Modeling ceres problem with heteroskedastic noise

[arrigo]

All,

I have an optimization problem involving measurements from a sensor with heteroskedastic (signal dependent) noise. In other words the noise is Gaussian but the variance is a function of the (true) signal value. As a consequence the log likelihood has an extra term:

- log(p(y|x))  = 2* log(sigma(x)^2) + (y-x)^2 / sigma(x)^2

The problem is that now the cost can be negative, so in principle Ceres cannot solve this problem. I know I could use Ceres' unconstrained minimization solver but the auto diff stuff is not available in this mode. Is there any principled way to handle this other than simple hacks like re-scaling the data and using log(1 + sigma^2(x)) instead of log(sigma^2(x)) , etc..

Thanks

-Arrigo
 

[Sameer Agarwal]

Arrigo,

The current API does not allow for this.

Sameer

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