Really nice video! I would suggest putting every video of this kind into a playlist so that it is easier for you to get views on other videos, since all of them are really good and they deserve to be viewed more. :)
are The variables μt bar and Σt bar are the same as the mean mt and the covariance Ψt (where here they are considered predicted to get a predicted x)?
Great question! Nono it is not the same in this case. Notice how we're taking the derivatives with respect to x_{t-1}. When we complete the square for x_{t-1} we get m_t and Psi_t. The point of finding m_t and Psi_t is to complete the square for x_{t-1}. Once we have this form, we can exploit that fact that the integral of e^quadratic is simply a constant (it is a constant because the integral of any probability distribution is 1. For a Gaussian, if we match the quadratic form in the exponential, everything in front is a constant that normalizes the distribution). Does that make sense?
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Really nice video! I would suggest putting every video of this kind into a playlist so that it is easier for you to get views on other videos, since all of them are really good and they deserve to be viewed more. :)
Thank you and thanks for the suggestion! I'll do that now :)
Wow, really useful - thanks for putting this together! Clear derivation and great animations!
Great work
It's really helpfull
are The variables μt bar and Σt bar are the same as the mean mt and the covariance Ψt (where here they are considered predicted to get a predicted x)?
Great question! Nono it is not the same in this case. Notice how we're taking the derivatives with respect to x_{t-1}. When we complete the square for x_{t-1} we get m_t and Psi_t. The point of finding m_t and Psi_t is to complete the square for x_{t-1}. Once we have this form, we can exploit that fact that the integral of e^quadratic is simply a constant (it is a constant because the integral of any probability distribution is 1. For a Gaussian, if we match the quadratic form in the exponential, everything in front is a constant that normalizes the distribution). Does that make sense?