If theoretical perplexityPP has a similar tendency as real perplexity PP on a log-log graph, i.e., ln PP(W ′ ) ≈ lnPP(W ′ ) + c for some constant c, we can approximate its deterioration rate as PP(W ′ )/PP(W ) ≈ exp (lnPP(W ′ ) + c)/ exp (lnPP(W ) + c) = PP(W ′ )/PP(W ).
we can use TheoryAve as a heuristic function for estimating the perplexity of topic models.