How is maximizing L(lambda1, lamda2, lamda3) equivalent to minimizing perplexity?
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In language modeling, L(lambda1, lambda2, lambda3) is defined as:
Sum(count of trigram(u,v,w) x q(w|u,v))
where u, v, w are words in the corpus
and
perplexity is defined as:
2^-l
where
l = (1/M)Sum(log(q(w|u,v)).
where M is the total no. of words in the corpus.
Also,
q(w|u,v) = lambda1*q(w|u,v) + lambda2*q(w|v) + lamdba3*q(w)
Some of the materials for Natural Language Processing state that maximizing L is same as minimizing perplexity. I don't see how that is true or can be mathematically proven.
natural-language-process language-model
asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
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$begingroup$
In language modeling, L(lambda1, lambda2, lambda3) is defined as:
Sum(count of trigram(u,v,w) x q(w|u,v))
where u, v, w are words in the corpus
and
perplexity is defined as:
2^-l
where
l = (1/M)Sum(log(q(w|u,v)).
where M is the total no. of words in the corpus.
Also,
q(w|u,v) = lambda1*q(w|u,v) + lambda2*q(w|v) + lamdba3*q(w)
Some of the materials for Natural Language Processing state that maximizing L is same as minimizing perplexity. I don't see how that is true or can be mathematically proven.
natural-language-process language-model
asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
New contributor
Crazed'n'Dazed is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
In language modeling, L(lambda1, lambda2, lambda3) is defined as:
Sum(count of trigram(u,v,w) x q(w|u,v))
where u, v, w are words in the corpus
and
perplexity is defined as:
2^-l
where
l = (1/M)Sum(log(q(w|u,v)).
where M is the total no. of words in the corpus.
Also,
q(w|u,v) = lambda1*q(w|u,v) + lambda2*q(w|v) + lamdba3*q(w)
Some of the materials for Natural Language Processing state that maximizing L is same as minimizing perplexity. I don't see how that is true or can be mathematically proven.
natural-language-process language-model
asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
New contributor
Crazed'n'Dazed is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
In language modeling, L(lambda1, lambda2, lambda3) is defined as:
Sum(count of trigram(u,v,w) x q(w|u,v))
where u, v, w are words in the corpus
and
perplexity is defined as:
2^-l
where
l = (1/M)Sum(log(q(w|u,v)).
where M is the total no. of words in the corpus.
Also,
q(w|u,v) = lambda1*q(w|u,v) + lambda2*q(w|v) + lamdba3*q(w)
Some of the materials for Natural Language Processing state that maximizing L is same as minimizing perplexity. I don't see how that is true or can be mathematically proven.
natural-language-process language-model
natural-language-process language-model
asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
New contributor
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asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
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asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
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asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
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asked 5 mins ago
Crazed'n'DazedCrazed'n'Dazed
1
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