Thanks for the video, I think it will be great if you can talk about all sorts of bounds and inequalities, and compare them, from the loosest bound of Markov inequality, to tighter and tighter ones, like Chebyshev, then Chernoff and also CLT bound. Also how is this used in real world applications? In this particular example, when given a=0, e.g. the Chernoff bound is 1, which is not very useful, given we know it should be
Sir, if we substitute a=0 then p(x>0) should be 1/2. But chernoff bound gives this value as 1. So, when will we get exact bounds with chernoff bound. Sir, please explain this in your free time. Thank you very much
I think you mean to ask when the bound is "tight", rather than when it is "exact". The bound is always "exact" (by which I mean that no approximations were made when deriving the equation for the bound). For the "tightness" question, that's a bit harder to answer. There is no universal definition for when a bound is "tight". To get a feel for it, you could plot the bound as a function of the variable "a", and also plot the true function using the error function, (1-erf(a/sqrt(2)))/2. I think I'll make another video to explain this better.
There's no intuitive significance of t. It's just the "input variable" to the moment generating function. See this video for more insights: "What is a Moment Generating Function (MGF)?" th-cam.com/video/wjwLTNYOuI4/w-d-xo.html
Thanks for the video, I think it will be great if you can talk about all sorts of bounds and inequalities, and compare them, from the loosest bound of Markov inequality, to tighter and tighter ones, like Chebyshev, then Chernoff and also CLT bound. Also how is this used in real world applications?
In this particular example, when given a=0, e.g. the Chernoff bound is 1, which is not very useful, given we know it should be
Thanks for the suggestion. I'll add this to my "to do" list.
i am happy with technology bcs this made my reach to your great lactures thanks a lots from INDIA
I'm glad you found my channel, and like the videos.
Very clearly explained, thanks a lot!
Glad it was helpful!
Sir, if we substitute a=0 then p(x>0) should be 1/2. But chernoff bound gives this value as 1. So, when will we get exact bounds with chernoff bound. Sir, please explain this in your free time. Thank you very much
I think you mean to ask when the bound is "tight", rather than when it is "exact". The bound is always "exact" (by which I mean that no approximations were made when deriving the equation for the bound). For the "tightness" question, that's a bit harder to answer. There is no universal definition for when a bound is "tight". To get a feel for it, you could plot the bound as a function of the variable "a", and also plot the true function using the error function, (1-erf(a/sqrt(2)))/2. I think I'll make another video to explain this better.
@@iain_explains Thank you very much sir. Sir, if possible please explain about the tightness in other video
this is great - thank you so much!
Glad it was helpful!
What is the significance of t in the chernoff equation
There's no intuitive significance of t. It's just the "input variable" to the moment generating function. See this video for more insights: "What is a Moment Generating Function (MGF)?" th-cam.com/video/wjwLTNYOuI4/w-d-xo.html
Thank you So much
You're most welcome
can go to the bed now
Is that because the video answered the question you were asking, or because it made you fall asleep? Hopefully the first option.
@@iain_explains definitely the first