# Solving Sparse Model with given Dictionary Using LASSO

I was trying to solve a problem where the basis matrix contains the components of $$\sin(nx)$$, $$\cos(nx)$$, $$\sinh(nx)$$ and $$\cosh(nx)$$.

Say the $$n$$ varies from 1 to 100. While solving the lasso linear regression, I should get the sparse coefficients on say $$n=10$$ for each of the components. To be clear say the data obtained from the equation is $$y= \alpha \sin(10x) + \beta \cos(10x) + \gamma \sinh(10x) + \delta \cosh(10x)$$.

I am getting some arbitrary coefficients and that is not representing the equation.

What am I doing wrong?

• Are you trying to solve $\arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$? – Royi Mar 1 '20 at 11:46