Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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**Training a Hypothesis Function Using Stochastic Gradient Ascent**

To manually train a hypothesis function \( h_{\vec{\theta}}(\vec{x}) = g(\vec{\theta}^T \vec{x}) \), we will apply the stochastic gradient ascent rule with the given dataset. The starting values for the parameters are:

- \(\theta_0 = 0.1\)
- \(\theta_1 = 0.1\)
- \(\theta_2 = 0.1\)

The learning rate \(\alpha\) is set at 0.1. It is necessary to update each parameter at least five times.

**Training Instances:**

\[
\begin{array}{|c|c|c|}
\hline
x_1 & x_2 & y \\
\hline
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 0 \\
1 & 1 & 0 \\
\hline
\end{array}
\]

This table represents the input features \(x_1\), \(x_2\), and the target output \(y\) for training the model. Conduct the training by iterating over these instances while adjusting the parameters using the specified learning rate.
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Transcribed Image Text:**Training a Hypothesis Function Using Stochastic Gradient Ascent** To manually train a hypothesis function \( h_{\vec{\theta}}(\vec{x}) = g(\vec{\theta}^T \vec{x}) \), we will apply the stochastic gradient ascent rule with the given dataset. The starting values for the parameters are: - \(\theta_0 = 0.1\) - \(\theta_1 = 0.1\) - \(\theta_2 = 0.1\) The learning rate \(\alpha\) is set at 0.1. It is necessary to update each parameter at least five times. **Training Instances:** \[ \begin{array}{|c|c|c|} \hline x_1 & x_2 & y \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 1 & 0 \\ \hline \end{array} \] This table represents the input features \(x_1\), \(x_2\), and the target output \(y\) for training the model. Conduct the training by iterating over these instances while adjusting the parameters using the specified learning rate.
Expert Solution
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Step 1

 

: Solution ::

step: 1

 

 
Gradient Descent algorithm:-
#1. Import All Librariesimport numpy as npimport pandas as pdfrom sklearn.linear_model import Linear Regressionimport math
 
#2. Train Model Using Sklearndef
predict_using_sklean():df = pd.read_csv("test.csv")r =
Linear Regression()r.fit(df[['x1','x2']],df.y)print(r.intercept_)return r.coef_,
r.intercept_predict_using_sklean()
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