get_h_hp: Generator of h and hp (derivative of h) functions.
In sqyu/genscore: Generalized Score Matching Estimators

Description Usage Arguments Details Value Examples

Generator of h and hp (derivative of h) functions.

1	get_h_hp(mode, para = NULL, para2 = NULL)

`mode`	A string, see details.
`para`	May be optional. A number, the first parameter. Default to `NULL`.
`para2`	May be optional. A number, the second parameter. If `mode` is one of the adaptive mode below, this specifies the percentile (see details). Default to `NULL`.

The mode parameter can be chosen from the options listed below along with the corresponding definitions of h under appropriate choices of para and para2 parameters. Unless otherwise noted, para and para2, must both be strictly positive if provided, and are set to 1 if not provided. Functions h and hp should only be applied to non-negative values x and this is not enforced or checked by the functions. Internally calls get_h_hp_vector.

asinh: An asinh function h(x)=asinh(para*x)=log(para*x+sqrt((para*x)^2+1)). Unbounded and takes one parameter. Equivalent to min_asinh(x, para, Inf).
cosh: A shifted cosh function h(x)=cosh(para*x)-1. Unbounded and takes one parameter. Equivalent to min_cosh(x, para, Inf).
exp: A shifted exponential function h(x)=exp(para*x)-1. Unbounded and takes one parameter. Equivalent to min_exp(x, para, Inf).
identity: The identity function h(x)=x. Unbounded and does not take any parameter. Equivalent to pow(x, 1) or min_pow(x, 1, Inf).
log_pow: A power function on a log scale log(1+x)^para. Unbounded and takes one parameter. Equivalent to min_log_pow(x, para, Inf).
mcp: Treating λ=para, γ=para2, the step-wise MCP function applied element-wise: λx-x^2/(2γ) if x<=λγ, or γλ^2/2 otherwise. Bounded and takes two parameters.
min_asinh: A truncated asinh function applied element-wise: pmin(asinh(para*x), para2). Bounded and takes two parameters.
min_asinh_ada: Adaptive version of min_asinh.
min_cosh: A truncated shifted cosh function applied element-wise: pmin(cosh(para*x)-1, para2). Bounded and takes two parameters.
min_cosh_ada: Adaptive version of min_cosh.
min_exp: A truncated shifted exponential function applied element-wise: pmin(exp(para*x)-1, para2). Bounded and takes two parameters.
min_exp_ada: Adaptive version of min_exp.
min_log_pow: A truncated power on a log scale applied element-wise: pmin(log(1+x), para2)^para. Bounded and takes two parameters.
min_log_pow_ada: Adaptive version of min_log_pow.
min_pow: A truncated power function applied element-wise: pmin(x, para2)^para. Bounded and takes two parameters.
min_pow_ada: Adaptive version of min_pow.
min_sinh: A truncated sinh function applied element-wise: pmin(sinh(para*x), para2). Bounded and takes two parameters.
min_sinh_ada: Adaptive version of min_sinh.
min_softplus: A truncated shifted softplus function applied element-wise: pmin(log(1+exp(para*x))-log(2), para2). Bounded and takes two parameters.
min_softplus_ada: Adaptive version of min_softplus.
pow: A power function h(x)=x^para. Unbounded and takes two parameter. Equivalent to min_pow(x, para, Inf).
scad: Treating λ=para, γ=para2, the step-wise SCAD function applied element-wise: λx if x<=λ, or (2γλx-x^2-λ^2)/(2(γ-1)) if λ<x<γλ, or λ^2(γ+1)/2 otherwise. Bounded and takes two parameters, where para2 must be larger than 1, and will be set to 2 by default if not provided.
sinh: A sinh function h(x)=sinh(para*x). Unbounded and takes one parameter. Equivalent to min_sinh(x, para, Inf).
softplus: A shifted softplus function h(x)=log(1+exp(para*x))-log(2). Unbounded and takes one parameter. Equivalent to min_softplus(x, para, Inf).
tanh: A tanh function h(x)=tanh(para*x). Bounded and takes one parameter.
truncated_sin: A truncated sin function applied element-wise: sin(para*x) if para*x<=π/2, or 1 otherwise. Bounded and takes one parameter.
truncated_tan: A truncated tan function applied element-wise: tan(para*x) if para*x<=π/4, or 1 otherwise. Bounded and takes one parameter.

For the adaptive modes (names ending with "_ada"), h and hp are first applied to x without truncation. Then inside each column, values that are larger than the para2-th quantile will be truncated. The quantile is calculated using finite values only, and if no finite values exist the quantile is set to 1. For example, if mode == "min_pow_ada", para == 2, para2 == 0.4, the j-th column of the returned hx will be pmin(x[,j]^2, stats::quantile(x[,j]^2, 0.4)), and the j-th column of hpx will be 2*x[,j]*(x[,j] <= stats::quantile(x[,j]^2, 0.4)).

A function that returns a list containing hx=h(x) (element-wise) and hpx=hp(x) (element-wise derivative of h) when applied to a vector (for mode names not ending with "_ada" only) or a matrix x, with both of the results having the same shape as x.

get_h_hp("mcp", 2, 4)(0:10)
get_h_hp("min_log_pow", 1, log(1+3))(matrix(0:11, nrow=3))
get_h_hp("min_pow", 1.5, 3)(seq(0, 5, by=0.5))
get_h_hp("min_softplus")(matrix(seq(0, 2, by=0.1), nrow=7))

get_h_hp("min_log_pow_ada", 1, 0.4)(matrix(0:49, nrow=10))
get_h_hp("min_pow_ada", 2, 0.3)(matrix(0:49, nrow=10))
get_h_hp("min_softplus_ada", 2, 0.6)(matrix(seq(0, 0.49, by=0.01), nrow=10))