get_h_hp: Generator of h and hp (derivative of h) functions.
In genscore: Generalized Score Matching Estimators
get_h_hp R Documentation
Generator of h and hp (derivative of h) functions.
Description
Generator of h and hp (derivative of h) functions.
Usage
get_h_hp(mode, para = NULL, para2 = NULL)
Arguments
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.
Details
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.
asinhAn asinh function \boldsymbol{h}(\boldsymbol{x})=\mathrm{asinh}(\mathrm{para}\cdot\boldsymbol{x})=\log\left(\mathrm{para}\cdot\boldsymbol{x}+\sqrt{(\mathrm{para}\cdot\boldsymbol{x})^2+1}\right). Unbounded and takes one parameter. Equivalent to min_asinh(x, para, Inf).
coshA shifted cosh function \boldsymbol{h}(\boldsymbol{x})=\cosh(\mathrm{para}\cdot\boldsymbol{x})-1. Unbounded and takes one parameter. Equivalent to min_cosh(x, para, Inf).
expA shifted exponential function \boldsymbol{h}(\boldsymbol{x})=\exp(\mathrm{para}\cdot\boldsymbol{x})-1. Unbounded and takes one parameter. Equivalent to min_exp(x, para, Inf).
identityThe identity function \boldsymbol{h}(\boldsymbol{x})=\boldsymbol{x}. Unbounded and does not take any parameter. Equivalent to pow(x, 1) or min_pow(x, 1, Inf).
log_powA power function on a log scale \boldsymbol{h}(\boldsymbol{x})=\log(1+\boldsymbol{x})^{\mathrm{para}}. Unbounded and takes one parameter. Equivalent to min_log_pow(x, para, Inf).
mcpTreating \lambda=para, \gamma=para2, the step-wise MCP function applied element-wise: \lambda x-x^2/(2\gamma) if x\leq\lambda\gamma, or \gamma\lambda^2/2 otherwise. Bounded and takes two parameters.
min_asinhA truncated asinh function applied element-wise: \min(\mathrm{asinh}(\mathrm{para}\cdot\boldsymbol{x}),\mathrm{para}_2). Bounded and takes two parameters.
min_asinh_adaAdaptive version of min_asinh.
min_coshA truncated shifted cosh function applied element-wise: \min(\cosh(\mathrm{para}\cdot\boldsymbol{x})-1,\mathrm{para}_2). Bounded and takes two parameters.
min_cosh_adaAdaptive version of min_cosh.
min_expA truncated shifted exponential function applied element-wise: \boldsymbol{h}(\boldsymbol{x})=\min(\exp(\mathrm{para}\cdot\boldsymbol{x})-1,\mathrm{para}_2). Bounded and takes two parameters.
min_exp_adaAdaptive version of min_exp.
min_log_powA truncated power on a log scale applied element-wise: \boldsymbol{h}(\boldsymbol{x})=\min(\log(1+\boldsymbol{x}),\mathrm{para}_2)^{\mathrm{para}}. Bounded and takes two parameters.
min_log_pow_adaAdaptive version of min_log_pow.
min_powA truncated power function applied element-wise: \boldsymbol{h}(\boldsymbol{x})=\min(\boldsymbol{x},\mathrm{para}_2)^{\mathrm{para}}. Bounded and takes two parameters.
min_pow_adaAdaptive version of min_pow.
min_sinhA truncated sinh function applied element-wise: \min(\sinh(\mathrm{para}\cdot\boldsymbol{x}),\mathrm{para}_2). Bounded and takes two parameters.
min_sinh_adaAdaptive version of min_sinh.
min_softplusA truncated shifted softplus function applied element-wise: \min(\log(1+\exp(\mathrm{para}\cdot\boldsymbol{x}))-\log(2),\mathrm{para}_2). Bounded and takes two parameters.
min_softplus_adaAdaptive version of min_softplus.
powA power function \boldsymbol{h}(\boldsymbol{x})=\boldsymbol{x}^{\mathrm{para}}. Unbounded and takes two parameter. Equivalent to min_pow(x, para, Inf).
scadTreating \lambda=para, \gamma=para2, the step-wise SCAD function applied element-wise: \lambda x if x\leq\lambda, or (2\gamma\lambda x-x^2-\lambda^2)/(2(\gamma-1)) if \lambda<x<\gamma\lambda, or \lambda^2(\gamma+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.
sinhA sinh function \boldsymbol{h}(\boldsymbol{x})=\sinh(\mathrm{para}\cdot\boldsymbol{x}). Unbounded and takes one parameter. Equivalent to min_sinh(x, para, Inf).
softplusA shifted softplus function \boldsymbol{h}(\boldsymbol{x})=\log(1+\exp(\mathrm{para}\cdot\boldsymbol{x}))-\log(2). Unbounded and takes one parameter. Equivalent to min_softplus(x, para, Inf).
tanhA tanh function \boldsymbol{h}(\boldsymbol{x})=\tanh(\mathrm{para}\cdot\boldsymbol{x}). Bounded and takes one parameter.
truncated_sinA truncated sin function applied element-wise: \sin(\mathrm{para}\cdot x) if \mathrm{para}\cdot x\leq\pi/2, or 1 otherwise. Bounded and takes one parameter.
truncated_tanA truncated tan function applied element-wise: \tan(\mathrm{para}\cdot x) if \mathrm{para}\cdot x\leq\pi/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)).
Value
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.
Examples
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))
genscore documentation built on May 31, 2023, 6:28 p.m.
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| get_h_hp | R Documentation |
Generator of h and hp (derivative of h) functions.
