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test_linear_regression.R
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test_linear_regression.R
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library(testthat)
library(purrr)
source('./linear_regression.R')
# 1. Hypothesis function
context('Hypothesis')
test_that('Hypothesis function for linear regression returns correct values', {
# Test settings
matr <- matrix(c(1, 2, 3, 4), nrow = 2, byrow = T)
matr2 <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, byrow = T)
expect_equal(hypothesis(c(0, 0, 0), matr),
as.vector(matrix(c(0, 0), nrow = 1)))
expect_equal(hypothesis(c(1, 1, 1), matr),
as.vector(matrix(c(4, 8), nrow = 1)))
expect_equal(hypothesis(c(0, 0, 0, 0), matr2),
as.vector(matrix(c(0, 0), nrow = 1)))
expect_equal(hypothesis(c(1, 1, 1, 1), matr2),
as.vector(matrix(c(7, 16), nrow = 1)))
expect_equal(hypothesis(c(1, 2, 3, 4), matr2),
as.vector(t(c(1, 2, 3, 4)) %*% t(cbind(1, matr2))))
})
# 2. Cost function
context('Cost')
# Test settings
test_that('Cost function returns correct values', {
matr <- matrix(c(1, 2, 3, 4), nrow = 2, byrow = T)
theta <- c(0, 0, 0)
y <- c(0, 0)
m <- nrow(matr)
co <- sum((hypothesis(theta, matr) - y) ^ 2) / (2 * m)
expect_equal(cost(theta, matr, y),
co)
y <- c(1, 1)
co <- sum((hypothesis(theta, matr) - y) ^ 2) / (2 * m)
expect_equal(cost(theta, matr, y), co)
theta <- c(1, 1, 1, 1)
matr2 <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, byrow = T)
m <- nrow(matr2)
y <- c(2, 3)
co <- sum((hypothesis(theta, matr2) - y) ^ 2) / (2 * m)
expect_equal(cost(theta, matr2, y), co)
})
# 3. Residuals helper for gradient descent
context('Residuals')
test_that('Residuals are computed properly for different number of coefficients
in linear regression function', {
theta <- c(0, 0)
X <- matrix(c(1, 1, 1), nrow = 3)
y <- c(1, 1, 1)
h <- hypothesis(theta, X)
result <- h - y
expect_equal(res(theta, X, y),
result)
theta <- c(0, 0, 0)
X <- matrix(c(1, 1, 1, 1, 1, 1), nrow = 3)
y <- c(2, 2, 2)
h <- hypothesis(theta, X)
result <- h - y
expect_equal(res(theta, X, y),
result)
}) # All tests passed
# 4. Derivatives helper for gradient descent
context('Derivatives')
test_that('Derivatives are computed properly for one independent variable case', {
theta <- c(0, 0)
X <- matrix(c(2, 3, 4), nrow = 3)
y <- c(1, 1, 1)
r <- res(theta, X, y)
X_ones <- cbind(1, X)
obs <- numeric(nrow(X))
drvs <- numeric(length(theta))
# compute derivatives in a for loop, implementation uses matrices operations
for (i in 1:length(theta)) { # for every theta
for (j in 1:nrow(X_ones)) { # for every observation
obs[j] <- res(theta, X[j, ], y[j]) * X_ones[j, i]
}
drvs[i] <- sum(obs)
}
expect_equal(drvs, derivatives(theta, X, y))
})
test_that('Derivatives are computed properly for two independent variables case', {
theta <- c(0, 0, 0)
X <- matrix(c(2, 3, 4, 5, 6, 7), nrow = 3)
y <- c(2, 3, 1)
r <- res(theta, X, y)
X_ones <- cbind(1, X)
obs <- numeric(nrow(X))
drvs <- numeric(length(theta))
# compute derivatives in a for loop, implementation uses matrices operations
for (i in 1:length(theta)) { # for every theta
for (j in 1:nrow(X_ones)) { # for every observation
obs[j] <- res(theta, matrix(X[j, ], nrow = 1), y[j]) * X_ones[j, i]
}
drvs[i] <- sum(obs)
}
expect_equal(drvs, derivatives(theta, X, y))
})
# 5. Gradient descent
context('Gradient descent')
test_that('Gradient descent and cost are computed properly for one independent variable', {
theta <- c(0, 0)
X <- matrix(c(1, 2, 3), nrow = 3)
y <- c(5, 4, 2)
iter <- 2
cost_vals <- numeric(iter)
m <- nrow(X)
alpha <- 0.01
for (i in 1:iter) {
cost_vals[i] <- cost(theta, X, y)
theta <- theta - alpha / m * derivatives(theta, X, y)
}
expect_equal(gradient_descent(c(0, 0), X, y, alpha, iter),
list(theta = theta, cost_vals = cost_vals))
})
test_that('Gradient descent and cost are computed properly for two independent variables', {
theta <- c(0, 0, 0)
X <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 3)
y <- c(5, 4, 2)
iter <- 5
cost_vals <- numeric(iter)
m <- nrow(X)
alpha <- 0.01
for (i in 1:iter) {
cost_vals[i] <- cost(theta, X, y)
theta <- theta - (alpha / m) * derivatives(theta, X, y)
}
expect_equal(gradient_descent(c(0, 0, 0), X, y, alpha, iter),
list(theta = theta, cost_vals = cost_vals))
})
context('Feature scaling - standarization')
test_that('Two features are standarized properly', {
X <- matrix(c(100, 250, 37, 2, 8, 6), nrow = 3)
sds <- apply(X, 2, sd)
means <- apply(X, 2, mean)
standarized_X <- X
for (i in 1:ncol(X)) {
standarized_X[, i] <- (X[, i] - means[i]) / sds[i]
}
result <- list(stand_feats = standarized_X, means = means, stds = sds)
expect_equal(standarize_features(X),
result)
})
test_that('Three features are standarized properly', {
X <- matrix(c(700, 200, 100, 150, 30, 400, 5, 6, 2), nrow = 3)
sds <- apply(X, 2, sd)
means <- apply(X, 2, mean)
standarized_X <- X
for (i in 1:ncol(X)) {
standarized_X[, i] <- (X[, i] - means[i]) / sds[i]
}
result <- list(stand_feats = standarized_X, means = means, stds = sds)
expect_equal(standarize_features(X),
result)
})