GPS task: harmonic mean

[dleshem]

harmonic average is used instead of arithmetic mean because it corresponds better to travel times, which are the ultimate criterion of optimization in a real-world setting.

I'm wondering why you decided to use the harmonic mean as the objective to predict, as opposed to the simple arithmetic mean.

It seems to me that using the harmonic mean would be justified if cars were reporting their speed every fixed distance (e.g. every 50m).
In the simulation, however, cars report their speed every fixed time (every 10 seconds).
See Wikipedia for a brief discussion.

Moreover, when using the harmonic mean a single outlier that reports 0-speed is enough to ignore all others and set the objective to 0.
Since the objective is never 0 in the training set's selected road segments (or maybe I missed some?), I'm wondering whether-
1) you didn't choose any road segments with traffic lights
2) you actually used the arithmetic mean

[Marcin]

Hi dleshem,
Thanks for questions.

In a real-world setting, what you'd be interested in is your predicted travel time. Or an arithmetic average of travel times, when a number of cars is considered. When you have a predicted velocity in hand, you must first invert it to get travel time over a unit distance, and only then you can calculate arithmetic mean of travel times. These two steps: inversion and calculation of arithmetic average - is the same as calculating harmonic average - so the harmonic average of velocities directly corresponds to (is an inversion of) arithmetic mean of travel times.

As to your concerns about averaging zero velocities: such velocities can't occur. We consider only cars that have passed a non-zero distance over a given segment and the velocity is calculated over this whole distance, so it's always a positive number. In other words, it's not an instantaneous velocity, but a mean velocity of this car over the whole segment (or its part if the car hasn't left the segment yet).

Regards, Marcin Wojnarski

[amrkabardy]

Hi,

As to your concerns about averaging zero velocities: such velocities can't occur. We consider only cars that have passed a non-zero distance over a given segment and the velocity is calculated over this whole distance, so it's always a positive number. In other words, it's not an instantaneous velocity, but a mean velocity of this car over the whole segment (or its part if the car hasn't left the segment yet).

I wanted to make sure of something about training data:
1- The velocity provided by notifications in training and testing data, is it the instantaneous velocity of the car at this reported position? or is it a the average velocity of the car since the last reported position? Or it's an average velocity since entering the segment?
2- The notifications already contains too many records reporting ZERO velocity. Should I disregard them? Or should I always ignore the reported velocity and use the position and timestamp info to predict average velocity?!

Thanks

[Marcin]

Hi,
1 - it's "Instantaneous velocity (km/h) of the car in a given second" (see task description)
2 - velocities in notifications are correct

Cheers, Marcin