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Xi'an
Xi'an
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In this page of Murphy's 'Machine Learning: a Probabilistic Perspective'Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model.

Reading this, I was trying to understand when to update parameters 'all together' and when to separate them: in Gibbs Sampling, you update one parameter at the time. According to this book, however, you update the 'multidimensional' means for each cluster 'all together'. That is, for each cluster k, it updates $[\mu_{k1}, \mu_{k2}] $ in one go. However, would it work if hypothetically I first update $\mu_{k1}$ and then $\mu_{k2}$?

I am asking to improve my understanding of this method. Thanks

enter image description here

In this page of Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model.

Reading this, I was trying to understand when to update parameters 'all together' and when to separate them: in Gibbs Sampling, you update one parameter at the time. According to this book, however, you update the 'multidimensional' means for each cluster 'all together'. That is, for each cluster k, it updates $[\mu_{k1}, \mu_{k2}] $ in one go. However, would it work if hypothetically I first update $\mu_{k1}$ and then $\mu_{k2}$?

I am asking to improve my understanding of this method. Thanks

enter image description here

In this page of Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model.

Reading this, I was trying to understand when to update parameters 'all together' and when to separate them: in Gibbs Sampling, you update one parameter at the time. According to this book, however, you update the 'multidimensional' means for each cluster 'all together'. That is, for each cluster k, it updates $[\mu_{k1}, \mu_{k2}] $ in one go. However, would it work if hypothetically I first update $\mu_{k1}$ and then $\mu_{k2}$?

I am asking to improve my understanding of this method. Thanks

enter image description here

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Vaaal
Vaaal
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Gibbs sampling for Multivariate: how to update?

In this page of Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model.

Reading this, I was trying to understand when to update parameters 'all together' and when to separate them: in Gibbs Sampling, you update one parameter at the time. According to this book, however, you update the 'multidimensional' means for each cluster 'all together'. That is, for each cluster k, it updates $[\mu_{k1}, \mu_{k2}] $ in one go. However, would it work if hypothetically I first update $\mu_{k1}$ and then $\mu_{k2}$?

I am asking to improve my understanding of this method. Thanks

enter image description here