# Convert a matrices multiplications to Ax=b

I have a training data matrix $S_{\tau \times n}$ and actual output $y_{1\times P}$. The weighted parameters for a linear model that maps the input to the output is

$$y = \alpha_{1 \times \tau}S_{\tau \times n}\beta_{n\times p}$$

Now my question is, is it possible to group this formula into the standard notation?

$$y=Ax$$

If the answer is no, what method can be used to find the optimal parameters of $\alpha$ and $\beta$ that minimizes the mean square error of the predicted $\hat{y}$ and the actual output $y$?

• What is $x$ in relation to $\alpha$ and $\beta$ Commented Jul 23, 2018 at 20:00
• @user7530 I don't know. I'm just trying to turn this optimization problem into something that is feasible to do using the traditional frameworks. Commented Jul 23, 2018 at 20:20
• How come the number of labels (y's) is not equal to the number of observed feature vectors in S? Commented Jul 23, 2018 at 21:21
• @MaziarSanjabi I mentioned nothing about the number of labels. How did you come to this conclusion? Commented Jul 23, 2018 at 22:12
• There is much that you "mentioned nothing about" in the setup of this problem. How do you expect Readers to analyze the possibility of expressing the output without more information about the supposedly "linear model"? Commented Jul 24, 2018 at 1:12