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## Prescriptive vs Predictive Analytics ExplainedImagine for one second that you are Loïc Peyron, the recent winner of the transatlantic yatch race La Route Du Rhum. What would you use to reach your destination as fast as possible? Of course, you would work on getting the fastest possible yacht. You would also train to maneuver your ship the best possible way. But once the race is on and you're on the sea, what tools would you use to decide in which direction you should steer the ship?
Credit: Wikipedia For several thousand years, skippers have always relies on the most advanced available hep they could get to route their ships to the right destination. I won't recap here the long string of very ingenious techniques developed over centuries, and will focus instead on today's technologies. Let us make a simple observation to start with. The maximal speed at which a sailboat can move depends primarily on the direction for the wind and its strength. There are other factors that influence the speed such as currents, and waves. We will ignore these for the sake of clarity here. Of course, the actual speed at which the ship moves depends also on how well it is maneuvered by the skipper and his team. Given you are Loïc Peyron we can assume that this is done perfectly. Given that, for the sake of this article, the speed of you boat depends on the wind strength and direction, the most natural thing to use is weather reports. Looking at the current wind direction one can adjust the direction of the boat to move as fast as possible towards the goal. I won't give a sailing course here, but this is a well known technique that you learn as soon as you start sailing. Let me simply describe two extreme cases. If the wind blows in the direction you want to go, then you should just go in that direction. The wind comes from the back of the boat, and you go straight ahead. Assume now that the wind comes precisely from where you want to go. You cannot move directly to the destination as it would mean moving in the exact opposite direction of the wind. In such case you move with an angle of about 45° to the wind, and make turns as you go, as depicted in the figure below. Credit: Wikipedia
If you wish to know more about how to get the fastest way to a given point as a function of the wind direction, then you can start with the wiki Is it really? For long distance race, like transatlantic races, the destination is several days, if not weeks, away. Wind speed and direction is not constant over the Atlantic Ocean . Moreover, wind can evolve on a period of several days. Therefore, optimizing locally your route based on the wind direction today, at the point you are, may not always be the best option. What if doing so moves you to a region where there is no wind forecast tomorrow? You would be stuck. It may be better to move around the no wind forecast region. This is why the next tool skipper use is weather forecast. Is that all? Not really, as you, the skipper, must actually decide where to move next. Experienced skippers may make the right decision looking at weather forecast, but nowadays they use algorithms that compute the best route. One such algorithm computes an isochrone map. An isochrone is a line that shows points at equal time distance to destination. See this ORMS Today paper to know more about isochrone and their first use by Francis Galton in 1873. Computing isochrone when using a transportation network such as roads, or rail tracks is quite easy. One needs to use a shortest path algorithm like Dijkstra algorithm . However, the problem is made more complex because boats can move arbitrarily on the sea. One needs to use dynamic programming using an adhoc discretization of possible routes when computing isochrone.
When preparing this blog entry I found an interesting paper by Andy Philpott and Geoff Leyland, Credit [1]
Let us now look at the big picture for a moment. We have been looking at three sets of analytics algorithms actually.
A first set of algorithms is used to produce weather reports. These algorithms are mostly aggregating data collected on a large number of locations, plus interpolation to fill missing pieces. These algorithms are used to describe the world as it is. For that reason they are part of
A second set of algorithms is used to produce weather forecasts. These algorithms solve differential equations occurring in physical models of the atmosphere and the oceans. These algorithms are used to make predictions. For that reason, they are part of
A third set of algorithms computes a route given predicted weather. These algorithms solve an optimization problem (minimize travel time). These algorithms compute a recommended direction to follow when sailing. For that reason they are part of The three flavors of analytics for sailing can be summarized as follow: - Descriptive: Weather reports tell you past and current wind speed and direction.
- Predictive: Weather forecasts tell you what the wind direction and speed will be.
- Prescriptive: Routing software tells you in which direction you should sail.
They are particular cases of a much more general view of analytics. I have blogged many times about it, see for instance the anal
Note that prescriptive analytics often relies on solving an optimization problem. |