Importance Sampling
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Calculating expectations is frequent task in Machine Learning. Monte Carlo methods are some of our most effective approaches to this problem, but they can suffer from high variance estimates. Importance Sampling is a clever technique to obtain lower variance estimates.
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SOURCES
[1] was my primary source. Chapter 17 of [2] and chapter 23 of [3] provided a useful discussion more directed at the use cases of Machine Learning.
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[1] E. Anderson, "Monte Carlo Methods and Importance Sampling", ib.berkeley.edu/labs/slatkin/...
[2] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016
[3] K. P. Murphy. Machine Learning: A Probabilistic Perspective, MIT Press, 2012
TIMESTAMP
0:00 Intro
0:16 Monte Carlo Methods
2:29 Monte Carlo Example
3:57 Distribution of Monte Carlo Estimate
6:06 Importance Sampling
9:00 Importance Sampling Example
11:40 When to use Importance Sampling
Пікірлер: 221
I think people underestimate how good this channel is. Can't wait for it to blow up! Good job
@Mutual_Information
2 жыл бұрын
lol I'm going with the slow and steady strategy
Im still confused.... why haven't you blown up yet?? Your content is levels higher than a lot of stuff in KZread!
@Mutual_Information
2 жыл бұрын
lol I hear it takes time for the algorithm to like you. I'm not terribly worried. Slow and steady for now
Hallelujah! Finally got a simple explanation of what Importance Sampling is! Thanks a ton!
One interesting use of importance sampling is in path tracing (similar to ray tracing) in computer graphics, since path tracing is a Monte-Carlo method for computing the rendering equation. You can use importance sampling to get a better (less noisy) image with the same number of samples by using a sampling distribution which provides more frequent samples where the contribution from the BRDF/BSDF is higher, essentially sampling fewer dim paths which don't contribute to the total lighting of a pixel.
This must be the best explanation of importance sampling available online, or at least on YT. And this channel in general is such a gem. Can't wait for more of your content
@Mutual_Information
Жыл бұрын
Second donation ever! Thank you! And yes more is coming. I'm working on a big fat series, hence no recent vids. But they're coming
The quality of these videos is always phenomenal.
I like how you really go deep on uncommonly shown but very powerful techniques.
@Mutual_Information
2 жыл бұрын
hell yea! Trying to make this for people who actually want to use this stuff one day. All these details become important.
This was SSSOOOOOO much easier to understand than the wikipedia page! Thank you!
Such a beautiful talk! I was searching for an intro on importance sampling. And this is beyond my expectation. Thank you.
The best explanation of Importance Sampling I've seen so far. Good job!!
Just sending a thanks for the clarity of the graphs. painting the samples the color of the distribution is a great touch
Every single word you say it's the absolute minimum for bestly conveying and explaining the full meaning of the formulas. Congratulations, and thank you for being an excellent teacher
@Mutual_Information
2 жыл бұрын
Thanks a lot - glad you appreciate the script
Fantastic video. It's clear that you put a massive amount of effort into your graphical representations and explanations!!
@Mutual_Information
Жыл бұрын
Yea I'm hoping that'll make the difference in the long run
Somehow you manage to give intuition _and_ technical detail. Fantastic video, like all your other videos! 😎
Wow - this must have been a lot of work to do. A clear structure, so many details, theoretical knowledge as well as practical tips, astonishing/valuable graphics and super clear audio. Thank you!
@Mutual_Information
Жыл бұрын
You nailed it - it was a lot of work lol. Thanks for noticing :)
You earned this sub. Fantastic quality! This is also the most intuitive explanation of a concept like this I've ever seen! I sometimes think other channels with similar topics either ramble a bit much or go too fast in parts and I get lost, but this is just the right amount of building the foundation slowly and confidently to arrive at the final idea. Keep going with these videos and you are sure to get algorithmed eventually 👍
@Mutual_Information
Жыл бұрын
Thank you very much! It's a work in progress too. I'm learning the rhythm and what does/doesn't need to be said. Things will get better and I'm sure it'll get recognized.
@sanjaythorat
Жыл бұрын
I second your opinion @Mute. Thanks @Mutual Information for the video.
This is how you suposed to make an explanation video. Very very clear and concise. Well scripted, well organized, keep up you great work!!
@Mutual_Information
2 жыл бұрын
Ha yea the script is the hard part!
Awesome! Keep it up, man! Your dedication is level is touching the 7th sky!
Well I was trying to understand variational inference but with no luck. This gem helped to me. To be honest this is the best video on topic and this guy is a brilliant teacher. Please make more of this kind of videos.
@Mutual_Information
2 жыл бұрын
Thanks! Variance inference will be covered one day - promise!
Amazing explanation. Top-notch delivery!
What an excellent explanation. Glad to see your latest video is performing well !
Among all the videos I've found on youtube about Importance Sampling., this video is so far the best explanation.
