Explain and apply Candidate Elimination Algorithm for the given dataset

Candidate Elimination Algorithm:

The Candidate Elimination algorithm finds the version space consisting of all hypotheses consistent with the given training data.

It maintains two boundaries:

• S (Specific Boundary): most specific hypothesis
• G (General Boundary): most general hypothesis

These boundaries are updated after each training instance to eliminate inconsistent hypotheses.

Steps of the Algorithm:

1. Initialize S to most specific hypothesis:
   S = <ϕ, ϕ, ϕ, ϕ, ϕ, ϕ>
2. Initialize G to most general hypothesis:
   G = <?, ?, ?, ?, ?, ?>
3. For each training instance:
   • If positive, generalize S to include it and prune inconsistent hypotheses from G
   • If negative, specialize G to exclude it and remove inconsistent hypotheses from S

Applying to the Dataset

Instance 1 (Positive):

Sunny, Warm, Normal, Strong, Warm, Same → Yes

• Update S to:
  S1 = <Sunny, Warm, Normal, Strong, Warm, Same>
• G remains unchanged:
  G1 = <?, ?, ?, ?, ?, ?>

Instance 2 (Positive):

Sunny, Warm, High, Strong, Warm, Same → Yes

Compare with S1. Difference at Humidity → change to ?:

• S2 = <Sunny, Warm, ?, Strong, Warm, Same>
• G remains unchanged (still consistent)

Instance 3 (Negative):

Rainy, Cold, High, Strong, Warm, Change → No

Now, we need to specialize G to exclude this negative instance but remain consistent with S2.

Current G = <?, ?, ?, ?, ?, ?>
Compare with the negative instance and specialize only in positions where S2 and the instance differ:

So, G3 becomes:

• <Sunny, ?, ?, ?, ?, ?>
• <?, Warm, ?, ?, ?, ?>
• <?, ?, ?, ?, ?, Same>

Remove any G hypotheses inconsistent with positive instances (like S2). All are consistent → keep them.

Instance 4 (Positive):

Sunny, Warm, High, Strong, Cool, Change → Yes

Compare with S2 = <Sunny, Warm, ?, Strong, Warm, Same>

Differences at:

• Water: Warm → Cool
• Forecast: Same → Change
  → Generalize these two to ?

Updated S4:
S4 = <Sunny, Warm, ?, Strong, ?, ?>

Now prune G3: Remove any hypothesis in G that is not consistent with this positive instance:

1. <Sunny, ?, ?, ?, ?, ?> ✅
2. <?, Warm, ?, ?, ?, ?> ✅
3. <?, ?, ?, ?, ?, Same> ❌ (Forecast is “Same”, instance has “Change”) → Remove this.

So, Final G4:

• <Sunny, ?, ?, ?, ?, ?>
• <?, Warm, ?, ?, ?, ?>

Final Version Space:

• S = <Sunny, Warm, ?, Strong, ?, ?>
• G = { <Sunny, ?, ?, ?, ?, ?>, <?, Warm, ?, ?, ?, ?> }

• The Candidate Elimination Algorithm produces a version space bounded by the most specific and most general consistent hypotheses.
• It uses both positive and negative examples to arrive at a reliable set of hypotheses.
• In this dataset, it learns that: “If Sky is Sunny and Temp is Warm, then EnjoySports is Yes” — with other attributes not significantly affecting the decision.