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Jun 24, 2014 · Clear and well written, however, this is not an introduction to Gradient Descent as the title suggests, it is an introduction tot the USE of gradient descent in linear regression. Gradient descent is not explained, even not what it is. It just states in using gradient descent we take the partial derivatives.

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One reasonable approach, which is supported by theory, is to move where the tangent line crosses the x-axis. The step to reach this intersection is given by the formula –f ðxÞ – ð– 1Þ x ¼ ¼ ¼1 f 9ðxÞ 1 which indicates that our next point is one unit to the right of x . Hence, x ¼1.

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Question: Obtain Expressions For The Gradient Vector And Hessian Matrix For The Functions Of N Variables : (i) ATx , Where A Is A Constant Vector. (ii) XTAx Where A Is A Constant Unsymmetric Matrix. (iii) (1/2) XTAx + BTxwhere A Is Symmetric And Both A And B Are Constant.

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In the case of ’(x) = xTBx;whose gradient is r’(x) = (B+BT)x, the Hessian is H ’(x) = B+ BT. It follows from the previously computed gradient of kb Axk2 2 that its Hessian is 2ATA. Therefore, the Hessian is positive de nite, which means that the unique critical point x, the solution to the normal equations ATAx ATb = 0, is a minimum.