Bayesian Hierarchical Additive Models
Home Page: https://boyiguo1.github.io/BHAM
License: Other
The goal of BHAM is to fit Bayesian hierarchical generalized additive models, and provide ancillary functions for high-dimensional model specification, model summary, variable selection, curve fitting.
The development version from GitHub with:
# install.packages("devtools")
devtools::install_github("boyiguo1/BHAM")Please visit the vignettes for a quick introduction
We rely on some of the c functions from the library survival for constructing counting process. However, these functions are internal. Without spending a lot of time, we will just to copy the internal functions to the current project
To develop the curve plotting functions
Parameters:
Test:
When running simulation with 190b084, errors are reported for bacoxph.
Error message for bacoxph is
initial values lead to overflow or underflow of the exp function
The minimum reproducible example is
library(tidyverse)
library(mgcv)
#> Loading required package: nlme
#>
#> Attaching package: 'nlme'
#> The following object is masked from 'package:dplyr':
#>
#> collapse
#> This is mgcv 1.8-38. For overview type 'help("mgcv-package")'.
library(BHAM)
library(BhGLM)
#>
#> Attaching package: 'BhGLM'
#> The following objects are masked from 'package:BHAM':
#>
#> De, mde, mt, NegBin, Student
library(survival)
library(simsurv)
# Fixed Parameters --------------------------------------------------------
# * Basic Parameters --------------------------------------------------------
k <- 10 # Smoothing function degrees
n_test <- 1000 # Training set Sample size
n_train <- 200
p <- c(4, 10, 50, 100, 200)[3]
rho <- c(0, 0.5)[1]
pi_cns <- c(0.15, 0.3, 0.4)[1]
# * Survival Parameters ---------------------------------------------------
shape.t <- 1.2 # Shape par of hazard distribution
scale.t <- 1 # Scale par of hazard distribution
shape.c <- 0.8 # Shape par of censoring distribution
# * Derived Parameters
n_total <- n_train + n_test
# Functions ---------------------------------------------------
# * Nonliner Functions ----------------------------------------------------
f_1 <- function(x) (x+1)^2/10
f_2 <- function(x) exp(x+1)/100
f_3 <- function(x) 3*sin(x)/20
f_4 <- function(x) (1.4*x+0.5)/10Auto-regressive correlation matrix
@param p integer, the number of dimension
@param rho double, range between 0-1, 0 means mutually independent, 1 means complete correlated
@return A p*p dimension matrix
@examples
p <- 5
rho <- 0.8
X_mat <- MASS::mvrnorm(n=100, rep(0, p), AR(p, rho))
AR <- function(p, rho){
rho^abs(outer(1:p,1:p,"-"))
}
it <- 1
set.seed(it)
# Helper Functions --------------------------------------------------------Estimate the Weibull scale parameter for controlled censoring proportion
find_censor_parameter <- function(
lambda, pi.cen,
shape_hazard, shape_censor
){
# Estimate the density function of the linear predictor
dens <- density(lambda, bw = "nrd0",na.rm=TRUE)
x<-dens$x
y<-dens$y
y.loess <-loess(y ~ x,span=0.1)
density.fun.lambda<-function(x){
pred.y <- predict(y.loess, newdata=x)
return(pred.y)
}
integration_over_time <- function(
u, # Different values of lambda
# Arguments for integration
theta, shape_hazard, shape_censor
){
ret <- integrate( # Start (Integrate of time)
f = function(ti, theta, alpha.t, alpha.c){
lambda.i<-u
part1<-density.fun.lambda(lambda.i)
part2<-dweibull(ti,alpha.c,theta)
part3<-exp(-(ti/lambda.i)^alpha.t)
return(part1*part2*part3)
},
0, Inf,
theta = theta, alpha.t = shape_hazard, alpha.c = shape_censor
)
return(ret$value)
}
censor.prop <- function(theta, p, shape_hazard, shape_censor){
cen.P <- integrate( # Start (Integrate of lambda)
function(u, theta, shape_hazard, shape_censor){
sapply(u, integration_over_time,
# Arguments of integration_over_time
theta = theta, shape_hazard = shape_hazard, shape_censor = shape_censor
)
},
# Limits of integration
lower = min(lambda), upper = max(lambda),
## Arguments for integration function
theta = theta, shape_hazard = shape_hazard, shape_censor = shape_censor
)$value # End(int of lambda)
return(cen.P-p)
}
theta<-uniroot(censor.prop, interval = c(0.1,200),
## Argument for censor.prop
p = pi.cen, shape_hazard = shape_hazard, shape_censor = shape_censor,
tol=0.00000001)$root
return(theta)
}Create spline formula for high-dimension applications
create_HD_formula <- function(formula, data, spl_df, rm_overlap = TRUE, verbose=T){
if(missing(formula) & missing(data))
stop("Either formula or data must be provided. The response variable of the model is not supplied.")
if(missing(formula)){
if(!is.data.frame(data)) data <- data.frame(data)
formula = DF2formula(data)
}
if(!missing(data)){
warning("Both formula and dat provided, dat is ignored.")
warning("Please consider use the function DF2formula and update to improve your formula.")
