Interface

Interface

Functions exported from ConstrainedLasso:

# ConstrainedLasso.lsq_constrsparsereg — Function.

  lsq_constrsparsereg(
      X         :: AbstractMatrix{T},
      y         :: AbstractVector{T},
      ρ         :: Union{AbstractVector, Number} = zero(T);
      Aeq       :: AbstractMatrix = zeros(T, 0, size(X, 2)),
      beq       :: Union{AbstractVector, Number} = zeros(T, size(Aeq, 1)),
      Aineq     :: AbstractMatrix = zeros(T, 0, size(X, 2)),
      bineq     :: Union{AbstractVector, number} = zeros(T, size(Aineq, 1)),
      obswt     :: AbstractVector = ones(T, length(y)),
      penwt     :: AbstractVector = ones(T, size(X, 2)),
      warmstart :: Bool = false,
      solver = ECOSSolver(maxit=10e8, verbose=0)
    )

Fit constrained lasso at fixed tuning parameter value(s) by minimizing 0.5sumabs2(√obswt .* (y - X * β)) + ρ * sumabs(penwt .* β) subject to linear constraints, using Convex.jl.

Arguments

  • X : predictor matrix.
  • y : response vector.
  • ρ : tuning parameter. Can be a number or a list of numbers. Default 0.

Optional arguments

  • Aeq : equality constraint matrix.
  • beq : equality constraint vector.
  • Aineq : inequality constraint matrix.
  • bineq : inequality constraint vector.
  • obswt : observation weights. Default is [1 1 1 ... 1].
  • penwt : predictor penalty weights. Default is [1 1 1 ... 1].
  • warmstart :
  • solver : a solver Convex.jl supports. Default is ECOS. Note that Mosek and Gurobi are more robust than ECOS. Unlike ECOS or SCS, both Mosek and Gurobi require a license (free for academic use). http://convexjl.readthedocs.io/en/latest/solvers.html

Returns

  • β : estimated coefficents.
  • objval : optimal objective value.
  • problem : Convex.jl problem.

source

# ConstrainedLasso.lsq_constrsparsereg_admm — Function.

  lsq_constrsparsereg_admm(
    X             :: AbstractMatrix{T},
    y             :: AbstractVector{T},
    ρ             :: Number = zero(T);
    proj          :: Function = x -> x,
    obswt         :: Vector{T} = ones(T, length(y)),
    penwt         :: Vector{T} = ones(T, size(X, 2)),
    β0            :: Vector{T} = zeros(T, size(X, 2)),
    admmmaxite    :: Int = 10000,
    admmabstol    :: Float64 = 1e-4,
    admmreltol    :: Float64 = 1e-4,
    admmscale     :: Float64 = 1 / length(y),
    admmvaryscale :: Bool = false
    )

Fit constrained lasso at a fixed tuning parameter value by applying the alternating direction method of multipliers (ADMM) algorithm.

Arguments

  • X : predictor matrix.
  • y : response vector.
  • ρ : tuning parameter. Default 0.

Optional arguments

  • proj : projection onto the constraint set. Default is identity (no constraint).
  • obswt : observation weights. Default is [1 1 1 ... 1].
  • penwt : predictor penalty weights. Default is [1 1 1 ... 1].
  • β0 : starting point.
  • admmmaxite : maximum number of iterations for ADMM. Default is 10000.
  • admmabstol : absolute tolerance for ADMM.
  • admmreltol : relative tolerance for ADMM.
  • admmscale : ADMM scale parameter. Default is 1/n.
  • admmvaryscale: dynamically chance the ADMM scale parameter. Default is false.

Returns

  • β : estimated coefficents.

source

  lsq_constrsparsereg_admm(
    X             :: AbstractMatrix{T},
    y             :: AbstractVector{T},
    ρlist         :: Vector;
    proj          :: Function = x -> x,
    obswt         :: Vector{T} = ones(T, length(y)),
    penwt         :: Vector{T} = ones(T, size(X, 2)),
    admmmaxite    :: Int = 10000,
    admmabstol    :: Float64 = 1e-4,
    admmreltol    :: Float64 = 1e-4,
    admmscale     :: Float64 = 1 / length(y),
    admmvaryscale :: Bool = false
    )

Fit constrained lasso at fixed tuning parameter values by applying the alternating direction method of multipliers (ADMM) algorithm.

Arguments

  • X : predictor matrix.
  • y : response vector.
  • ρlist : a vector of tuning parameter values.

