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Statistical Approaches

  • Statistical approaches assume that the objects in a data set are generated by a stochastic process (a generative model)
  • Idea: learn a generative model fitting the given data set, and then identify the objects in low probability regions of the model as outliers
  • Methods are divided into two categories: parametric vs. non-parametric
  • Parametric method
    • Assumes that the normal data is generated by a parametric distribution with parameter θ
    • The probability density function of the parametric distribution f(x, θ) gives the probability that object x is generated by the distribution
    • The smaller this value, the more likely x is an outlier
  • Non-parametric method
    • Not assume an a-priori statistical model and determine the model from the input data
    • Not completely parameter free but consider the number and nature of the parameters are flexible and not fixed in advance
    • Examples: histogram and kernel density estimation

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