Timeline for Can simple linear regression be done without using plots and linear algebra?
Current License: CC BY-SA 3.0
8 events
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| Apr 2, 2016 at 7:50 | comment | added | Chris Rackauckas | For least squares regression you don't need to do gradient decent since you can solve for an equation which is the answer, but this gives a good way of understanding what machine learning is. It boils down to choosing a way of measuring error, and then finding some way to minimize the error equation. The result is the "best" estimating equation learned via the data. I hope that helps you on your path to machine learning! | |
| Apr 2, 2016 at 7:49 | comment | added | Chris Rackauckas | This idea then brings you to machine learning. One of the basic methods in machine learning is gradient decent. That basically translates to "follow the slope". if you keep on letting the ball roll in the direction where the hill is steepest, you'll hit a minimum. So the gradient decent method is to do precisely this: find out which way of changing $\beta$ causes the error to decrease the most and go that way! | |
| Apr 2, 2016 at 7:42 | comment | added | Chris Rackauckas | I linked to some notes that explain it at a pretty elementary level. I think any answer will need calculus because the way you solve problems like "find the minimum of $E(\beta)$" is to take a derivative and set it equal to zero. Intuitively, this is just saying that the minimum (or maximum) of a hill will be where the hill is flat (since the slope is highest along the side of the hill!). Derivative = slope. So in areas changing $\beta$ starts causing little change in $E$ you're near the minimum (or maximum. You need to make sure it's not a maximum!). | |
| Apr 2, 2016 at 7:37 | history | edited | Chris Rackauckas | CC BY-SA 3.0 |
added 221 characters in body
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| Apr 2, 2016 at 7:37 | comment | added | Parham Doustdar | OMG. Finally! A non-linear-algebra way to calculate this. The concepts you are talking about in your answer are over my head, but I'll definitely look into derivatives in an effort to understand this line of thinking better. | |
| Apr 2, 2016 at 7:28 | history | edited | Chris Rackauckas | CC BY-SA 3.0 |
grammar.
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| Apr 2, 2016 at 7:22 | vote | accept | Parham Doustdar | ||
| Apr 2, 2016 at 6:55 | history | answered | Chris Rackauckas | CC BY-SA 3.0 |