Show that the maximum likelihood estimate of the noise variance in our linear model, [widehat{sigma^{2}}=frac{1}{N}left(mathbf{t}^{top} mathbf{t}-mathbf{t}^{top} mathbf{X}

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Show that the maximum likelihood estimate of the noise variance in our linear model,

\[\widehat{\sigma^{2}}=\frac{1}{N}\left(\mathbf{t}^{\top} \mathbf{t}-\mathbf{t}^{\top} \mathbf{X} \widehat{\mathbf{w}}\right)\]

can also be expressed as

\[\widehat{\sigma^{2}}=\frac{1}{N} \sum_{n=1}^{N}\left(t_{n}-\mathbf{x}_{n}^{\top} \mathbf{w}\right)^{2}\]

(work backwards from the second expression.)

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A First Course In Machine Learning

ISBN: 9781498738484

2nd Edition

Authors: Simon Rogers , Mark Girolam

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Question Posted: May 23, 2024 02:01 AM

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Show that the maximum likelihood estimate of the noise variance in our linear model, [widehat{sigma^{2}}=frac{1}{N}left(mathbf{t}^{top} mathbf{t}-mathbf{t}^{top} mathbf{X}

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A First Course In Machine Learning

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