}
if(missing(spl_df)) {
warning(" No additional spline terms supplied")
} else {
# Manipulate spl_df
sp_trm <- spl_df %>%
dplyr::filter(Func!="") %>% # Removing unnecessary terms
glue::glue_data("{Func}( {Var}{ifelse(is.na(Args)||Args=='', '', paste0(',', Args))})") %>%
paste(collapse = " + ")
sp_trm <- paste0("~ . + " , sp_trm)
}
# Adding Spline Terms
ret <- update(formula, sp_trm)
if(verbose){
cat("Create formula:\n")
print(ret)
}
return(ret)
}
# * Generate Data -------------------------------------------------
x_all <- MASS::mvrnorm(n_train+n_test, rep(0, p), AR(p, rho)) %>%
data.frame
eta_all <- with(x_all, f_1(X1) + f_2(X2) + f_3(X3) + f_4(X4))
dat_all <- simsurv::simsurv(dist = "weibull",
lambdas = scale.t,
gammas = shape.t,
x = data.frame(eta = eta_all) ,
beta = c(eta = 1)) %>%
data.frame( x_all, eta = eta_all, .)
train_dat <- dat_all[1:n_train, ]
test_dat <- dat_all[(n_train+1):n_total, ]
## Censoring Distribution, Weibull(alpha.c, scale.p)
scale.p <- find_censor_parameter(lambda = exp(-1*train_dat$eta/shape.t),
pi.cen = pi_cns,
shape_hazard = shape.t, shape_censor = shape.c)
train_dat <- train_dat %>%
data.frame(
c_time = rweibull(n = n_train, shape = shape.c, scale = scale.p)
) %>%
mutate(
cen_ind = (c_time < eventtime),
status = (!cen_ind)*1
) %>%
rowwise() %>%
mutate(time = min(c_time, eventtime)) %>%
ungroup()
# Fit Models------------------------------------------------------------------
# * Spline Specification --------------------------------------------------
mgcv_df <- data.frame(
Var = grep("X", names(train_dat), value = TRUE),
Func = "s",
Args = paste0("bs='cr', k=", k)
)
train_sm_dat <- construct_smooth_data(mgcv_df, train_dat)
train_smooth_data <- train_sm_dat$data
test_sm_dat <- BHAM::make_predict_dat(train_sm_dat$Smooth, dat = test_dat)
bacox_raw_mdl <- bacoxph(Surv(time, event = status) ~ ., data = data.frame(time = train_dat$time, status = train_dat$status,
train_smooth_data),
prior = mde(), group = make_group(names(train_smooth_data)))
s0_seq <- seq(0.005, 0.1, length.out = 20) # TODO: need to be optimized
cv_res <- tune.bgam(bacox_raw_mdl, nfolds = 5, s0= s0_seq, verbose = FALSE)
#> Fitting ncv*nfolds = 5 models:
#> Error in coxph(formula = formula, init = init, weights = weights, control = coxph.control(iter.max = 1, : initial values lead to overflow or underflow of the exp function
Created on 2022-01-02 by the reprex package (v2.0.1)
The group updating algorithm via the argument method.coef uses offset when fitting coxph internally, which reserves the wrong offset when outputting the final model.
When we use nested cross-validation in cv.bgam via the argument ncv = 10, the outcome is not organized well and misaligned due to the default vector concatenation.
cv.bgam(mdl, ncv = 10)
mdl3 <- bgam(y~.-y,
data = data.frame(train_smooth_data, y = dat$y), family = "binomial", prior = mt(df=Inf), group = make_group(names(train_smooth_data), penalize_null = FALSE))We need to rename the bases in align with construct_smooth_data, as var1.nullX and var1.penX
smoothCon()[[1]] still makes senseI was using some packages from tidyverse to ease the programming. For example, I imported %>% function from magrittr package. However, in the DESCRIPTION file, I imported the whole magrittr package. Some other examples include glue_data from glue package, unbglue_unnest from unglue package. Is there any way to include one function instead of the whole package.
