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Let's assume that one has the following inputs and corresponding outputs:

x1 = (a,b,c) with corresponding output y1, which is a number.
x2 = (d,e,?) with unknown output
x3 = (?,?,g) with known output y2, which is a number

and so on.

So, by "incomplete input data" I don't just mean that some input data is unlabeled but some data-points from certain data-vectors are missing and are sometimes labeled and sometimes unlabeled.

Is there at least one known online semi-supervised learning algorithm for this kind of "input data with gaps"?

So far I only found algorithms for online semi-supervised learning for "input data without any gaps".

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I came across a new paper that does just this, however I have not read it carefully: Max-Ordinal Learning.

Another option is the E-M algorithm, which is commonly used with missing data.

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