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Support combining two LMs
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Given two LMs "A" and "B", this script modifies
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probabilities in A such that
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P_{A_{new}}(w_n|w0,w1,...,w_{n-1}) = P_{A_{original}}(w_n|w0,w1,...,w_{n-1}) / P_{B}(w_n|w0,w1,...,w_{n-1})
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P_{A_{new}}(w_n|w_0,w_1,...,w_{n-1}) = P_{A_{original}}(w_n|w_0,w_1,...,w_{n-1}) / P_{B}(w_n|w_0,w_1,...,w_{n-1})
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When it is formulated in log-space, it becomes
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\log P_{A_{new}}(w_n|w0,w1,...,w_{n-1}) = \log P_{A_{original}}(w_n|w0,w1,...,w_{n-1}) - \log P_{B}(w_n|w0,w1,...,w_{n-1})
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\log P_{A_{new}}(w_n|w_0,w_1,...,w_{n-1}) = \log P_{A_{original}}(w_n|w_0,w_1,...,w_{n-1}) - \log P_{B}(w_n|w_0,w_1,...,w_{n-1})
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Optionally, you can pass a scale for the LM "B", such that
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