rmse

Builtin index · Statistics & ML

result = rmse(actual, predicted)

Input: actual, predicted · Output: result

What it is

The regression-error trio, each taking a length-N vector of true values actual and a length-N vector of predictions predicted, and returning a single number: mae the mean absolute error, mse the mean squared error, rmse its square root. .score(X, y) on a model already gives R-squared; these three give the plain error numbers instead, in the target's own units for mae and rmse (mse is in squared units).

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = rmse(actual, predicted)`	`actual` vector or numbernot documented yet `predicted` vector or numbernot documented yet	`result` scalar or Num	Returns a scalar `Num`.

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

n = 200
k = 8
m = 60
truth = zeros(n)
for j in (11, 27, 48, 76, 103, 140, 168, 191)
    truth[j] = 1
end for

A = randn(m, n, seed = 12) / sqrt(m)
y = A * truth
r = cs_recover(A, y, method = "omp", sparsity = k)

print("{m} measurements, {n} unknowns, {k} non-zeros")
print("support found:  {r.support}")
print("recovery error: {round(rmse(truth, r.x), 8)}")

plot(0 to n - 1, truth, color = "#0f172a", width = 2, label = "truth")
scatter(0 to n - 1, r.x, color = "#e11d48", label = "recovered")
legend()
title("8 spikes from 60 measurements")

output

60 measurements, 200 unknowns, 8 non-zeros
support found:  [11, 27, 48, 76, 103, 140, 168, 191]
recovery error: 0
· plot: figure 1 (200 points)
· scatter: figure 2 (200 points)

from compressed-sensing

truth = zeros(60)
meas = zeros(60)
for t = 0 to 59
    truth[t] = 0.5 * t
    meas[t] = truth[t] + randn() * 2
end for

F = [1, 0, 1, 1] as matrix(2, 2)     # column-major: rows are [1, 1] and [0, 1]

Q = [0.01, 0, 0, 0.01] as matrix(2, 2)
H = [1, 0] as matrix(1, 2)
R = [4] as matrix(1, 1)

s = kalman_init([0, 0], [10, 0, 0, 10] as matrix(2, 2))
est = zeros(60)
for t = 0 to 59
    s = s.predict(F, Q)
    s = s.update(H, [meas[t]], R)
    est[t] = s.estimate()[0]
end for

print("measurement error: {round(rmse(truth, meas), 3)}")
print("filtered error:    {round(rmse(truth, est), 3)}")
scatter(0 to 59, meas, color = "#94a3b8", label = "measured")
plot(0 to 59, truth, color = "#0f172a", label = "truth")
plot(0 to 59, est, color = "#e11d48", width = 2, label = "Kalman")
legend()
title("constant-velocity Kalman filter")

output

measurement error: 2.197
filtered error:    1.193
· scatter: figure 11 (60 points)
· plot: figure 12 (60 points)
· plot: figure 13 (60 points)

from statistics-ml

How it works

mae(actual, predicted) / mse(actual, predicted) / rmse(actual, predicted) — the standard regression-error trio. .score(X, y) on a _model handle already gives R^2; these are the companion plain-number metrics for scripts that want the error in the target's own units (mae/rmse) or need mse directly (e.g. as a loss to compare against gradient_boosting_model's own train_mse_history).

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.

rmse

What it is

Overloads

Examples

How it works

See also