Remember that div(f) is just a convenient notation for \sum_i df_i/dx_i. If you'll try to take the jacobian of the formula for x' you will end up evaluating the determininant of a large matrix, and there you should see that some terms of this determinant are negligible: o(dt). Thus, in some sense, the diagonal of the matrix (which is 1+df_i/dx_i*dt) plays the main role and, thus, div appears.
thetas are the parameters of the model, which could be a regression or a classifier in this case. hence, here we sample the parameters of a model (say weights of linear regression), and then we should average the predictions over all these sampled parameterrs.
Hi Stefan! Thanks a lot for your feedback! I totally agree that this talk taking separately lacks motivation and practical examples. The reason is that this talk was designed as a part of Day 5, which is about MCMC. You can also find the discussion of the Langevin dynamics in this talk czcams.com/video/Q_Bi2H9NKzc/video.html.
![[DeepBayes2019]: Day 5, Lecture 4. Variational inference with implicit and semi-implicit models](http://i.ytimg.com/vi/LIfel_gR1vI/mqdefault.jpg)
![[DeepBayes2019]: Day 5, Lecture 4. Variational inference with implicit and semi-implicit models](/img/tr.png)
great presentation. It gave me a lot of insight especially given the current developments in score-based models and generation with them.
Fantastic talk! Clear, informative and vivid.
Very good presentation. Thank you
Very good. Well done.
Simply super!
Thank you for this informative discussion and amazing presentation!
Could you also share the codes of your animations?
great talk!
Super clear, thanks!
Fantastic,,,, i want to go samsung
very good talk!
Helpful talk! Thank you . I just don't understand why there is a 'div' in the equation at 16:45. Could you show me some references?
Remember that div(f) is just a convenient notation for \sum_i df_i/dx_i. If you'll try to take the jacobian of the formula for x' you will end up evaluating the determininant of a large matrix, and there you should see that some terms of this determinant are negligible: o(dt). Thus, in some sense, the diagonal of the matrix (which is 1+df_i/dx_i*dt) plays the main role and, thus, div appears.
I know it is old post but could you solve this? I am stuck on the same part.
At 34:01, are \thetas parameters of the model or the sampled data points from a model which is parameterised by \theta?
thetas are the parameters of the model, which could be a regression or a classifier in this case. hence, here we sample the parameters of a model (say weights of linear regression), and then we should average the predictions over all these sampled parameterrs.
@@k_neklyudov I see, thanks a lot for the clarification.
Maybe its useful to motivate a little more before showing only slides packed with equations for half an hour straight
I understand you. But you can look who he uses final derived equation by just skipping derivation.
Hi Stefan! Thanks a lot for your feedback! I totally agree that this talk taking separately lacks motivation and practical examples. The reason is that this talk was designed as a part of Day 5, which is about MCMC. You can also find the discussion of the Langevin dynamics in this talk czcams.com/video/Q_Bi2H9NKzc/video.html.