the main thing remaining about the old dataset that I can see that's
different from the latest one is that there is more overlap between
components. Maybe there wasn't enough overlap between the components
in the new datasets. If I extend the range of component 1 to [0,1], we
have

http://pages.cs.wisc.edu/~nathanae/hall/synthhole_lunifnomargin.png
http://pages.cs.wisc.edu/~nathanae/hall/synthhole_lunifnomargin_oldh.png

which looks good again. Here's another dataset

http://pages.cs.wisc.edu/~nathanae/hall/synthhole_lunif_onetoten.png
http://pages.cs.wisc.edu/~nathanae/hall/synthhole_lunif_onetoten_oldh.png

This dataset is generated like this:

for j=1, x_d~unif[1,9], for d=1..3
for j=2, x_d~unif[0,3]U[7,10], for d=1..3

Our lambda is better than theirs:

l0 =

   0.4051
   0.5949


lstar =

   0.4866
   0.5134

>> sum([y==1 y==2])

ans =

  495   505


Here is w:

>> w0(1:10,:),wstar(1:10,:)

ans =

   0.1648    0.8352
   0.0525    0.9475
   0.1314    0.8686
   0.1522    0.8478
   0.0687    0.9313
   0.8915    0.1085
   0.0884    0.9116
   0.6086    0.3914
   0.0565    0.9435
   0.8156    0.1844


ans =

   0.5875    0.4125
        0    1.0000
        0    1.0000
        0    1.0000
        0    1.0000
   1.0000         0
        0    1.0000
   1.0000         0
        0    1.0000
   1.0000         0

>> [y(1:10)==1 y(1:10)==2]

ans =

    0     1
    0     1
    1     0
    0     1
    0     1
    1     0
    0     1
    1     0
    0     1
    1     0

As previously, our w is more confident i.e. sparse than theirs, but
not always right, e.g. we assign all weight on x(3) to component 2,
but really it is in component 1. x(3) is:
   8.9953    7.4295    2.1911
so it actually does look like it's from component 2, though it could
be from either. They also get this one wrong.

I think I need to look at Benegalia et al 07 and understand exactly
how their algorithm works.



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