When running simulation with 190b084, errors are reported for bamlasso(family = "cox")
Error message for bamlasso is
Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 't': 'data' must be of a vector type, was 'NULL'
The minimum reproducible example is
library(tidyverse)
library(mgcv)
#> Loading required package: nlme
#>
#> Attaching package: 'nlme'
#> The following object is masked from 'package:dplyr':
#>
#> collapse
#> This is mgcv 1.8-38. For overview type 'help("mgcv-package")'.
library(BHAM)
library(survival)
library(simsurv)
# Fixed Parameters --------------------------------------------------------a
# * Basic Parameters --------------------------------------------------------
k <- 10 # Smoothing function degrees
n_test <- 1000 # Training set Sample size
n_train <- 200
p <- c(4, 10, 50, 100, 200)[1]
rho <- c(0, 0.5)[1]
pi_cns <- c(0.15, 0.3, 0.4)[1]
# * Survival Parameters ---------------------------------------------------
shape.t <- 1.2 # Shape par of hazard distribution
scale.t <- 1 # Scale par of hazard distribution
shape.c <- 0.8 # Shape par of censoring distribution
# * Derived Parameters
n_total <- n_train + n_test
# Functions ---------------------------------------------------
# * Nonliner Functions ----------------------------------------------------
f_1 <- function(x) (x+1)^2/10
f_2 <- function(x) exp(x+1)/100
f_3 <- function(x) 3*sin(x)/20
f_4 <- function(x) (1.4*x+0.5)/10Auto-regressive correlation matrix
@param p integer, the number of dimension
@param rho double, range between 0-1, 0 means mutually independent, 1 means complete correlated
@return A p*p dimension matrix
@examples
p <- 5
rho <- 0.8
X_mat <- MASS::mvrnorm(n=100, rep(0, p), AR(p, rho))
AR <- function(p, rho){
rho^abs(outer(1:p,1:p,"-"))
}
it <- 1
set.seed(it)
# Helper Functions --------------------------------------------------------Estimate the Weibull scale parameter for controlled censoring proportion
find_censor_parameter <- function(
lambda, pi.cen,
shape_hazard, shape_censor
){
# Estimate the density function of the linear predictor
dens <- density(lambda, bw = "nrd0",na.rm=TRUE)
x<-dens$x
y<-dens$y
y.loess <-loess(y ~ x,span=0.1)
density.fun.lambda<-function(x){
pred.y <- predict(y.loess, newdata=x)
return(pred.y)
}
integration_over_time <- function(
u, # Different values of lambda
# Arguments for integration
theta, shape_hazard, shape_censor
){
ret <- integrate( # Start (Integrate of time)
f = function(ti, theta, alpha.t, alpha.c){
lambda.i<-u
part1<-density.fun.lambda(lambda.i)
part2<-dweibull(ti,alpha.c,theta)
part3<-exp(-(ti/lambda.i)^alpha.t)
return(part1*part2*part3)
},
0, Inf,
theta = theta, alpha.t = shape_hazard, alpha.c = shape_censor
)
return(ret$value)
}
censor.prop <- function(theta, p, shape_hazard, shape_censor){
cen.P <- integrate( # Start (Integrate of lambda)
function(u, theta, shape_hazard, shape_censor){
sapply(u, integration_over_time,
# Arguments of integration_over_time
theta = theta, shape_hazard = shape_hazard, shape_censor = shape_censor
)
},
# Limits of integration
lower = min(lambda), upper = max(lambda),
## Arguments for integration function
theta = theta, shape_hazard = shape_hazard, shape_censor = shape_censor
)$value # End(int of lambda)
return(cen.P-p)
}
theta<-uniroot(censor.prop, interval = c(0.1,200),
## Argument for censor.prop
p = pi.cen, shape_hazard = shape_hazard, shape_censor = shape_censor,
tol=0.00000001)$root
return(theta)
}Create spline formula for high-dimension applications
create_HD_formula <- function(formula, data, spl_df, rm_overlap = TRUE, verbose=T){
if(missing(formula) & missing(data))
stop("Either formula or data must be provided. The response variable of the model is not supplied.")
if(missing(formula)){
if(!is.data.frame(data)) data <- data.frame(data)
formula = DF2formula(data)
}
if(!missing(data)){
warning("Both formula and dat provided, dat is ignored.")
warning("Please consider use the function DF2formula and update to improve your formula.")
