I am looking to solve the following estimation problem. Consider a blackbox where (given below) given an input X, its N observations are recorded as output.
These observations are denoted by $Y_1, \cdots, Y_N$. The observations are identically distributed, i.e. $Y_i \sim \mathcal{P}(Y|X) $. However, they are not independent.
I would like to know, how can I estimate $\mathcal{P}(Y|X)$ given these N observations. An exemplary solution for binary symbols would be great (i.e. $X,Y \in \{0,1\}$).
X
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Y_1 Y_2 Y_3 Y_4 Y_N