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Paperium
Paperium

Posted on • Originally published at paperium.net

1-Bit Matrix Completion

How tiny 1-bit answers can rebuild a whole table

What if you could rebuild a full ratings table from just yes/no replies? A clever method shows you can, using only a few 1-bit answers that are noisy and simple.
By treating those tiny marks as binary signals, the method guesses the missing numbers when the data comes from a few hidden patterns and no entry is extreme.
The trick uses probability to turn noisy bits into a clear picture, and under mild rules the approach gives an accurate estimate of the unknown values.
If the model behaves well the guess comes from an ordinary program, so you don't need supercomputers, though some care is required.
Even better, when you only want the chance someone says yes the method relaxes some limits and still works.
Tests on movie scores were eye opening: after turning five-star ratings into single bits, the binary-based method was surprisingly better than the usual way that used all five stars.
Little bits can hold big clues, so look twice at simple data, it may hide more than you think.

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1-Bit Matrix Completion

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