Description
Generator of h and hp (derivative of h) functions.
Usage
get_h_hp(mode, para = NULL, para2 = NULL)
Arguments
mode |
A string, see details. |
para |
May be optional. A number, the first parameter. Default to |
para2 |
May be optional. A number, the second parameter. If |
Details
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.
asinhAn asinh function
\boldsymbol{h}(\boldsymbol{x})=\mathrm{asinh}(\mathrm{para}\cdot\boldsymbol{x})=\log\left(\mathrm{para}\cdot\boldsymbol{x}+\sqrt{(\mathrm{para}\cdot\boldsymbol{x})^2+1}\right). Unbounded and takes one parameter. Equivalent tomin_asinh(x, para, Inf).coshA shifted cosh function
\boldsymbol{h}(\boldsymbol{x})=\cosh(\mathrm{para}\cdot\boldsymbol{x})-1. Unbounded and takes one parameter. Equivalent tomin_cosh(x, para, Inf).expA shifted exponential function
\boldsymbol{h}(\boldsymbol{x})=\exp(\mathrm{para}\cdot\boldsymbol{x})-1. Unbounded and takes one parameter. Equivalent tomin_exp(x, para, Inf).identityThe identity function
\boldsymbol{h}(\boldsymbol{x})=\boldsymbol{x}. Unbounded and does not take any parameter. Equivalent topow(x, 1)ormin_pow(x, 1, Inf).log_powA power function on a log scale
\boldsymbol{h}(\boldsymbol{x})=\log(1+\boldsymbol{x})^{\mathrm{para}}. Unbounded and takes one parameter. Equivalent tomin_log_pow(x, para, Inf).mcpTreating
\lambda=para,\gamma=para2, the step-wise MCP function applied element-wise:\lambda x-x^2/(2\gamma)ifx\leq\lambda\gamma, or\gamma\lambda^2/2otherwise. Bounded and takes two parameters.min_asinhA truncated asinh function applied element-wise:
\min(\mathrm{asinh}(\mathrm{para}\cdot\boldsymbol{x}),\mathrm{para}_2). Bounded and takes two parameters.min_asinh_adaAdaptive version of
min_asinh.min_coshA truncated shifted cosh function applied element-wise:
\min(\cosh(\mathrm{para}\cdot\boldsymbol{x})-1,\mathrm{para}_2). Bounded and takes two parameters.min_cosh_adaAdaptive version of
min_cosh.min_expA truncated shifted exponential function applied element-wise:
\boldsymbol{h}(\boldsymbol{x})=\min(\exp(\mathrm{para}\cdot\boldsymbol{x})-1,\mathrm{para}_2). Bounded and takes two parameters.min_exp_adaAdaptive version of
min_exp.min_log_powA truncated power on a log scale applied element-wise:
\boldsymbol{h}(\boldsymbol{x})=\min(\log(1+\boldsymbol{x}),\mathrm{para}_2)^{\mathrm{para}}. Bounded and takes two parameters.min_log_pow_adaAdaptive version of
min_log_pow.min_powA truncated power function applied element-wise:
\boldsymbol{h}(\boldsymbol{x})=\min(\boldsymbol{x},\mathrm{para}_2)^{\mathrm{para}}. Bounded and takes two parameters.min_pow_adaAdaptive version of
min_pow.min_sinhA truncated sinh function applied element-wise:
\min(\sinh(\mathrm{para}\cdot\boldsymbol{x}),\mathrm{para}_2). Bounded and takes two parameters.min_sinh_adaAdaptive version of
min_sinh.min_softplusA truncated shifted softplus function applied element-wise:
\min(\log(1+\exp(\mathrm{para}\cdot\boldsymbol{x}))-\log(2),\mathrm{para}_2). Bounded and takes two parameters.min_softplus_adaAdaptive version of
min_softplus.powA power function
\boldsymbol{h}(\boldsymbol{x})=\boldsymbol{x}^{\mathrm{para}}. Unbounded and takes two parameter. Equivalent tomin_pow(x, para, Inf).scadTreating
\lambda=para,\gamma=para2, the step-wise SCAD function applied element-wise:\lambda xifx\leq\lambda, or(2\gamma\lambda x-x^2-\lambda^2)/(2(\gamma-1))if\lambda<x<\gamma\lambda, or\lambda^2(\gamma+1)/2otherwise. Bounded and takes two parameters, wherepara2must be larger than 1, and will be set to 2 by default if not provided.sinhA sinh function
\boldsymbol{h}(\boldsymbol{x})=\sinh(\mathrm{para}\cdot\boldsymbol{x}). Unbounded and takes one parameter. Equivalent tomin_sinh(x, para, Inf).softplusA shifted softplus function
\boldsymbol{h}(\boldsymbol{x})=\log(1+\exp(\mathrm{para}\cdot\boldsymbol{x}))-\log(2). Unbounded and takes one parameter. Equivalent tomin_softplus(x, para, Inf).tanhA tanh function
\boldsymbol{h}(\boldsymbol{x})=\tanh(\mathrm{para}\cdot\boldsymbol{x}). Bounded and takes one parameter.truncated_sinA truncated sin function applied element-wise:
\sin(\mathrm{para}\cdot x)if\mathrm{para}\cdot x\leq\pi/2, or 1 otherwise. Bounded and takes one parameter.truncated_tanA truncated tan function applied element-wise:
\tan(\mathrm{para}\cdot x)if\mathrm{para}\cdot x\leq\pi/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)).
Value
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.
Examples
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))
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