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Avoiding the Zero-Probability Problem

  • Naïve Bayesian prediction requires each conditional prob. be non-zero. Otherwise, the predicted prob. will be zero

\[P(X|C_{i})=\prod_{k=1}^{n}P(x_{k}|C_{i})\]

  • Ex. Suppose a dataset with 1000 tuples, income=low (0), income= medium (990), and income = high (10)
  • Use Laplacian correction (or Laplacian estimator)
    • Adding 1 to each case
      • Prob(income = low) = 1/1003
      • Prob(income = medium) = 991/1003
      • Prob(income = high) = 11/1003
    • The “corrected” prob. estimates are close to their “uncorrected” counterparts

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