So far, we computed the error (MSE/MAE) of λ comparing the learned on with the actual one.
In this experiment, we check we test the error in prediction.
So,
Part I
M=256 sample points, generating histogram H of size K; H[k] = number of samples in bin k, i.e., count how
many sample points. Therefore K is computed, but will be small for typical values of λ.
λ=0.5 ... 1.5
N = 10K
Let *V = (H[k] - M Poisson(λ,k)|**
Then V is parameterized by
k, the current bin
i=1,...,N; sample number.
All computation must include therefore K*N values of V.
Objective: compute MAE(V), MSE(V), MEAN_BIAS(V), with respect to all these values.
Part II
Repeat with λ computed by the expectation of the sample, i.e., (Σ_{0 <= k <= K) k*H[k])/M
Part III
Combine Part I and Part II, to find out which is better; ours should be. We need a single table/graph/plot.
Show that the expectation of the sample, gives a biased estimate, and that ours does not. To do so: Same data as stage I, but NO LEARNING. Use N=10,000, compute λ by its expectation; compare with the λ you selected at random, and show that there is bias between the two.
So far, we computed the error (MSE/MAE) of λ comparing the learned on with the actual one. In this experiment, we check we test the error in prediction. So,
Part I
M=256 sample points, generating histogram H of size K; H[k] = number of samples in bin k, i.e., count how many sample points. Therefore K is computed, but will be small for typical values of λ.
λ=0.5 ... 1.5
N = 10K
Let *V = (H[k] - M Poisson(λ,k)|**
Then V is parameterized by
All computation must include therefore K*N values of V.
Objective: compute MAE(V), MSE(V), MEAN_BIAS(V), with respect to all these values.
Part II
Repeat with λ computed by the expectation of the sample, i.e., (Σ_{0 <= k <= K) k*H[k])/M
Part III
Combine Part I and Part II, to find out which is better; ours should be. We need a single table/graph/plot.
Show that the expectation of the sample, gives a biased estimate, and that ours does not. To do so: Same data as stage I, but NO LEARNING. Use N=10,000, compute λ by its expectation; compare with the λ you selected at random, and show that there is bias between the two.