From 2f85e20ee5a532449d4ce3111210c49409a4892b Mon Sep 17 00:00:00 2001 From: Uzair Mohammed Date: Wed, 1 May 2024 12:37:18 -0700 Subject: [PATCH] Completed HW4 --- end.aux | 20 ++++ hw4/Gemini_Chart_Image_5v3caz5v3caz5v3c.png | Bin 0 -> 318397 bytes hw4/Picture1.png | Bin 0 -> 5619 bytes hw4/bn.py | 124 +++++++++++++++++--- hw4/problem1a.py | 45 +++++++ main.aux | 3 +- main.fdb_latexmk | 14 ++- main.fls | 14 +++ main.log | 32 +++-- main.pdf | Bin 382453 -> 554351 bytes main.synctex.gz | Bin 65850 -> 68990 bytes main.tex | 35 +++++- 12 files changed, 252 insertions(+), 35 deletions(-) create mode 100644 end.aux create mode 100644 hw4/Gemini_Chart_Image_5v3caz5v3caz5v3c.png create mode 100644 hw4/Picture1.png create mode 100644 hw4/problem1a.py diff --git a/end.aux b/end.aux new file mode 100644 index 0000000..22271c1 --- /dev/null +++ b/end.aux @@ -0,0 +1,20 @@ +\relax +\@setckpt{end}{ +\setcounter{page}{16} +\setcounter{equation}{0} +\setcounter{enumi}{2} +\setcounter{enumii}{0} 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With more samples, the estimated probabilities get closer to the real chances we calculated before. This shows that using a bigger sample size is helpful for getting better results. +\end{itemize} + +\subsection{Gradient Descent} + +\begin{itemize} + \item[a. ] + \begin{center} + \includegraphics[scale=0.5]{hw4/Gemini_Chart_Image_5v3caz5v3caz5v3c.png} + \end{center} + + + Hinge loss is a reasonable cost function for binary classification because it focuses on creating a good margin between classes. It only penalizes models when their predictions fall close to the wrong class, and ignores classified points even with a small margin. This makes the model prioritize a clear separation between positive and negative classes. + + \item[b. ] + + $$ + \frac{\partial c(h(x), y)}{\partial w_0} = 0 + $$ + + $$ + \frac{\partial c(h(x), y)}{\partial w_1} = \begin{cases} + -y, & \text{if } w_0 + w_1x < 1 \\ + 0, & \text{if } w_0 + w_1x \geq 1 + \end{cases} + $$ + + \item[c. ] + + \begin{center} + \includegraphics[scale=0.3]{hw4/Picture1.png} + \end{center} + + \end{itemize} \end{document} \ No newline at end of file