The business problem is to put a lifeguard station on a beach to save some lives (i.e., find the best location for the lifeguard station). This is not really a predictive modeling problem. But that’s the hammer our data scientists have and they have access to fancy libraries. There is also some historical data: swimmers rescued and drowned at other beaches. It all checks out. Resistance to 𝘱𝘪𝘱 𝘪𝘯𝘴𝘵𝘢𝘭𝘭 𝘱𝘳𝘰𝘱𝘩𝘦𝘵 is futile.
Transforming the problem into an objective function could have signaled that this is an optimization problem (a prescriptive modeling problem), but that step was skipped. In the picture shown, we may need a solution:
– minimizes distance => 𝗦𝗼𝗹𝘃𝗲𝗱 𝘂𝘀𝗶𝗻𝗴 𝗽𝗶𝗽 𝗶𝗻𝘀𝘁𝗮𝗹𝗹 𝗳𝗮𝗻𝗰𝘆_𝗹𝗶𝗯𝗿𝗮𝗿𝘆
while also…
– minimizing time => 𝗧𝗵𝗲 𝗱𝗼𝗺𝗮𝗶𝗻 𝗲𝘅𝗽𝗲𝗿𝘁 𝗲𝗻𝘁𝗲𝗿𝘀 𝘁𝗵𝗲 𝗿𝗼𝗼𝗺
– minimizing swimming => 𝗧𝗵𝗲 𝗹𝗮𝗯𝗼𝗿 𝘂𝗻𝗶𝗼𝗻 𝗶𝗻𝘁𝗲𝗿𝘃𝗲𝗻𝗲𝘀
– minimizing time to ice cream => 𝗧𝗵𝗲 𝗲𝘅𝗲𝗰𝘂𝘁𝗶𝘃𝗲 𝗹𝗲𝗮𝗱𝗲𝗿𝘀𝗵𝗶𝗽 𝘀𝘁𝗲𝗽𝘀 𝗶𝗻
– [not shown] minimizing walking on sand => 𝗧𝗵𝗲 𝗗𝗲𝗽𝗮𝗿𝘁𝗺𝗲𝗻𝘁 𝗼𝗳 𝗟𝗮𝗯𝗼𝗿 𝗿𝗲𝗾𝘂𝗶𝗿𝗲𝗺𝗲𝗻𝘁
and hopefully not…
– maximizing time => 𝗔 𝗷𝘂𝗻𝗶𝗼𝗿 𝗱𝗮𝘁𝗮 𝘀𝗰𝗶𝗲𝗻𝘁𝗶𝘀𝘁 𝘀𝗼𝗹𝘃𝗲𝘀 𝘁𝗵𝗲 𝗽𝗿𝗼𝗯𝗹𝗲𝗺
So, the ideal solution requires more thinking about the problem. For example, maximizing the number of lives saved may actually require constraints on how to minimize time so that lifeguards don’t risk their lives during the rescue.
The law of the instrument works a little too well in predictive modeling (and more generally in machine learning). Objective functions are often lost in translation when they should be an explicit step in the modeling process. Best practice tends to favor performance metrics, even though achieving the highest performance on the wrong function is clearly useless (and sometimes detrimental).
More focus on objective functions and less obsession with “better performance” may be what we need. This would underline the importance of problem formulation and domain knowledge, and undermine the 𝘱𝘪𝘱 𝘪𝘯𝘴𝘵𝘢𝘭𝘭 𝘱𝘳𝘰𝘱𝘩𝘦𝘵 solution.
A combination of Warren Powell‘s writing and the accompanying xkcd comic inspired this post (courtesy of xkcd.com).