THE LOG-SUM-EXP GUARD
Intermediate
Difficulty: Medium Tags: Numerical Stability, Probability, Loss Functions
Story
A probabilistic model computes a log partition function. Directly exponentiating large scores overflows, so the stable log-sum-exp trick (subtracting the max before exponentiating) must be used instead.
The Math
For scores x_1, ..., x_n:
LSE(x) = log(sum_i e^{x_i}) = m + log(sum_i e^{x_i - m}), m = max_i x_i
Input Format
scores (length n).
Output Format
LSE(x), 6 decimal places.
Constraints
1 <= n <= 10^5,|x_i| <= 10^6.- Time limit: 1.0 second.
Example
Input
scores = [1000, 1001, 999]
Output
1001.407606
Explanation: The result is 1001 + log(1 + e^-1 + e^-2).
Keywords
numerical-stabilityprobabilityloss-functions
Python
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