quadDeriv: Gradient and Diagonal of Hesse Matrix of Quadratic...

Description Usage Arguments Value Note Author(s) See Also

Description

Computes gradient and diagonal of the Hesse matrix w.r.t. to η of a quadratic approximation to the reparametrized original log-likelihood function

L(φ) = ∑_{i=1}^m w_i φ(x_i) - int_{-∞}^{∞} exp(φ(t)) dt.

where L is parametrized via

η(φ) = (φ_1, (η_1 + ∑_{j=2}^i (x_i-x_{i-1}) η_i)_{i=2}^m).

φ: vector (φ(x_i))_{i=1}^m representing concave, piecewise linear function φ,
η: vector representing successive slopes of φ.

Usage

1
quadDeriv(dx, w, eta)

Arguments

dx

Vector (0, x_i-x_{i-1})_{i=2}^m.

w

Vector of weights as in activeSetLogCon.

eta

Vector η.

Value

m \times 2 matrix. First column contains gradient and second column diagonal of Hesse matrix.

Note

This function is not intended to be invoked by the end user.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

See Also

quadDeriv is used by the function icmaLogCon.


logcondens documentation built on May 2, 2019, 6:11 a.m.