🐛 Test was failling due to sampling.

[davibarreira]

The current test returns an error in the "1D continuous case". The problem is that the sample used to evaluate the transport plan is taken from a Normal(0,1) while the acutal mu and nu distributions are something like Normal(-0.6,1), so when calculating the cdf(\mu, x), it actually returns Inf, and thus becoming incomparable to \gamma.

I fixed to sample from mu instead, to avoid such distant value. Also, I did multiple sampling to provide a more robust test.

[devmotion]

The problem is that the sample used to evaluate the transport plan is taken from a Normal(0,1) while the acutal mu and nu distributions are something like Normal(-0.6,1), so when calculating the cdf(\mu, x), it actually returns Inf,

I can't follow, why would it ever return Inf? 0 <= cdf(\mu, x) <= 1, regardless of x.

[davibarreira]

Sorry, not cdf(mu,x) returns Inf, but quantile(nu, cdf(mu,x)). Since x is so far from mu, one gets cdf(mu,x) =1, and then quantile(nu, cdf(mu,x)) = Inf.

[devmotion]

Maybe just perform computations in log-space? This should be more stable anyways. I.e., use invlogcdf(nu, logcdf(mu, x)).

[davibarreira]

Just tried, but it didn't solve the issue. What's the problem of sampling from mu as I have coded?

[devmotion]

I think it would be nice if we don't have to use our knowledge about mu. Nevertheless computations in log space are better.

I opened another PR with some additional fixes.