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I want to find a function, let's say $y= a x + b$ but I don't have sample $(x,y)$ pairs but what I have is samples of following form $((x_1, x_2, ..., x_n), \sum_{i=1}^n y_i)$ where n is also a known random variable. Is there a specific algorithm for this problem. I tried to minimize the following expectation with stochastic gradient descent. $$ \mathbb{E}[(\sum_{i=1}^n y_i - \sum_{i=1}^n (ax_i +b) )^2]$$

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