# Log-Loss

The Log-Loss

$LL(E)$

reflects the number of bits required to encode an n-dimensional piece of evidence (or observation) $E$

given the current Bayesian network $B$

. As a shorthand for "the number of bits required to encode," we use the term "cost" in the sense that "more bits required" means computationally "more expensive."

$L{L_B}(E) = - {\log _2}\left( {{P_B}(E)} \right),$

where

${{P_B}(E)}$

is the joint probability of the evidence $E$

computed by the network $B$

:

$P_B(E) = P_B({e_1},...,{e_n})$

In other words, the lower the probability of

$E$

given the network $B$

, the higher the Log-Loss $LL(E)$

. Note that

$E$

refers to a single piece of n-dimensional evidence, not an entire dataset.Last modified 1mo ago