8 · Hyperparameter Optimisation & Model Selection · Hyperparameter Optimisation

Random search

Random search samples independent configurations and often explores important dimensions more effectively than a full Cartesian grid for the same budget. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.

Reference lessonPython exampleVisual explanation

Intuition first

What this concept means in practice

The practical value of Random search comes from understanding both the transformation and the boundary around it: what information is allowed to enter, what assumption is being made, and how you know the result is still valid after the transformation.

A beginner-friendly way to reason about it is to start with a tiny case where the correct result can be checked independently. Once the mechanism is clear, scale the exact same reasoning to larger tables, pipelines or models.

PurposeUse for medium/high-dimensional spaces when only some hyperparameters strongly matter.

MechanismSample configurations from probability distributions instead of enumerating a grid.

EvidenceInspect intermediate and final output; compare with an independent expectation.

Main cautionUse appropriate distributions; uniform sampling of a scale parameter can oversample large values.

Mechanism

Trace the operation from input to decision

Sample configurations from probability distributions instead of enumerating a grid.

1Input→

2Apply rule→

3Inspect state→

4Validate→

5Use result

Key rule

θ ~ search distribution

Visual explanation

Make the structure visible

The interactive view uses a concept-specific plot when the topic maps naturally to one; otherwise it uses a workflow view instead of leaving a broken placeholder.

Loading visual…

Practical example

Where you would use it

Draw learning rate log-uniformly from 1e-4–1e-1 and depth uniformly from 3–12 for 50 trials.

Use when

Use for medium/high-dimensional spaces when only some hyperparameters strongly matter.

Pitfall

What can make the result misleading

Watch out

Use appropriate distributions; uniform sampling of a scale parameter can oversample large values.

A useful diagnostic question is: Could the same code still run successfully if the analytical assumption were wrong? If yes, add an explicit validation check rather than relying on execution success.

Implementation

Miniature Python example

Keep the example small enough that you can inspect each stage manually.

Python

# Step 1 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from scipy.stats import loguniform
# Step 2 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.datasets import make_classification
# Step 3 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.linear_model import LogisticRegression
# Step 4 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.model_selection import RandomizedSearchCV

# Step 5 — Compute the right-hand expression and store its result in `X, y` for the next step.
X, y = make_classification(n_samples=120, n_features=6, random_state=4)
# Step 6 — Instantiate `search` with the chosen algorithm/configuration before fitting it to data.
search = RandomizedSearchCV(LogisticRegression(max_iter=1000), {"C": loguniform(1e-2, 1e2)}, n_iter=6, cv=3, random_state=4)
# Step 7 — Fit the model or transformer, learning its parameters from the supplied training data.
search.fit(X, y)
# Step 8 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · candidates tried:", len(search.cv_results_["params"]))
# Step 9 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 2 · best C:", round(search.best_params_["C"], 3))
# Step 10 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · best CV score:", round(search.best_score_, 3))

Expected / illustrative output

STEP 1 · candidates tried: 6
STEP 2 · best C: 1.545
STEP 3 · best CV score: 0.908

Implementation checklist

Before you move on

Can you state what data or object enters the operation?
Can you explain what changes and what must remain invariant?
Have you checked the result on a tiny case you can verify independently?
Have you considered the main failure mode described above?
Can the operation be reproduced from code/formulas and documented assumptions?