ridge-solve — Discord case

Discord-inspired abuse-detection experiment has correlated features that make an ordinary least-squares solution unstable. You need to compute the ridge-regression solution with the supplied regularization strength so the team has a stable baseline.

Solve the ridge-regression problem without an intercept: $\widehat{w}=(X^{\mathrm{\top }}X+\lambda I{)}^{-1}{X}^{\mathrm{\top }}y\backslash hat\; w=(X^\backslash top\; X+\backslash lambda\; I)^\{-1\}X^\backslash top\; y$, computed with a linear solve rather than an explicit inverse.

Implement solve(X, y, lam).

Returns. Return the coefficient vector (one entry per column of X). lam must be non-negative.

Examples

Example 1

Input:

solve([[1, 0], [0, 1]], [1, 2], 1)

Output:

[0.5, 1.0]

Example 2

Input:

solve([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0]], [1.0, 2.0, 3.0], 0.1)

Output:

[0.498221, 0.498221]