@Mutual_Information
2 жыл бұрын
That's a win!
Wow that's an awesome explanation. I'm taking a Monte Carlo STATS class right now and this was far more clear then my professor was about what is actually happening here. Great video!
@Mutual_Information
Жыл бұрын
Happy to hear it Eric !
Amazing visualization and lucid explanation ❤This was the kind of video that bring you joy of understanding, appreciate the beauty of math and people behind the original idea! Bring your favorite wine to watch this!
@Mutual_Information
Жыл бұрын
You're too kind Y Li - thank you!
Like many others, I’m surprised you’re not bigger than you are! I’ve been binging your videos and they’re all very high quality. Liked and subbed 😊
Thank you so much for this. A topic I considered very complex is now crystal clear thanks to you!
great video. i bounced off from a lot of videos just for Importance sampling and this was the best of all.
Excellent explanation and video! Congratulations for that, and THANKS!
This is the best video to understand importance sampling. Thank you❤
My professor tells nothing about importance sampling, this clip really can help me to understand
I spent nearly two days to try to working this out and all you did just show me some figures, that's incredible, thanks!
@Mutual_Information
5 ай бұрын
My job is done ;)
Loved the vid. Thanks a lot, and appreciate the effort that went into making this. Keep up the good work, and hoping for this channel to grow big.
@Mutual_Information
Жыл бұрын
Thank you - glad you like it!
Omg, I struggled with these concepts for a while. Thank you so much for the explanation and visualization!
@Mutual_Information
Жыл бұрын
The struggle is over Wendy! Happy it helped :)
impressive teaching skills, this was an amazing lesson
That is absurdly well-explained. Very high quality in the every aspect of the video!
@Mutual_Information
7 ай бұрын
Thank you - more good stuff coming!
Absolutely great video. Keep making this kind of content please. It is very helpful!
Very professional explanation on every detail of IS!
This is THE best explanation of importance sampling I have come across. I'm studying for a PhD in Astrophysics, I've been linked to so many textbooks and college courses that make it really confusing. This was so simple and has really helped me understand this and move on to further topics. Thank you so much!
@Mutual_Information
Ай бұрын
Thank you for telling me - I love hearing about those cases where this stuff hits just right!
This channel is so haunting. It's like no matter what I search, this channel always returns
An absolute phenomenon 💪💪💪 Beautiful explanation.
Excellent video! I find myself lost in graduate statistic books, since they often explain concepts like this based on a lot of other statistical concepts, that I do not always have a good understanding for. It certainly helped to broaden the perspective a bit. It is easy to find excellent recourses on the most common and hyped methods, but not important but often overlooked topics like this. Thanks!
@Mutual_Information
2 жыл бұрын
Thank you that's a big point of the channel. All the basic topics get covered at a high quality level, but there's clearly a real appetite for a few steps beyond it.
Thank you very much for the great intuition on this technique ! I am using it to understand the SMC algorithm, where Importance Sampling is a key ingredient.
@Mutual_Information
Жыл бұрын
Excellent, glad it helps
That was actually a very nice way of presenting Importance Sampling. Thank you!
@Mutual_Information
Жыл бұрын
Glad you liked it and thanks for watching ;)
Fantastic video! I'm giving an internal lit review on quasi-adiabatic path integrals and this really helped me get some perspective on the core of the method! Super clear lecture and great use of visuals! Thank you so much!
@Mutual_Information
8 ай бұрын
Excellent, glad it helped!
Outstanding as always. Really a standout in this space. Thanks!
@Mutual_Information
2 жыл бұрын
Thanks Tyler, the appreciation goes a long way
OMG, YOU SAVE MY excessive thoughts about how to handle the theoretical side in the practical side (in Particle filter - based SLAM algorithms for probabilistic mobile robotics systems) . Many thanks.
@Mutual_Information
2 жыл бұрын
excellent! Glad I could help
Exceptional explanation! Thank's a ton!
Man ! I wish you I could learn real time analysis from you !! Superb !!!
high quality, excellent tutorial, thx
thanks for making statistics feel comprehensible for me
I stumbled upon your kelly criterion video some time ago and liked it. Now, properly looking at your channel, I'm blown away. Really high quality explanations (props to the usage of manim as well) of hard to understand ideas 👏👏👏
@Mutual_Information
11 ай бұрын
Oh yea, the quality is improving. Took me a long time but I think I'm getting the essentials. I'm also not using Manim.. maybe I should but I've always wanted to build something bespoke for this.
Perfect intro. Please share more of the available methods over finding q(x)!
Fantastic explanation , thank you
Thank you. It's very clear.
Amazing video, thank you for this.
Excellent work, thanks!
Wonderful animations!
Fantastic explanation, thanks !
A good explanation. Thanks.
Very useful, the intuition, visualizations and math have a nice combined flow!