}
if(missing(spl_df)) {
warning(" No additional spline terms supplied")
} else {
# Manipulate spl_df
sp_trm <- spl_df %>%
dplyr::filter(Func!="") %>% # Removing unnecessary terms
glue::glue_data("{Func}( {Var}{ifelse(is.na(Args)||Args=='', '', paste0(',', Args))})") %>%
paste(collapse = " + ")
sp_trm <- paste0("~ . + " , sp_trm)
}
# Adding Spline Terms
ret <- update(formula, sp_trm)
if(verbose){
cat("Create formula:\n")
print(ret)
}
return(ret)
}
# * Generate Data -------------------------------------------------
x_all <- MASS::mvrnorm(n_train+n_test, rep(0, p), AR(p, rho)) %>%
data.frame
eta_all <- with(x_all, f_1(X1) + f_2(X2) + f_3(X3) + f_4(X4))
dat_all <- simsurv::simsurv(dist = "weibull",
lambdas = scale.t,
gammas = shape.t,
x = data.frame(eta = eta_all) ,
beta = c(eta = 1)) %>%
data.frame( x_all, eta = eta_all, .)
train_dat <- dat_all[1:n_train, ]
test_dat <- dat_all[(n_train+1):n_total, ]
## Censoring Distribution, Weibull(alpha.c, scale.p)
scale.p <- find_censor_parameter(lambda = exp(-1*train_dat$eta/shape.t),
pi.cen = pi_cns,
shape_hazard = shape.t, shape_censor = shape.c)
train_dat <- train_dat %>%
data.frame(
c_time = rweibull(n = n_train, shape = shape.c, scale = scale.p)
) %>%
mutate(
cen_ind = (c_time < eventtime),
status = (!cen_ind)*1
) %>%
rowwise() %>%
mutate(time = min(c_time, eventtime)) %>%
ungroup()
# Fit Models------------------------------------------------------------------
# * Spline Specification --------------------------------------------------
mgcv_df <- data.frame(
Var = grep("X", names(train_dat), value = TRUE),
Func = "s",
Args = paste0("bs='cr', k=", k)
)
train_sm_dat <- construct_smooth_data(mgcv_df, train_dat)
train_smooth_data <- train_sm_dat$data
test_sm_dat <- BHAM::make_predict_dat(train_sm_dat$Smooth, dat = test_dat)
bamlasso_raw_mdl <- bamlasso( x = train_smooth_data, y = Surv(train_dat$time, event = train_dat$status),
family = "cox", group = make_group(names(train_smooth_data)),
ss = c(0.04, 0.5))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 't': 'data' must be of a vector type, was 'NULL'Created on 2021-12-29 by the reprex package (v2.0.1)
sessioninfo::session_info()
#> ─ Session info 🛶 🕥 🛀🏽 ─────────────────────────────────────────────────
#> hash: canoe, ten-thirty, person taking bath: medium skin tone
#>
#> setting value
#> version R version 4.1.1 (2021-08-10)
#> os macOS Catalina 10.15.7
#> system x86_64, darwin17.0
#> ui X11
#> language (EN)
#> collate en_US.UTF-8
#> ctype en_US.UTF-8
#> tz America/Chicago
#> date 2021-12-29
#> pandoc 2.14.0.3 @ /Applications/RStudio.app/Contents/MacOS/pandoc/ (via rmarkdown)
#>
#> ─ Packages ───────────────────────────────────────────────────────────────────
#> package * version date (UTC) lib source
#> assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.1.0)
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#> ──────────────────────────────────────────────────────────────────────────────bglm_spline one predictor per group and compare to Lasso and bglmCurrently, the "design matrix" returned from contruct_smooth_data are named in the pattern var_name.baseX. However, such a naming convention doesn't help to distinguish the null space from the penalized space, which creates more problems during variable/function selection.
The naming convention should be a combination of var_name.nullX and var_name.penX. It also helps with creating groups.
We should be implementing the feature selection function for bglm_spline and bmlasso_spline model.
For bmlasso_spline model,
we can check the p or ptheta of the fitted model, and soft-thresholding to get which one would be selected in the model.
For bglm_spline, there could be two ways
p, like described for bmlasso_spline modelIn the commit 408874c
TODO:
shared_indicatormake_group as well as update.scale.p.group similar to the branch eff_hrd via 6244a7d/data/user/boyiguo1/bgam/sim_res_6244a7d/ . The simulation results is not fine-tuned. Create a new branch eff_hrd
Implement the new prior and updating algorithm according to the attached pdf.SS_GAM.pdf via 3270a96
Examine performance of the new algorithm with simulation
See Simulation Result at /data/user/boyiguo1/bgam/sim_res_3270a96/ . The simulation results is not fine-tuned.
Remove TODO(boyiguo1) message as inline comments
Pull request to main
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
An Open Source Machine Learning Framework for Everyone
Django
The Web framework for perfectionists with deadlines.
Laravel
A PHP framework for web artisans
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
Some thing interesting about web. New door for the world.
A server is a program made to process requests and deliver data to clients.
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
Some thing interesting about visualization, use data art
Some thing interesting about game, make everyone happy.
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
Microsoft
Open source projects and samples from Microsoft.
Google
Google ❤️ Open Source for everyone.
Alibaba
Alibaba Open Source for everyone
D3
Data-Driven Documents codes.
Tencent
China tencent open source team.