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y train a linear function ing stochastic gradient = 0.1,0₁ = 0.1, 02 = C

y train a linear function ing stochastic gradient = 0.1,0₁ = 0.1, 02 = C

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Training a Linear Function using Stochastic Gradient Descent** In this exercise, we will manually train a linear function \( h_{\theta}(\vec{x}) = \vec{\theta}^T \cdot \vec{x} \) based on the training instances provided below, using the stochastic gradient descent algorithm. ### Initial Parameters and Learning Rate - The initial values of the parameters are: - \( \theta_0 = 0.1 \) - \( \theta_1 = 0.1 \) - \( \theta_2 = 0.1 \) - The learning rate \( \alpha \) is set at 0.1. ### Objective Each parameter should be updated at least five times. ### Training Instances The dataset consists of three variables: \( x_1 \), \( x_2 \), and \( y \), given as: | \( x_1 \) | \( x_2 \) | \( y \) | |:--------:|:--------:|:------:| | 0 | 0 | 2 | | 0 | 1 | 3 | | 1 | 0 | 3 | | 1 | 1 | 4 | Utilize these values to apply stochastic gradient descent and iteratively refine the parameters for at least five iterations each.
Transcribed Image Text:**Training a Linear Function using Stochastic Gradient Descent** In this exercise, we will manually train a linear function \( h_{\theta}(\vec{x}) = \vec{\theta}^T \cdot \vec{x} \) based on the training instances provided below, using the stochastic gradient descent algorithm. ### Initial Parameters and Learning Rate - The initial values of the parameters are: - \( \theta_0 = 0.1 \) - \( \theta_1 = 0.1 \) - \( \theta_2 = 0.1 \) - The learning rate \( \alpha \) is set at 0.1. ### Objective Each parameter should be updated at least five times. ### Training Instances The dataset consists of three variables: \( x_1 \), \( x_2 \), and \( y \), given as: | \( x_1 \) | \( x_2 \) | \( y \) | |:--------:|:--------:|:------:| | 0 | 0 | 2 | | 0 | 1 | 3 | | 1 | 0 | 3 | | 1 | 1 | 4 | Utilize these values to apply stochastic gradient descent and iteratively refine the parameters for at least five iterations each.
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