the data element. Refer to my post on micro modelling <<click here to read>>. Often, the analyst will find clusters of customers behaving differently. Hence, he starts segmenting and building different models for each segments. Eventually, there may be many segments and each segment will have different data elements defining the influence of customer attrition within the segment. Thus, though the end state is customer attrition, there are different sets of data elements or paths to the end state.

Sherlock Holmes' art lies in starting from the end state and knowing all possible paths to that state. For example, examining the state of the corpse, he would deduce the possible sequence of events that could lead to that state. Its like knowing all possible behaviour, across customer segments, that would lead to the attrition within the segment. The next step is to go back on the path and arrive at the source. That is arrive at the segment the customer belongs to. Apparently, in the earlier life of Holmes, which is not covered in the book, Holmes is supposed to have conducted a number of experiments to deduce various paths to the states of interest, whether this was the state of corpse, the footsteps on the ground, hand writing analysis, etc.

Once Holmes could deduce the various paths, he goes about the case of elimination to arrive at the surviving path. This logic is not hard to understand. We are exposed to it very regularly whenever we visit the doctor. The medical practice uses this logic of elimination. The doctor observes the symptoms and then asks some questions such as "did you have fever", "do you feel nausea", "hows your stool". Basis the answers, he starts eliminating illness till he has narrowed down to a few. Then he may prescribe some generic drugs to address them. If the illness does not respond, then he recommends detailed observation (read tests) to further target specific illness (such as malaria). Eventually, there is only one path left, and Holmes has the sequence of events leading to the crime. This is the same algorithm that has been adopted for Text Mining and Document Tagging. The author, Doyle, was a doctor by profession. He applied the medical approach to crime fighting. It sounds so obvious after a century.

If one is analysing customer attrition and assuming we are in the know of all behaviours that lead to attrition for each segment, we can analyse each customer and narrow down the customer to a specific segment and path to customer attrition. Once this is done, we can then plan our interventions in the customer life to prevent the end state.. ie customer attrition.

But, alas, we may seldom know every path to attrition and hence will keep building predictive models and testing them. Till then, we will always be impressed by Mr. Sherlock Holmes.
 
 
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