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This diagram is from Andrew Ng course for ML/DL:

enter image description here

But isn't the cost function (least squares function) shape depends on scatter of the data ?

For example below, the minimum will be at (0,1):

enter image description here

that doesn't correspond to convex shape (if you will imagine it in 3d plot), that Andrew Ng showed above.

UPDATE

Oh, i think I understand... my example is a convex shape too, but simply shifted by coordinates, relatively to the Andrew's example.

Am i right?

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    $\begingroup$ the cost function should be convex, which corresponds roughly to a "bow" shape $\endgroup$ – Tony S.F. Mar 8 '18 at 17:34
  • $\begingroup$ sorry, updating question $\endgroup$ – uptoyou Mar 8 '18 at 17:39
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Because the cost function is given by:

$$ \frac{1}{2} \left\| X \theta - y \right\|_{2}^{2} $$

Which is a Linear Regression Problem with the Least Squares cost function which is a Convex Function of $ \theta $.

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  • $\begingroup$ Can you please add more details to your answer? Thank you! $\endgroup$ – Alex Yursha Oct 10 '18 at 1:58
  • $\begingroup$ Could you point me what would you like to be extended? $\endgroup$ – Royi Oct 10 '18 at 14:32
  • $\begingroup$ The notation || is not familiar to me. Perhaps, at least provide links to supplemental resources of your choice, which will help to interpret the formula you wrote. Thank you! $\endgroup$ – Alex Yursha Oct 14 '18 at 5:52
  • $\begingroup$ The notation $ \left\| \cdot \right\| $ stands for norm. So the $ {\left\| \cdot \right\|}_{2} $ stands for the $ {L}_{2} $ norm and $ {\left\| \cdot \right\|}_{2}^{2} $ is the $ {L}_{2} $ norm squared. $\endgroup$ – Royi Oct 14 '18 at 6:04

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