8 · Hyperparameter Optimisation & Model Selection · Hyperparameter Optimisation

Bayesian optimisation and TPE

Sequential model-based methods use earlier trials to focus future samples on promising regions while retaining exploration. 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 Bayesian optimisation and TPE 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 when each trial is expensive and the search space is structured.

MechanismFit a surrogate to previous trial results and choose new configurations that trade off exploitation with exploration. TPE models promising and non-promising regions separately.

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

Main cautionSurrogates can be misled by noisy CV objectives; repeated evaluation or robust objectives may help.

Mechanism

Trace the operation from input to decision

Fit a surrogate to previous trial results and choose new configurations that trade off exploitation with exploration. TPE models promising and non-promising regions separately.

1Input→

2Apply rule→

3Inspect state→

4Validate→

5Use result

Key rule

next θ = argmax acquisition(θ)

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.

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Practical example

Where you would use it

After ten initial trials, the optimiser concentrates learning-rate proposals near the best region while occasionally exploring alternatives.

Use when

Use when each trial is expensive and the search space is structured.

Pitfall

What can make the result misleading

Watch out

Surrogates can be misled by noisy CV objectives; repeated evaluation or robust objectives may help.

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

# Purpose: demonstrate Bayesian optimisation and TPE with a small, inspectable example.
# Follow the comments and printed stages to connect each operation with its result.
# Import the library or helper used in this example.
# Step 1 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.datasets import make_classification
# Import the library or helper used in this example.
# Step 2 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.linear_model import LogisticRegression
# Import the library or helper used in this example.
# Step 3 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.model_selection import GridSearchCV

# Store this intermediate value with a descriptive name for the next step.
# Step 4 — Compute the right-hand expression and store its result in `X,y` for the next step.
X,y = make_classification(n_samples=80,n_features=5,n_informative=3,random_state=7)
# Print this intermediate result so you can verify the workflow step by step.
# Step 5 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · Data:", X.shape, "positive rate:", round(y.mean(),2))
# Store this intermediate value with a descriptive name for the next step.
# Step 6 — Instantiate `search` with the chosen algorithm/configuration before fitting it to data.
search = GridSearchCV(LogisticRegression(max_iter=500), {"C":[0.1,1,10]}, cv=4, scoring="accuracy")
# Fit only on the training data so the model learns from allowed information.
# Step 7 — Fit the model or transformer, learning its parameters from the supplied training data.
search.fit(X,y)
# Print this intermediate result so you can verify the workflow step by step.
# Step 8 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 2 · Tried C values:", search.param_grid["C"])
# Print this intermediate result so you can verify the workflow step by step.
# Step 9 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · Best C:", search.best_params_["C"])
# Print this intermediate result so you can verify the workflow step by step.
# Step 10 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · Best CV accuracy:", round(search.best_score_,3))

Expected / illustrative output

STEP 1 · Data: (80, 5) positive rate: 0.5
STEP 2 · Tried C values: [0.1, 1, 10]
STEP 3 · Best C: 0.1
STEP 3 · Best CV accuracy: 0.925

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?