get_g0_ada {genscore}

Adaptively truncates the l2 distance to the boundary of the domain and its gradient for some domains.

Description

Adaptively truncates the l2 distance to the boundary of the domain and its gradient for some domains.

Usage

get_g0_ada(domain, percentile)

Arguments

domain

A list returned from make_domain() that represents the domain.

percentile

A number between 0 and 1, the percentile. The returned l2 distance will be truncated to its percentile-th quantile, i.e. the function returns pmin(g0(x), stats::quantile(g0(x), percentile)) and its gradient. The quantile is calculated using finite values only, and if no finite values exist the quantile is set to 1.

Details

Calculates the l2 distance to the boundary of the domain, with the distance truncated above at a specified quantile. Matches the g0 function and its gradient from Liu (2019) if percentile == 1 and domain is bounded. Currently only R, R+, simplex, uniform and polynomial-type domains of the form sum(x^2) <= d or sum(x^2) >= d or sum(abs(x)) <= d are implemented.

Value

A function that takes x and returns a list of a vector g0 and a matrix g0d.

Examples

n <- 15
p <- 5
K <- diag(p)
eta <- numeric(p)

domain <- make_domain("R", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.3)(x)

domain <- make_domain("R+", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.3)(x)

domain <- make_domain("uniform", p=p, lefts=c(-Inf,-3,3), rights=c(-5,1,Inf))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.6)(x)

domain <- make_domain("simplex", p=p)
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
max(abs(get_g0_ada(domain, 0.4)(x)$g0 - get_g0_ada(domain, 0.4)(x[,-p])$g0))
max(abs(get_g0_ada(domain, 0.4)(x)$g0d - get_g0_ada(domain, 0.4)(x[,-p])$g0d))

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)>1.3", "nonnegative"=FALSE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.5)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)>1.3", "nonnegative"=TRUE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.7)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)<1.3", "nonnegative"=FALSE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.6)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x^2)<1.3", "nonnegative"=TRUE, "abs"=FALSE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.25)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x)<1.3", "nonnegative"=FALSE, "abs"=TRUE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.37)(x)

domain <- make_domain("polynomial", p=p, ineqs=
     list(list("expression"="sum(x)<1.3", "nonnegative"=TRUE, "abs"=TRUE)))
x <- gen(n, "gaussian", FALSE, eta, K, domain, 100)
get_g0_ada(domain, 0.45)(x)