swk82

Is the ability to reproduce an input value to the network?

I've noticed that those who bunch together reproduce very well but the planks sometimes form death traps killing the entire group. Some creatures are left over but they seem to avoid each other; sometimes one creature is chasing the other and they don't seem to reproduce very much.

Bunching and spreading out are two different behaviors which both have their pros and cons. I wonder if the neural net is complex enough to enable them to switch between these behaviors depending on the age and ability to reproduce.

Thanks, this is informative and pretty similar to what I've been implementing in JavaScript. I guess I'll have to take a deeper look into literature when doing an update to that topic.

I find this part of statistics very hard to argue about. Simulations only work with well-known distributions, but even then not all of them. Even when you have a simulation that confirms hypothesis A1 using distribution D1 it says little about some pathetical distribution D2.

Using mathematical precision might take years to get it right and often there is no easy answer.

What I've been looking for is something that is fast and works "good enough". Estimating the 95th percentile and averaging it did not work well in my use case. Using the histogram method does work well although it certainly is not perfect.

Matlab / GNU/Octave code:

    rand('seed',123);

    outer_rounds = 100;
    inner_rounds = 100;
    items = 500;

    q99_mean_vec = [];
    q99_complete_vec = [];

    for ior = 1:outer_rounds;

      q99_vec = [];

      x = rand( 1, rounds*items );

      for iir = 1:inner_rounds
	
	q99_vec(iir) = quantile( x( (iir-1)*items+(1:items) )', 0.99 );
	
      end

      q99_complete_vec(ior) = quantile( x', 0.99 );
      q99_mean_vec(ior) = mean( q99_vec' );

    end

    hist( [ q99_complete_vec; q99_mean_vec ]', [0.988:0.0001:0.991] );
    xlim( [0.988, 0.991] );
    legend( 'from complete data', 'from means' );

This looks biased to me even though the distribution is uniform. I did not expect that. Maybe the quantile function is broken.

EDIT: I've installed R and run your code. You use a very low number of samples in the mean, so I changed it a bit. 1. I use the uniform distribution, so we know the true value of the 99th percentile is 0.99. 2. I've increased the number of samples:

  x <- runif(100000)
    quantile(x, 0.99)
    mean(sapply(1:2000, function(i) {
      i <- i * 50
      quantile(x[i-49:i], 0.99)
    }))

When run multiple times, I've found that the mean is always lower than the quantile over the full sample.

> Even P99 estimates averaged from many tiny samples are at most inaccurate, they won't be biased.

Are you sure about this?

You are right when looking at the true P99 of the whole distribution. Then the P99 will always have the same value. The problem arises when estimating a distribution from incomplete data.

E.g. estimating the P99 from 200 data points each will give you a large variation. In this case averaging will be wrong. This gets worse if you experience bunching. E.g. a server will have a high ping on several packets when the load is high; after that it will have a low ping for thousands of packets when the load is low. Here, it just doesn't work.

Instead, you can get a better result by adding the (estimated) histograms and resampling the quantiles from the combined distribution function.

Here I've written how that works with a live demonstration: http://www.siegfried-kettlitz.de/blog/posts/2015/11/28/linlo...

I've recently written a page about "averaging" percentiles correctly by approximating the combined histograms of two distributions. This is demonstrated in a live time diagram with logarithmic time axis here:

http://www.siegfried-kettlitz.de/blog/posts/2015/11/28/linlo...

If you have questions or comments, feel free to reply or email.