Key Differences

  • Flexibility: Non-parametric models are more flexible and can model complex relationships, while parametric models are simpler and rely on assumptions about the data.
  • Data Requirements: Non-parametric models typically require more data to achieve good performance compared to parametric models.
  • Computation: Parametric models are usually computationally less intensive than non-parametric models.

Parametric Models

  • Definition: Models that summarize data with a set of parameters of fixed size, regardless of the number of data points.
  • Characteristics:
    • Assumes a specific form for the function mapping inputs to outputs (e.g., linear regression assumes a linear relationship).
    • Requires estimation of a finite number of parameters.
    • Generally faster to train and predict due to their simplicity.
    • Risk of underfitting if the model assumptions do not align well with the data.
  • Examples: Linear regression, logistic regression, neural networks (with a fixed architecture).

Non-parametric Models

  • Definition: Models that do not assume a fixed form for the function mapping inputs to outputs and can grow in complexity with more data.
  • Characteristics:
    • Do not make strong assumptions about the underlying data distribution.
    • Can adapt to the data’s complexity, potentially capturing more intricate patterns.
    • Generally require more data to make accurate predictions.
    • Risk of overfitting, especially with small datasets, as they can model noise in the data.
  • Examples: K-nearest neighbors, decision trees, support vector machines (with certain kernels).