Variance parameter faulty implementation

[WillDudley]

A lower variance is not better - need to look into this asap

[WillDudley]

Ya so there's two things here:

1. The codomain of the target function f equals its domain, with the target function as identity. This makes interoperability worse as it implies that the codomain is a probability. However, this is not true. Indeed, a bell curve with mean close to 1 implies a probability of landing beyond 1.

2. Switching the mean to be around the centre of the margin seems like an incorrect thing to do. The target is still at f(prob_b), and this should not be changed.

[WillDudley]

Probs should change f from f(x)=x to f(x)=logit(x). This maps (0,1) to R instead of just (0,1). The blow-up around 1 may be an issue as O(logit) may be bigger than O(cost_function), but we'll see and we usually only consider probs up to 0.9, maybe 0.95, at a maximum.

[WillDudley]

Probs should change f from f(x)=x to f(x)=logit(x). This maps (0,1) to R instead of just (0,1). The blow-up around 1 may be an issue as O(logit) may be bigger than O(cost_function), but we'll see and we usually only consider probs up to 0.9, maybe 0.95, at a maximum.

Ignore this, this is garbage.

I've addressed problem 2 though and at worst it's a lot more readable. Checked with manual working out.

Back to the variance issue. I think the problem lies with two things: (i) the ranges of the deltas and variances considered, and (ii) taking variance into account when calculating the margin midpoint is not what we want to do.

(i) - We can tackle this empirically if needed. Or do it theoretically, idk. Currently focussing on (i)
(ii) - Indeed, if we do this, then the margin midpoint is very much dependent on the variance. This is not what we want.

[WillDudley]

Should be fixed in V0.2.7. Attacker heatmaps have the intuitive gradient (lower variance is better), at least at minimum costs.