Linear regression aims to fit the parameters \(\hat{\theta}\) based on the training set \[ D = \{ (\vec{x}^{(i)}, y^{(i)}), i = 1, 2, \ldots, m \} \]so that the hypothesis function \[ h_{\theta}(\vec{x}) = \hat{\theta}^T \cdot \vec{x} = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \ldots + \theta_n x_n \]can better predict the output \( y \) of a new input vector \(\vec{x}\). Please derive the stochastic gradient descent update rule which can update \(\hat{\theta}\) repeatedly to minimize the least squares cost function \( J(\hat{\theta}) \).

Introduction The linear regression analysis is expected to play out the forecast of the variable by…

Linear regression aims to fit the parameters based on the training set Tx D = {(x(i),y(i)), i = 1, 2,...,m} so that the hypothesis function he (x) 00+ 01x₁ + 0₂x₂+.. + Onxn can better predict the output y of a new input vector x. Please derive the stochastic gradient descent update rule which can update repeatedly to minimize the least squares cost function J(0). ...... = =

Linear regression aims to fit the parameters based on the training set Tx D = {(x(i),y(i)), i = 1, 2,...,m} so that the hypothesis function he (x) 00+ 01x₁ + 0₂x₂+.. + Onxn can better predict the output y of a new input vector x. Please derive the stochastic gradient descent update rule which can update repeatedly to minimize the least squares cost function J(0). ...... = =

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

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Question

Linear regression aims to fit the parameters \(\hat{\theta}\) based on the training set

\[ D = \{ (\vec{x}^{(i)}, y^{(i)}), i = 1, 2, \ldots, m \} \]

so that the hypothesis function

\[ h_{\theta}(\vec{x}) = \hat{\theta}^T \cdot \vec{x} = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \ldots + \theta_n x_n \]

can better predict the output \( y \) of a new input vector \(\vec{x}\). Please derive the stochastic gradient descent update rule which can update \(\hat{\theta}\) repeatedly to minimize the least squares cost function \( J(\hat{\theta}) \).

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