Gradient descent is a nonlinear search algorithm. It's very powerful for large, complex problems that have no closed-form solution. But regression has a closed-form solution (least squares) that can be mathematically proven to be optimal.
What is your nulhypothesis and alternative hypothesis when you have a polynimial term in your regression when we are doing a t-test for each variable? Imagine you have y = b1 + b2 age + b3 age ^2? And you think that age has a negative effect on y over time?
Hi Philipp. There are many ways to simulate noise, depending on the goal. The easiest thing to do is to use white noise (randn in MATLAB or np.random.randn in Python) with a suitable standard deviation.
@@mikexcohen1 Thank you for the reply. What I am looking at is a neural network that approximates a polynomial given x values as input and their associated function values (y) as the label. I want to test the robustness of the model by adding noise to the function values of the training data. Would you say that the use of a normal distribution with a suitable standard deviation and the original, "true" y as the mean is appropriate for this endeavor?
Yikes! Yes, you're correct, and it's a bit of a typo there. I guess I was mixing code and math while writing out that equation. Anyway, my apologies for the confusion, and good catch!
hi mike, I have a question, that is, lets say i have data points, now I made a curve a manually (lets imagine it is possible ) joining each points one by one. it will give a some crooked curve obviously, now if I calculate BIC for this crooked curve will it give minimize value ?
Thank you for this video, pls give examples for calculating best fit no. of degree & sample size calculation for polynomial equation, As per Bayes (BIC) equation.
BIC at 7:05
great explanation, insanely good
Just found your content and I find it far clearer than most other creators who try to explain similar concepts. Good job
Thank you kindly, Drew.
Hey great vid!
Where can I watch your video about the sum of squares of the residuals?
Looking for that too
Udemy Mike Cohen, Machine Learning Course
Thank you
How can I define polynomial regression coefficient, which method can I use?
Please refer the video, where you taught how to calculate SSE for specific K in the BIC formula
Hello is there a video of implementing polynomial regression in python
Not in this video, but in the full course, yes, there are examples in Python code with explanations.
Excellent content
Glad you enjoyed it :)
At 7:45 what is formula for SS?
I think it's MSE only
I can't find the video about the SSe formula
It's actually the mse
Why did not you say about decent gradient algorithm? Is BIC the alternative algorithm?
Gradient descent is a nonlinear search algorithm. It's very powerful for large, complex problems that have no closed-form solution. But regression has a closed-form solution (least squares) that can be mathematically proven to be optimal.
WOW, amazing thank you, the best video about Polynomial regression.
Thank you, kind internet stranger.
Really helpful stuff! Thank you.
Very nice explanation.. Thank you so much
Nice and short explanation, thanks my dude!
You got it, bro
What is your nulhypothesis and alternative hypothesis when you have a polynimial term in your regression when we are doing a t-test for each variable? Imagine you have y = b1 + b2 age + b3 age ^2? And you think that age has a negative effect on y over time?
The null hypothesis of regressors in a model is always the same: That the coefficient (the beta value) is statistically indistinguishable from zero.
Bayes information criterioN. Criteria is plural.
why is a sub 2 equal to 0?
Mike! I really enjoyed this insightful video. What method do you regard as the best when incorporating noise for polynomial functions?
Hi Philipp. There are many ways to simulate noise, depending on the goal. The easiest thing to do is to use white noise (randn in MATLAB or np.random.randn in Python) with a suitable standard deviation.
@@mikexcohen1 Thank you for the reply. What I am looking at is a neural network that approximates a polynomial given x values as input and their associated function values (y) as the label. I want to test the robustness of the model by adding noise to the function values of the training data. Would you say that the use of a normal distribution with a suitable standard deviation and the original, "true" y as the mean is appropriate for this endeavor?
@@philippu1455 yeah that should work
shouldn't natural log be ln? I though log is base 10 log
Yikes! Yes, you're correct, and it's a bit of a typo there. I guess I was mixing code and math while writing out that equation. Anyway, my apologies for the confusion, and good catch!
@@mikexcohen1 All good :) like your video !!!
If memory serves, in some math books, e is the default for a log base instead of 10, i.e. "log" is used for "ln".
hi mike, I have a question, that is, lets say i have data points, now I made a curve a manually (lets imagine it is possible ) joining each points one by one. it will give a some crooked curve obviously, now if I calculate BIC for this crooked curve will it give minimize value ?
This video helped me a lot, thank you!
Great explanation. Thank you!
well narrated..Thank you
My first video, already hooked!
Welcome to the team ;)
Appreciated Man !!
Great Job
Thank you for this video, pls give examples for calculating best fit no. of degree & sample size calculation for polynomial equation, As per Bayes (BIC) equation.
you are awesome
No, you're awesome!
... well, let's both be awesome ;)
Tq
Humm