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# L5 - EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 5...

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EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 5: Parameter Estimation

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Introduction So far, we have seen how to develop decision regions when the underlying density is known Bayesian Decision Theory introduced the general formulation Bayes classifier for Gaussian data was examined in detail. In most situations, the knowledge of the true distribution is not available and must be determined from experimental data. Two possible approaches: Parametric density estimation Maximum likelihood Bayesian estimation Non-parametric density estimation Kernel density estimation Nearest neighbour rule
Maximum Likelihood vs. Bayesian (| ) (, | ) (|, )(| ) (|)(| ) px d p d p d θθ θ == = ∫∫ XX X X X (|)( ) ) () ) pp p p d X X X

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Maximum Likelihood Estimation
Maximum Likelihood Estimation

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Maximum Likelihood Estimation
Maximum Likelihood Estimation 0 0 ⎡ ⎤ ⎢ ⎥ ⎣ ⎦

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Maximum Likelihood Estimation
Bayesian Estimation

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Bayesian Estimation (| ) (, | ) (|, )(| ) (|)(| ) px d p d p d θθ θ == = ∫∫ XX X X X (|)( ) ) () ) pp p p d X X X
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L5 - EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 5...

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