o

scalation.minima

LassoAdmm

object LassoAdmm

The LassoAdmm class performs LASSO regression using Alternating Direction Method of Multipliers (ADMM). Minimize the following objective function to find an optimal solutions for 'x'.

argmin_x (1/2)||Ax − b||_2^2 + λ||x||_1

A = data matrix b = response vector λ = weighting on the l_1 penalty x = solution (coefficient vector)

See also

https://web.stanford.edu/~boyd/papers/admm_distr_stats.html

euler.stat.yale.edu/~tba3/stat612/lectures/lec23/lecture23.pdf

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  8. def fast_sthresh(v: VectoD, thr: Double): VectoD

    Return the fast soft thresholding function.

    Return the fast soft thresholding function.

    v

    the vector to threshold

    thr

    the threshold

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  16. def reset: Unit

    Reset the warm start map.

  17. def solve(a: MatrixD, b: VectoD, λ: Double = 0.01): VectoD

    Solve for 'x' using ADMM.

    Solve for 'x' using ADMM.

    a

    the data matrix

    b

    the response vector

    λ

    the regularization l_1 penalty weight

  18. def solveCached(ata_ρI_inv: MatriD, atb: VectoD, λ: Double): VectoD

    Solve for 'x' using ADMM using cached factorizations for efficiency.

    Solve for 'x' using ADMM using cached factorizations for efficiency.

    ata_ρI_inv

    cached (a.t * a + ρI)^-1

    atb

    cached a.t * b

    λ

    the regularization l_1 penalty weight

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  24. val ρ: Int

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