The linear regression is simply $y=Wx+b$, where the server holds $W$ and $b$ and the client holds $x$. The private linear regression means the client sends encrypted $x$ to the server, and receives encrytped $y$. Then the client can decrypt $y$ for result. I have read some papers about privacy-preserving linear (logistic) regression. But I have a question before designing protocols for it. One goal of using private linear regression is to protect the weights $W$ and $b$. If the client can accumulate numerous pairs of $x$ and $y$, she can obtain both $W$ and $b$ by solving a linear system. This problem also holds for logistic regression since its addtional activation function $\frac{1}{1+e^{-y}}$ is a one-to-one mapping and cannot hide the output. Therefore, why it is necessary to use the secure protocols for the linear (logistic ) regression?



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