Posts Tagged ‘approximation’

Linear Addition from the Log Domain

February 24, 2013

Some speech recognizers and machine learning algorithms need to quickly calculate the quantity:

\log(x+y)

when given only \log(x) and \log(y). The straightforward algorithm first uses the exponential function to convert the log values to the linear domain representation x and y, then performs the sum, and finally uses the log function to convert back to the log domain:

\log(x+y) = \log(\exp(\log(x)) + \exp(\log(y)))

These conversions between log and linear domains are slow and problems arise when x is too large or small for a machine’s floating point representation.

Luckily, there is a clever approximation method that allows quick, accurate calculation with a relatively small precomputed table.

(more…)

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