@Mutual_Information
Жыл бұрын
Thanks Samson - glad you liked it. Come back anytime ;)
Great channel! Lucky I found this. I like the quality of the presentation and the LaTeX math displayed. Well done sir!
@Mutual_Information
11 ай бұрын
I'm for the people who think Latex looks beautiful
Great video. Really liked the visualizations.
@Mutual_Information
Жыл бұрын
Thanking me dollars - thank you very much!
Excellent job. Thank you!
Nice video, thank you ! The last condition for "When is Important Sampling used" is a sufficient condition for the use of IS rather than a necessary condition in my opinion. In Reinforcement Learning we try to evaluate values (the f(x)) for a target policy (the p(x)) using a sampling policy (the q(x)). It is used because using p is not sample efficient as it only can be used with recently sampled data. Using q allows us to make use of the all data sampled since the beginning of the training. But we are not at all choosing q to be high where |pf| is.
@Mutual_Information
Жыл бұрын
!! It's wild you mentioned that. I actually made this vid as a pre-req to my RL sequence. Yes! The IS case I mentioned here is not the full story. I tried to allude to that a bit in the intro :)
excellent as always.
Thank you. Great video.
Great intuitive recap of jensens inequality,!
this is a great video. thank you!
Well done! And thank you.
Amazing video!
I subscribe the channel because of this video, the quality is insane
@Mutual_Information
Жыл бұрын
Thank you Ming ;)
I think this is the kind of video that you have to look when you already have more or less idea of what the algorithm does, and then it helps you to summarize and understand better.
thanks for sharing. I'm an undergrad CS student and this was cool
@Mutual_Information
2 жыл бұрын
Glad it helped - there's plenty more to come!
@Mutual_Information
2 жыл бұрын
Also, if this topic is covered any of your classes.. I would greatly appreciate the favor of sharing this vid with the class :)
Very informative channel
This is exceptionally well explained. Just one suggestion, when explaining remove yourself when going down the analytical steps and bring yourself back. Grabs attention instantly.
@Mutual_Information
8 ай бұрын
Smart idea, I'll try that. Seriously, you'll see in the next vid, thanks!
One of the best explanation so far i have seen....If you can show how we can code it in python that would be helpfull......Thanks...
Great video ❤
Fantastic video, well done! I'm watching for path tracing rather than ML :)
great to see you again I have no idea why your video has such a low view... This deserves millions
@Mutual_Information
2 жыл бұрын
lol thank you, we'll see! millions is a very very high bar for technical stuff. I'm happy with a lot less
I think what I like the most about your videos is the reference book by your right, always showing up :) Do you have a complete list of your recommended/favorite books?
@Mutual_Information
2 жыл бұрын
lol you noticed! Yea these textbooks are essential :) I think one day I'll put together a list of my favorites. I can tell you a few of them here: Machine Learning: A Probabilistic Perspective is definitely my number 1. There's actually a new edition available for pre-order on Kevin Murphy's site. Second would be The Elements of Statistical Learning, a classic. Then Deep Learning by Bengio et al. And, just because I'm reading it right now, I really love Reinforcement Learning by Sutton and Barto. It does a great job creating a unifying framework on a wide and rapidly evolving field.
Great video! If I would like to add anything it would be maybe 2-3 questions in the end of the presented material to see if you did grasp the key points in the video (with answers in the description)! Thank you
@Mutual_Information
Жыл бұрын
That's.. a good idea. OK I think I'll give that a shot in future video.. I need some ways to build interaction with the audience. Thanks!
Well explained!
Those topics are widely used in computer graphics but they are explained in such a convoluted way. For example I only understood what "unbiased" means with your explanation. You do have a tallent to explain things!
@Mutual_Information
Жыл бұрын
Thank you RexDex!
excellent explanation
Thank you.
That's a great video which helps me alot! Could you please also introduce a little bit about Resampled Importance Sampling (RIS)? Thank you so much
Awesome visualizations!
@Mutual_Information
6 ай бұрын
Thank you Sarah!
Super clear!
Thanks that was super helpful!!!
@Mutual_Information
Жыл бұрын
Mission accomplished!
Wow this is great!
god these videos are invaluable
Hey, I'm blown away by your visulizations, what do you make them in? BTW your vid on prob. distributions helped me in my stats class :D thanks!
@Mutual_Information
2 жыл бұрын
Happy to help!
very nice lecture!thanks,i am just about to give a presentation about sampling and that covers the IS, very great and inspiring video👍
@Mutual_Information
2 жыл бұрын
Nice, glad it helped :)
Thank you
I think the pace of this video is great, but I missed the motivation for this up until the very end. The why should generally come first: "why do I need this explanation?"
Now the true question is: how can one be clearer than that? Wonderful work, thank you so much
brilliant!
awesome!
I tip my hat, thank you for this
Somehow I am able to follow this.