Given a target vector and a feature vector, how to computer the weight












1












$begingroup$


In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.



$$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
$$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$




  • Then:


$$w=(X^TX)^{-1}X^Tt$$






machine-learning







share|improve this question









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user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$

















    1












    $begingroup$


    In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.



    $$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
    $$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$




    • Then:


    $$w=(X^TX)^{-1}X^Tt$$






    machine-learning







    share|improve this question









    New contributor




    user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.



      $$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
      $$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$




      • Then:


      $$w=(X^TX)^{-1}X^Tt$$






      machine-learning







      share|improve this question









      New contributor




      user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      In page 13 of the slide, given $t$ and $X$ as following. I don't understand how we get $w$.



      $$t=[t^{(1)},t^{(2)}, ldots, t^{(N)} ]^T$$
      $$X=begin{bmatrix}1, x^{(1)} \ 1, x^{(2)} \ vdots\1, x^{(N)} end{bmatrix}$$




      • Then:


      $$w=(X^TX)^{-1}X^Tt$$






      machine-learning




      machine-learning






      share|improve this question









      New contributor




      user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question









      New contributor




      user8314628 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question








      edited 3 hours ago









      Siong Thye Goh

      1,177418




      1,177418






      New contributor




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      asked 5 hours ago









      user8314628user8314628

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          1 Answer
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          $begingroup$

          The least square problem is to minimize $$|Xw-t|^2$$



          Differentiating it with respect to $w$ and equating it to $0$, we have



          $$2X^T(Xw-t)=0$$



          Hence, we have



          $$X^TXw-X^Tt=0$$



          That is $$X^TXw=X^Tt$$



          $$w=(X^TX)^{-1}X^Tt$$






          share|improve this answer









          $endgroup$













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            $begingroup$

            The least square problem is to minimize $$|Xw-t|^2$$



            Differentiating it with respect to $w$ and equating it to $0$, we have



            $$2X^T(Xw-t)=0$$



            Hence, we have



            $$X^TXw-X^Tt=0$$



            That is $$X^TXw=X^Tt$$



            $$w=(X^TX)^{-1}X^Tt$$






            share|improve this answer









            $endgroup$


















              2












              $begingroup$

              The least square problem is to minimize $$|Xw-t|^2$$



              Differentiating it with respect to $w$ and equating it to $0$, we have



              $$2X^T(Xw-t)=0$$



              Hence, we have



              $$X^TXw-X^Tt=0$$



              That is $$X^TXw=X^Tt$$



              $$w=(X^TX)^{-1}X^Tt$$






              share|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                The least square problem is to minimize $$|Xw-t|^2$$



                Differentiating it with respect to $w$ and equating it to $0$, we have



                $$2X^T(Xw-t)=0$$



                Hence, we have



                $$X^TXw-X^Tt=0$$



                That is $$X^TXw=X^Tt$$



                $$w=(X^TX)^{-1}X^Tt$$






                share|improve this answer









                $endgroup$



                The least square problem is to minimize $$|Xw-t|^2$$



                Differentiating it with respect to $w$ and equating it to $0$, we have



                $$2X^T(Xw-t)=0$$



                Hence, we have



                $$X^TXw-X^Tt=0$$



                That is $$X^TXw=X^Tt$$



                $$w=(X^TX)^{-1}X^Tt$$







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 3 hours ago









                Siong Thye GohSiong Thye Goh

                1,177418




                1,177418






















                    user8314628 is a new contributor. Be nice, and check out our Code of Conduct.










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