check out this shape

[mobeets]

i mean, check it out: it's got clear BOUNDARIES

D = io.quickLoadByDate('20120601');
Y = D.blocks(2).latents;
NB = D.blocks(2).fDecoder.NulM2;
[u,s,v] = svd(D.blocks(2).latents*NB);
Y2 = Y*NB*v;

Y2p = Y2(:,1:3);
plot3(Y2p(:,1), Y2p(:,2), Y2p(:,3), '.')

[mobeets]

and here by thetaGrp

[mobeets]

[mobeets]

note that in all these cases, the colors are very clearly clustered. but the overall distribution still is in a sort of balloon.

and for 20120525, it has the same nub, but then from another view, two lobes:

and then the two 2013 days just have way less data:

[mobeets]

"You could treat your data as a sample from a three-dimensional probability density, and estimate that density on a grid, e.g. via a 3d histogram, or better a 3d kernel density estimator. Then apply a threshold and extract the surface using isosurface."

[mobeets]

no isosurface, but i've evaluated by p-hat density estimation and found points where the p-hat is in the 75-76th percentile

[mobeets]

the black dots are data, and the red dots are the boundary defined by where p-hat is in the 90-91st percentile

[mobeets]

here's observed on the left, and cloud-hab on the right. note how cloud-hab doesn't fill the same space at all--it's less spread out. but at least it's not outside of it!

[mobeets]

and it turns out that left clump are the kinematics the cloud does poorly at:

(green are the 180+ directions)

[mobeets]

so this realization has led to two things:

• resampling hypothesis predictions when they create latent activity not observed in intuitive block. otherwise, hypotheses that predict things out of bounds are clearly going to be wrong. this made the volitional SO much better, and then same for a few others as well
• trial conditions/directions where the range of spikes are less constrained (see: light green and yellow above) are usually less well predicted by cloud-hab et al., and also it seems like learning happens here more quickly, probably because variability is bigger here, so there's more room to explore?