Bayesian Optimization - Math and Algorithm Explained

Learn the algorithmic behind Bayesian optimization, Surrogate Function calculations and Acquisition Function (Upper Confidence Bound). Visualize a scratch implementation on how the approximation works iteratively. Finally, understand how to use scikit-optimize package todo hyperparameter tuning using bayesian optimization.
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[@saleemun8842]

by far the clearest explanation of bayesian optimization, great work, thanks man!

[@machinelearningmastery]

Glad it was helpful!

[@Xavier-Ma]

Wonderful explaination! Thanks professor.

[@machinelearningmastery]

You are welcome!

[@saremish]

Very clear and informative. Thanks!

[@machinelearningmastery]

Glad you found it helpful.

[@syedtalhaabidalishah961]

what a video!!! simple and straight forward

[@machinelearningmastery]

I am glad it was helpful.

[@sm-pz8er]

Very well simplified explanation. Thank you

[@machinelearningmastery]

Glad it was helpful!

[@youssefbakadir2625]

First comment on this video :D, and basicaly the 666 subscriber!
Thanks a lot for this content it was very helpful! plz continue

[@nicolehuang9337]

Thanks for your sharing, u explained clearer than my professor

[@isultan]

Wow!!! Excellent lecture!!

[@machinelearningmastery]

Glad you liked it!

[@1412-kaito]

Thanks I think now I would be able to use it in hyperparameter training without having to check every single combination.

[@machinelearningmastery]

Glad I could help!

[@dhanushka5]

Thanks

[@hanserj169]

Great explanation. Do you sample more than one point at each iteration (sampled and evaluated in the target function)? or are the 23 points that you have in iteration 17 cumulative? I am asking that because the "sampled points" in the plots increases at each iteration.

[@machinelearningmastery]

Excellent question. We have sampled one point each time doe evaluation and to build up the surrogate(hopefully to converge to real black box). But when I starr this process, we need anywhere from 5%-20% initially sampled to starr the process without which variance play delays convergence. So I started with 5-6 points as I started the buildup and at each iteration, I am sampling one point to further refine my surrogate. Hope that clarifies.

[@hanserj169]

@@machinelearningmastery It does. Thanks again and keep up the great work

[@masyitahabu]

It very good explaination but for the acquisition function I hope u can explain more detail how it help surrogate choose next point.

[@machinelearningmastery]

Acquisition function in general are picking a point which gives minimum expected loss when evaluating a function fx. (fx usually is our surrogate approximation learnt till now). There are a well known strategies for acquisition functions that gives minimum expected loss - UCB, EI, POI, Entropy,etc.. And a sklearn implementaiton is using the "momentum" effect to use the best strategy that works for your usecase. If you still want to see more details on acquisition functions, let me know, I shall see if I can add it to one of my next videos.

[@sinaasadiyan]

great video, any link to your code?

[@Uma7473]

Thank You so much...

[@machinelearningmastery]

You're most welcome

[@YuekselG]

is there a mistake in 9:10 ? there is 1 f(x) too much i think. Has to be N(f(x_1), ... (x_n) l o, C*)) / N(f(x_1), ... (x_n) l o, C)). Can anyone confirm this? ty

[@ranaiit]

Thanks....missing negative sign in exponent of Gaussian function !

[@machinelearningmastery]

Typo. Thanks for highlighting. Shall update notes

[@mikehawk4583]

Why do you add the mean of the predicted points back to the predicted points?

[@machinelearningmastery]

Lets see if can correlate it with a hypotheses that humans would do to learn. Lets say we are in a Forest & searching for trails of human foot marks to get out of it. Every time we find a footprint, we valid & learn about surroundings, vegetation, terrain,etc. Over a period of time we learn ehat leads to exit And what doen't. That precisely the idea here. Hope that helps.

[@mikehawk4583]

@@machinelearningmastery I'm sorry but I still don't get it. You can explain it with more math. What I don't get is after predicting a miu, why do we need to add omega? Like what does omega do where?