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I know that we can use Gaussian processes effectively for function approximation and regression. However,suppose there is a sequence of points in time $S = \{s_1, s_2, \dots, s_n\}$, where $s_i$ can be either 0 or 1 at random. If we have a new point at a time i = n+1 and we want to predict if its state is 0 or 1 based on the given set $S$, can we use a Gaussian Process for this purpose? and if so, how? is there a resource where such idea is explained?

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    $\begingroup$ +1. There are even R packages for this: see cran.nexr.com/web/packages/geoRglm/index.html, for instance. $\endgroup$
    – whuber ♦
    Commented Mar 25 at 16:46
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    $\begingroup$ I would go with a latent Gaussian process where the observables are the elements of the binary sequence. Something like Bernoulli observables with probability equal to the inverse logit of a linear combination of the outputs of the Gaussian process. At least as a starting point anyway. $\endgroup$
    – Galen
    Commented Mar 25 at 19:51

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