Loss functions

superres-tomo comes with a series of loss functions not found in the ml packages that it is built on. These are primarily useful in cases where there is class imbalance in the training/test set.

Weighted cross entropy

The weighted cross entropy (WCE) is an extension of the standard cross entropy. WCE can be used where there is a large class imbalance (excess of a particular label). In WCE all positive examples get weighted by a coefficient, which can be set in inverse proportion to the amount of a given label in the training set.

WCE is defined as

\[WCE(p, \hat{p}) = -(\beta p \log(\hat{p}) + (1 - p)\log(1 - \hat{p}))\]

To bias against false positives set \(\beta < 1\) to bias against false positives set \(\beta < 1\)

Balanced cross entropy

Balanced cross entropy (BCE) is similar to WCE, but it also biases negatives as well as poitives.

\[BCE(p, \hat{p}) = -(\beta p \log(\hat{p}) + (1 - \beta)(1 - p)\log(1 - \hat{p}))\]

Dice Loss

The Dice loss is a loss function that is particularly useful if boundary detection is important in your image analysis. The dice loss is defined as

\[DL(p, \hat{p}) = 1 - \frac{2p\hat{p} + 1}{p + \hat{p} +1}\]