In [2]:
[global]
parameter: beta = [3, 1.5, 0, 0, 2, 0, 0, 0]
ridge_result = [f'data_{x+1}.ridge.mse.csv' for x in range(5)]
lasso_result = [f'data_{x+1}.lasso.mse.csv' for x in range(5)]
In [3]:
# Simulate sparse data-sets
[simulation: provides = ["data_{id}.train.csv", "data_{id}.test.csv"]]
depends: R_library("MASS>=7.3")
parameter: N = (40, 200) # training and testing samples
parameter: rstd = 3
output: f"data_{id}.train.csv", f"data_{id}.test.csv"
R: expand = "${ }"
set.seed(${id})
N = sum(c(${paths(N):,}))
p = length(c(${paths(beta):,}))
X = MASS::mvrnorm(n = N, rep(0, p), 0.5^abs(outer(1:p, 1:p, FUN = "-")))
Y = X %*% c(${paths(beta):,}) + rnorm(N, mean = 0, sd = ${rstd})
Xtrain = X[1:${N[0]},]; Xtest = X[(${N[0]}+1):(${N[0]}+${N[1]}),]
Ytrain = Y[1:${N[0]}]; Ytest = Y[(${N[0]}+1):(${N[0]}+${N[1]})]
write.table(cbind(Ytrain, Xtrain), ${_output[0]:r}, row.names = F, col.names = F, sep = ',')
write.table(cbind(Ytest, Xtest), ${_output[1]:r}, row.names = F, col.names = F, sep = ',')
In [4]:
# Ridge regression model implemented in R
# Build predictor via cross-validation and make prediction
[ridge: provides = ["data_{id}.ridge.predicted.csv", "data_{id}.ridge.coef.csv"]]
parameter: nfolds = 5
depends: f"data_{id}.train.csv", f"data_{id}.test.csv", R_library("glmnet>=2.0")
output: f"data_{id}.ridge.predicted.csv", f"data_{id}.ridge.coef.csv"
R: expand = "${ }"
train = read.csv(${_depends[0]:r}, header = F)
test = read.csv(${_depends[1]:r}, header = F)
model = glmnet::cv.glmnet(as.matrix(train[,-1]), train[,1], family = "gaussian", alpha = 0, nfolds = ${nfolds}, intercept = F)
betahat = as.vector(coef(model, s = "lambda.min")[-1])
Ypred = predict(model, as.matrix(test[,-1]), s = "lambda.min")
write.table(Ypred, ${_output[0]:r}, row.names = F, col.names = F, sep = ',')
write.table(betahat, ${_output[1]:r}, row.names = F, col.names = F, sep = ',')
In [5]:
# LASSO model implemented in Python
# Build predictor via cross-validation and make prediction
[lasso: provides = ["data_{id}.lasso.predicted.csv", "data_{id}.lasso.coef.csv"]]
parameter: nfolds = 5
depends: f"data_{id}.train.csv", f"data_{id}.test.csv", Py_Module("sklearn>=0.18.1"), Py_Module("numpy>=1.6.1"), Py_Module("scipy>=0.9")
output: f"data_{id}.lasso.predicted.csv", f"data_{id}.lasso.coef.csv"
python: expand = "${ }"
import numpy as np
from sklearn.linear_model import LassoCV
train = np.genfromtxt(${_depends[0]:r}, delimiter = ",")
test = np.genfromtxt(${_depends[1]:r}, delimiter = ",")
model = LassoCV(cv = ${nfolds}, fit_intercept = False).fit(train[:,1:], train[:,1])
Ypred = model.predict(test[:,1:])
np.savetxt(${_output[0]:r}, Ypred)
np.savetxt(${_output[1]:r}, model.coef_)
In [6]:
# Evaluate predictors by calculating mean squared error
# of prediction vs truth (first line of output)
# and of betahat vs truth (2nd line of output)
[evaluation: provides = 'data_{id}.{method}.mse.csv']
depends: f"data_{id}.test.csv", f"data_{id}.{method}.predicted.csv",
f"data_{id}.{method}.coef.csv"
R: expand = "${ }", stderr = False
b = c(${paths(beta):,})
Ytruth = as.matrix(read.csv(${_depends[0]:r}, header = F)[,-1]) %*% b
Ypred = scan(${_depends[1]:r})
prediction_mse = mean((Ytruth - Ypred)^2)
betahat = scan(${_depends[2]:r})
estimation_mse = mean((betahat - b) ^ 2)
cat(paste(prediction_mse, estimation_mse), file = ${_output:r})
In [7]:
[get-pandoc-css: provides = 'pandoc.css']
download:
https://raw.githubusercontent.com/vatlab/sos-docs/master/css/pandoc.css
In [8]:
# Compute and report error estimates
# in HTML table format
[default]
depends: ridge_result, lasso_result, "pandoc.css", executable('pandoc')
import numpy as np
ridge_summary = np.mean(np.array([sum([x.strip().split() for x in open(f).readlines()], []) for f in ridge_result], dtype = float).T, axis = 1).tolist()
lasso_summary = np.mean(np.array([sum([x.strip().split() for x in open(f).readlines()], []) for f in lasso_result], dtype = float).T, axis = 1).tolist()
report: expand = "${ }", output = "report.md"
%% Comparison summary
| Method | Avg. Estimation Error | Avg. Prediction Error |
|:------:|:-------:|:-------:|
| LASSO | ${lasso_summary[1]} | ${lasso_summary[0]} |
| Ridge | ${ridge_summary[1]} | ${ridge_summary[0]} |
pandoc: input = "report.md", output = "report.html", args = '{input:q} --css pandoc.css --self-contained -s --output {output:q}'
In [ ]:
%sosrun
In [ ]:
%preview report.html