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PDF Editor FAQ

How does it feel to have an old father?

I would guess that my daughter should be answering this, but she would not understand exactly how to answer it. My 28-year-old quadriplegic daughter is in a wheelchair and needs help with most everything. There is no mother involved with her and has not been for 27 years (drugs). She is deceased now.We are as happy as we possibly can be under the circumstances. I was 47 when she was born and I am now 76. I do worry about her future though. I really feel like my daughter loves me a lot but it breaks my heart for my daughter to not be able to do the things that other normal young people do at her age. She also is beautiful and has never had a boyfriend and she probably never will and she is mentally delayed as well as physically.If I could push a button ending my life to take her back to before she got hurt, I would do it in an instant with a smile on my face. She will never be able to experi, nce the wonderful blessing of having her own children as I have.

Why didn't word2vec simply use noise contrastive estimation (NCE) to approximate the impractical partition function?

This paper discusses both these methods in detail. https://arxiv.org/pdf/1410.8251.pdfEseentially the paper says while both are quite similar ( negative sampling could be considered a special case of NCE) in some ways, NCE is a more general estimator and is best suited for language modeling whereas both negative sampling and NCE could be for learning word representations.As to why Word2vec uses negative sampling over NCE - Iam not sure -other than the hand wavy answer that it may be a simpler implementation (see comment for additional details).

Is there an intuitive explanation for why Noise-contrastive Estimation yields distributions which are approximately normalized?

At a high level of explaination without math, noise-contrastive estimation (NCE) estimates an unknown distribution Pd by comparing it to a known distribution Pn. In many cases, the distribution Pd is only specified up to the partition function, and often the partition function does not have a closed form. Numerical approximations of the partition function are often computationally expensive. NCE aims to estimate the ratio Pd/Pn instead. This ratio is estimated by using a nonlinear logistic regression to discriminate between observed data (generated from Pd) and noise data (drawn from Pn).When Pd is an unnormalized distribution, NCE treats the normalizing constant C as just an another parameter which DOES NOT depend on model parameters. The normalizing constant is not computed explicitly but instead, is estimated just like other parameters. Thus the estimated distribution Pd* is approximately normalized.I would suggest to read section 2 in noise-constrastive paperMichael U. Gutmann and Aapo Hyvarinen (2012) Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics. Journal of Machine Learning Research 13:307-361.or, a very short note on NCE I wrotehttps://staff.fnwi.uva.nl/m.k.tran/notes/nce.pdf

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