CareerCup

the question is simple. you need to know the guessing pattern. If not available the best way is to think of it as finding the average of the cluster of the sample points given after identifying the outliers. To find these clusters use a density based clustering algorithm. If a single cluster is formed, print its mean, but if there is more than 1 clusters are found the number could be the centroid of any of these clusters. Hence, in case of more clusters the result will not necessarily give you the right answer.

What kind of guesses? How were these guesses formed?

How about just taking the averages? If there are n given points (x', y') = (sum(x)/n, sum(y)/n).

I believe it could be solved by Expectation Maximization method.

fentoyal -- I wrote the answer in the name field.

best guess is the average point
x'=sum of all xs divided by the number of points
y'=sum of all ys divided by the number of points

maybe we can firstly find the mean using k-means, then calculate the average distance among all other points and the mean?

You can mathematically prove that the optimal solution is [sum(x)/n , sum(y)/n].

I just can't figure out a way to type it out here though. Let me give it a try

You can try to minimize summation((x-x')^2) + summation((y-y')^2) and take partial derivatives on x and y. You get 2 equations. Upon solving them you get the optimal solution to be what is mentioned above.

Typical machine learning regression problem.
You can use a bunch of method like Linear regression or Neuron Network.

We can find the best guess by finding the distance between two points.
1) Take original point (x,y)
2) Now take first point from points set, say (x1, y1)
3) Now calculate the distance between (x, y) and (x1, y1).
4) Store the distance and first point.
5) Now take second coordinate and find distance between original point (x,y)
6) If second distance is smaller then store second point distance and second point.

Similarly iterate on all points to find best approximate point.