My man! This is the best explaination I've found, yet I've searched in 3 languages. Great explaining, awesome visualisation, simply an incredible video and a great help! Thank you very much!!!!
@@sharonlima8913 function? Perhaps you meant explanation. In my case I feel the same, other math professors always assume we remember some concepts and aspect, some of us dont and when they assume we get easily lost in the subject.
Excellent video!!! The only thing I'm wondering about is about the strictly convex/concave functions. It seems to me that whenever lambda is either 0 or 1, the two sides of the "inequality" will always be equal. You even mentioned that in your video. But how can we EVER have a strictly convex/concave function then, with this definition? Do you have to change lambda to be 0
Explained a pretty complicated topic very nicely. It is easy to visualize and understand the definition after watching this video. However, the points x and y are chosen such that f(L) > both f(x) and f(y). I have been trying to convince myself how this would have worked if y was such that f(y) was more around the crest and f(L) in that case would have lied between f(x) and f(y).
Honestly, a brilliant explanation! 🤩 Short question: other videos on this topic talk about taking the weighted average of x and y. How/where does that fit within your explanation, sir?
Tl;dr the "weighted average" stuff is supposed to motivate Jensen's inequality from probability. Read "f(E[X])" as "a function of weights" and "E[f(X)]" as "the weighted average of functions." If we apply the probability weights (t,1-t) to the interval endpoints a and b, we get ta+(1-t)b = W1, and if we apply the same weights to corresponding maps of the endpoints, f(a) and f(b), we get tf(a)+(1-t)f(b) = W2. The function f is concave over [a,b] if, for all weights (t,1-t), f(W1) ≥ W2. In other words, the value of a function of the weights (LHS) vs. the value of a weighted function (RHS). Jensen's inequality states that if f is *convex* (so f(W1) ≤ W2), and X is a random variable, then f(E[X]) ≤ E[f(X)]. If we think of taking the expectation of X as applying weights to the values that X can take on, then obtaining the expected value E[X] is much like getting W1. Thus, f(E[X]) is analogous to f(W1). Likewise, if we think of E[f(X)] as the weighted average of the random variable Y=f(X), then E[f(X)] weights f(X) to obtain W2.
I really appreciate your efforts! Could you help me with something unrelated: I have a SafePal wallet with USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). What's the best way to send them to Binance?
If you pick an x or y such that f(x) or f(y) is the max value on the y-axis, then based on lambda, the right side of the eqn can be either < or > f(L). For example if the "curve" is a straight line. Also, if LHS == RHS, how can you tell if it's convex or concave?
Good question. I'd be willing to say that if f(x) or f(y) value were to endat infinity, then it would be neither concave or convex function. But we need confirmation
Hey, good explanation, but about the strictly concave function, the λ should be ]0,1[, right ? Because if lambda can be 0 or 1, there would be a paradox as f(x) > f(x) in that case.
maybe a question. Why do we derive twice! We do not equate the first derivative with zero, as in Rolle's theorem.!! Why do we derive twice and not 3 or 4 times?
My man! This is the best explaination I've found, yet I've searched in 3 languages.
Great explaining, awesome visualisation, simply an incredible video and a great help! Thank you very much!!!!
Been breaking my head over understanding jensen's inequality, this was a really clear, unassuming explanation! Thank you a ton
Same with me watched it for trigono
hey, any other resources you can tell which can help with Jensen's inequality too? I can't understand it at all
what do you mean by unassuming function?
@@shireenkhan6847 what about this one? th-cam.com/video/LOwj7UxQwJ0/w-d-xo.html
@@sharonlima8913 function? Perhaps you meant explanation. In my case I feel the same, other math professors always assume we remember some concepts and aspect, some of us dont and when they assume we get easily lost in the subject.
Now the defination do not seem daunting at all after you've explained the design of the defination. Very helpful to me. Thank you.
6:37 that is the face of my Brain when trying to understand Concave and Convex Functions.
I have been stuck on this for days. thank you so much
Simply best! Thank you for such a detailed and step-by-step explanation.
Finally i understood. Thank you for this great explanation
Thank you very much. You've just gained a new subscriber.
