Linear-model based prediction

This script fits linear models using Lasso and Ridge regression and summarizes their prediction performance This script is written in the "outcome-oriented" style, demonstrating dynamic input, grouped output and step dependencies.


In [2]:
[global]
parameter: beta = [3, 1.5, 0, 0, 2, 0, 0, 0]
id = [x+1 for x in range(5)]
ridge_result = [f'data_{x}.ridge.mse.csv' for x in id]
lasso_result = [f'data_{x}.lasso.mse.csv' for x in id]

In [3]:
# Simulate sparse data-sets
[simulation]
depends: R_library("MASS>=7.3")
parameter: N = (40, 200) # training and testing samples
parameter: rstd = 3
input: for_each = 'id'
output: [(f"data_{x}.train.csv", f"data_{x}.test.csv") for x in id], group_by = 2
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]
parameter: nfolds = 5
depends: sos_step('simulation'), R_library("glmnet>=2.0")
input: dynamic(paths([(f"data_{x}.train.csv", f"data_{x}.test.csv") for x in id])), group_by = 2
output: [(f"data_{x}.ridge.predicted.csv", f"data_{x}.ridge.coef.csv") for x in id], group_by = 2
R: expand = "${ }"
  train = read.csv(${_input[0]:r}, header = F)
  test = read.csv(${_input[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]
parameter: nfolds = 5
depends: sos_step('simulation'), Py_Module("sklearn>=0.18.1"), Py_Module("numpy>=1.6.1"), Py_Module("scipy>=0.9")
input: dynamic(paths([(f"data_{x}.train.csv", f"data_{x}.test.csv") for x in id])), group_by = 2
output: [(f"data_{x}.lasso.predicted.csv", f"data_{x}.lasso.coef.csv") for x in id], group_by = 2
python: expand = "${ }"
  import numpy as np
  from sklearn.linear_model import LassoCV
  train = np.genfromtxt(${_input[0]:r}, delimiter = ",")
  test = np.genfromtxt(${_input[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_core]
parameter: input_files = list
parameter: output_files = list
input: dynamic(input_files), group_by = 3
output: output_files, group_by = 1
R: expand = "${ }", stderr = False
  b = c(${paths(beta):,})
  Ytruth = as.matrix(read.csv(${_input[0]:r}, header = F)[,-1]) %*% b
  Ypred = scan(${_input[1]:r})
  prediction_mse = mean((Ytruth - Ypred)^2)
  betahat = scan(${_input[2]:r})
  estimation_mse = mean((betahat - b) ^ 2)
  cat(paste(prediction_mse, estimation_mse), file = ${_output:r})

In [7]:
[evaluation_lasso]
depends: sos_step('simulation'), sos_step('lasso')
input_files = paths([(f"data_{x}.test.csv", f"data_{x}.lasso.predicted.csv", f"data_{x}.lasso.coef.csv") for x in id])
output: lasso_result 
sos_run("evaluation_core", input_files = input_files, output_files = lasso_result)

In [8]:
[evaluation_ridge]
depends: sos_step('simulation'), sos_step('ridge')
input_files = paths([(f"data_{x}.test.csv", f"data_{x}.ridge.predicted.csv", f"data_{x}.ridge.coef.csv") for x in id])
output: ridge_result 
sos_run("evaluation_core", input_files = input_files, output_files = ridge_result)

In [9]:
[default]
depends: sos_step('evaluation_lasso'), sos_step('evaluation_ridge')
output: lasso_result, ridge_result

In [ ]:
%sosrun