Optional arguments

  • proj : projection onto the constraint set. Default is identity (no constraint).
  • obswt : observation weights. Default is [1 1 1 ... 1].
  • penwt : predictor penalty weights. Default is [1 1 1 ... 1].
  • admmmaxite : maximum number of iterations for ADMM. Default is 10000.
  • admmabstol : absolute tolerance for ADMM.
  • admmreltol : relative tolerance for ADMM.
  • admmscale : ADMM scale parameter. Default is 1/n.
  • admmvaryscale: dynamically chance the ADMM scale parameter. Default is false.

Returns

  • βpath : estimated coefficents along the grid of ρ values.

source

# ConstrainedLasso.lsq_classopath — Function.

  lsq_classopath(
    X      :: AbstractMatrix{T},
    y      :: AbstractVector{T};
    Aeq    :: AbstractMatrix = zeros(T, 0, size(X, 2)),
    beq    :: Union{AbstractVector, Number} = zeros(T, size(Aeq, 1)),
    Aineq  :: AbstractMatrix = zeros(T, 0, size(X, 2)),
    bineq  :: Union{AbstractVector, Number} = zeros(T, size(Aineq, 1)),
    ρridge :: Number = zero(T),
    penidx :: Array{Bool} = fill(true, size(X, 2)),
    solver = ECOSSolver(maxit=10e8, verbose=0)
    )

Calculate the solution path of the constrained lasso problem that minimizes 0.5sumabs2(√obswt .* (y - X * β)) + ρ * sumabs(penwt .* β) subject to linear constraints.

Arguments

  • X : predictor matrix.
  • y : response vector.

Optional arguments

  • Aeq : equality constraint matrix.
  • beq : equality constraint vector.
  • Aineq : inequality constraint matrix.
  • bineq : inequality constraint vector.
  • ρridge : tuning parameter for ridge penalty. Default is 0.
  • penidx : a logical vector indicating penalized coefficients.
  • solver : a solver Convex.jl supports. Default is ECOS. Note that Mosek and Gurobi are more robust than ECOS. Unlike ECOS or SCS, both Mosek and Gurobi require a license (free for academic use). For details, see http://convexjl.readthedocs.io/en/latest/solvers.html.

Examples

See tutorial examples at https://hua-zhou.github.io/ConstrainedLasso.jl/latest/demo/path/.

source

# ConstrainedLasso.genlasso — Function.

  genlasso(
      X    :: AbstractMatrix{T},
      y    :: AbstractVector{T};
      path :: Bool = true,
      ρ    :: Union{AbstractVector, Number} = zero(T),
      D    :: AbstractMatrix{T} = eye(size(X, 2)),
      solver = ECOSSolver(maxit=10e8, verbose=0)
    )

Solve generalized lasso problem by reformulating it as constrained lasso problem. Note genralized lasso minimizes 0.5sumabs2(√obswt .* (y - X * β)) + ρ * sumabs(D * β).

Arguments

  • X : predictor matrix.
  • y : response vector.

Optional arguments

  • path : set path=false if user wishes to supply parameter value(s). Default is true.
  • ρ : tuning parameter value(s). Default is 0.
  • D : penalty matrix. Default is identity matrix.
  • solver : a solver Convex.jl supports. Default is ECOS. Note that Mosek and Gurobi are more robust than ECOS. Unlike ECOS or SCS, both Mosek and Gurobi require a license (free for academic use). http://convexjl.readthedocs.io/en/latest/solvers.html

Returns

  • β : estimated coefficents.
  • objval : optimal objective value.
  • problem : Convex.jl problem.

source

Private function in ConstrainedLasso:

# ConstrainedLasso.find_ρmax — Function.

  find_ρmax(
    X      :: AbstractMatrix,
    y      :: AbstractVector;
    Aeq    :: AbstractMatrix = zeros(eltype(X), 0, size(X, 2)),
    beq    :: Union{AbstractVector, Number} = zeros(eltype(X), size(Aeq, 1)),
    Aineq  :: AbstractMatrix = zeros(eltype(X), 0, size(X, 2)),
    bineq  :: Union{AbstractVector, Number} = zeros(eltype(X), size(Aineq, 1)),
    penidx :: Array{Bool} = fill(true, size(X, 2)),
    solver = ECOSSolver(maxit=10e8, verbose=0)
    )

Find the maximum tuning parameter value ρmax to kick-start the solution path.

source