Pdf Lab 1 Linear Regression And Backpropagation Uu Sml Github Io

This repository is used to host the files needed for the exercise sessions and the computer lab in the course Statistical Machine Learning at Uppsala University. The material associated with each session is given below together with a set of recommended problems. For each session, the material consists of the following: Data used in the computer classes can be downloaded directly in the notebooks. For offline use, we recommend you download the whole repository and make the necessary changes to the notebook by commenting/uncommenting appropriate lines. For the computer lab about deep learning the following resources are available:

This repository is used to host the files needed for the exercise sessions and the computer lab in the course Statistical Machine Learning at Uppsala University. The material associated with each session is given below together with a set of recommended problems. For each session, the material consists of the following: Data used in the computer classes can be downloaded directly in the notebooks. For offline use, we recommend you download the whole repository and make the necessary changes to the notebook by commenting/uncommenting appropriate lines. For the computer lab about deep learning the following resources are available:

There was an error while loading. Please reload this page. Instantly share code, notes, and snippets. Implement the linear regression problems from Exercises 1.1(a), (b), (c), (d) and (e) in Python using matrix multiplications. A matrix $$ \textbf{X} = \begin{bmatrix} 1 & 2 \\ 1 & 3 \\ \end{bmatrix} $$ can be constructed with numpy as X=np.array([[1, 2], [1, 3]]) (Make sure that numpy has been imported. Here it is imported as np).

The commands for matrix multiplication and transpose in numpy are @ or np.matmul and .T or np.transpose() respectively. A system of linear equations $\textbf{A}x=\textbf{b}$ can be solved using np.linalg.solve(A,b). A $k \times k$ unit matrix can be constructed with np.eye(k). Assume that you record a scalar input $x$ and a scalar output $y$. First, you record $x_1 = 2, y_1 = -1$, and thereafter $x_2 = 3, y_2 = 1$. Assume a linear regression model $y = \theta_0 + \theta_1 x + \epsilon$ and learn the parameters with maximum likelihood $\widehat{\boldsymbol{\theta}}$ with the assumption $\epsilon \sim \mathcal{N}(0,\sigma_\epsilon^2)$.

Use the model to predict the output for the test input $x_\star = 4$, and plot the data and the model. Now, assume you have made a third observation $y_3 = 2$ for $x_3 = 4$ (is that what you predicted in (a)?). Update the parameters $\widehat{\boldsymbol{\theta}}$ to all 3 data samples, add the new model to the plot (together with the new data point) and find the prediction for $x_\star = 5$. Repeat (b), but this time using a model without intercept term, i.e., $y = \theta_1x + \epsilon$. Repeat (b), but this time using Ridge Regression with $\gamma=1$ instead.

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