Manually train a linear function \( h_\theta(\mathbf{x}) = \boldsymbol{\theta}^T \cdot \mathbf{x} \) based on the following training instances using the stochastic gradient descent algorithm. The initial values of parameters are \( \theta_0 = 0.1 \), \( \theta_1 = 0.1 \), \( \theta_2 = 0.1 \). The learning rate \( \alpha \) is 0.1. Please update each parameter at least five times.The table of training instances is as follows:\[\begin{array}{ccc}x_1 & x_2 & y \\\hline0 & 0 & 2 \\0 & 1 & 3 \\1 & 0 & 3 \\1 & 1 & 4 \\\end{array}\]

Answered: Manually train a linear function he (x)…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Manually train a linear function \( h_\theta(\mathbf{x}) = \boldsymbol{\theta}^T \cdot \mathbf{x} \) based on the following training instances using the stochastic gradient descent algorithm. The initial values of parameters are \( \theta_0 = 0.1 \), \( \theta_1 = 0.1 \), \( \theta_2 = 0.1 \). The learning rate \( \alpha \) is 0.1. Please update each parameter at least five times.

The table of training instances is as follows:

\[
\begin{array}{ccc}
x_1 & x_2 & y \\
\hline
0 & 0 & 2 \\
0 & 1 & 3 \\
1 & 0 & 3 \\
1 & 1 & 4 \\
\end{array}
\]

Expert Solution

Step 1 The answer provided below has been developed in a clear step by step manner;

First of all we have to write Gradient Descent algorithm. Here I'm choosing python language because there is no given language in your query.

Gradient Descent algorithm:- #1. Import All Libraries import mumpy as np import pandas as pd from sklearn. linear_model import Linear Regression import math.

#2. Train Model Using Sklearn def predict_using_sklean(): df = pd.read_csv("test.csv") r = LinearRegression() r.fit(df[['x1','x2']],df.y) print(r.intercept_) return r.coef_, r.intercept_ predict_using_sklean() #Output:

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