Excellent video!!! The only thing I'm wondering about is about the strictly convex/concave functions. It seems to me that whenever lambda is either 0 or 1, the two sides of the "inequality" will always be equal. You even mentioned that in your video. But how can we EVER have a strictly convex/concave function then, with this definition? Do you have to change lambda to be 0
Thanks ! This is so helpful and breaks it down really easily
im coming in from time series for deep learning , keep it up broo
bro why I am watching this for my econ class when I took Calc 1, 2, and 3 years ago and I just so lost
that is a truly great video.
thank you so much, you explained it exceptionally well
Explained a pretty complicated topic very nicely. It is easy to visualize and understand the definition after watching this video. However, the points x and y are chosen such that f(L) > both f(x) and f(y). I have been trying to convince myself how this would have worked if y was such that f(y) was more around the crest and f(L) in that case would have lied between f(x) and f(y).
Insanely good, thanks a ton
Very clear explanation, thanks a lot.
amazing explanation
Honestly, a brilliant explanation! 🤩 Short question: other videos on this topic talk about taking the weighted average of x and y. How/where does that fit within your explanation, sir?
Tl;dr the "weighted average" stuff is supposed to motivate Jensen's inequality from probability. Read "f(E[X])" as "a function of weights" and "E[f(X)]" as "the weighted average of functions."
If we apply the probability weights (t,1-t) to the interval endpoints a and b, we get ta+(1-t)b = W1, and if we apply the same weights to corresponding maps of the endpoints, f(a) and f(b), we get tf(a)+(1-t)f(b) = W2. The function f is concave over [a,b] if, for all weights (t,1-t), f(W1) ≥ W2. In other words, the value of a function of the weights (LHS) vs. the value of a weighted function (RHS).
Jensen's inequality states that if f is *convex* (so f(W1) ≤ W2), and X is a random variable, then f(E[X]) ≤ E[f(X)]. If we think of taking the expectation of X as applying weights to the values that X can take on, then obtaining the expected value E[X] is much like getting W1. Thus, f(E[X]) is analogous to f(W1). Likewise, if we think of E[f(X)] as the weighted average of the random variable Y=f(X), then E[f(X)] weights f(X) to obtain W2.
@@slavojivaneie1924Wow! Thank you!
Great explanation!!
thank you! this was very helpful!!!
Excellent sir🌹🌹🌹🌹
Awesome explanation
I really appreciate your efforts! Could you help me with something unrelated: I have a SafePal wallet with USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). What's the best way to send them to Binance?
Super helpful. Thank you so much.
this was super helpful thank you!
Well explained, thank you!
Great explanation
Thank you so much
This is really good⚘️⚘️
Thanks for this.❤
Can you post a video on how to do sums of this type
amazingly explained, Thank you!
sir your voice is so cool
I got this... 😊 Thanks a ton.. !!
Nice graphical explanation
Extremely helpful
Was very helpful, cheers 🍺
Appreciated🙏
What are u guys majoring in?
this was very helpful
If you pick an x or y such that f(x) or f(y) is the max value on the y-axis, then based on lambda, the right side of the eqn can be either < or > f(L). For example if the "curve" is a straight line. Also, if LHS == RHS, how can you tell if it's convex or concave?
Good question. I'd be willing to say that if f(x) or f(y) value were to endat infinity, then it would be neither concave or convex function. But we need confirmation
That was really helpful thanks
I got understand 1st time ❤❤❤
Hey, good explanation, but about the strictly concave function, the λ should be ]0,1[, right ? Because if lambda can be 0 or 1, there would be a paradox as f(x) > f(x) in that case.
really good video
maybe a question. Why do we derive twice! We do not equate the first derivative with zero, as in Rolle's theorem.!! Why do we derive twice and not 3 or 4 times?
How about the sine and cosine function?
could you please help me understand how to check if this function f(x,y)=xy. How is it concave and how do I do the check for it
Grt explanation
just great thanks a lot
That was a really good explanation! Very clear!
I have a problem understanding the nature of f. Is it a function a single variable or more?
I don't get it, how can you compare a point, f(λx+(1-λ)y), with a line f(λx) + (1-λ)f(y)?
can you please confirm that how to find f(x) and f(y) , the points placed on vertical axis?
Thank you!
thankyou bro...
❤❤❤❤wow
excellent, but better use x1 and x2 rather than x and y to avoid confusion
Bro, sorry for my cheap english, but God will bless you :*
thank you :)
Eureka! She cried.
thanks!
And why is this for?
legend
Well dons and thanks for memory boost.
plz do more video plz plz
Exetra->et cetera
The content is okay, but brother you have to work on your speech , you're very monotonours.
wasted 22 min of my life
wasted 10 seconds of my life