The question is detailled and explained in the picture attached **Problem Statement:**Suppose we have four training examples under the two-category case, i.e., \[D^* = \{(x_i, \omega_i) \mid 1 \leq i \leq 4\}\]where \[x_1 = (1, 2)^t, \quad x_2 = (2, 2)^t, \quad x_3 = (1, 1)^t, \quad x_4 = (2, 0)^t\]and \[\omega_1 = \omega_2 = -1, \quad \omega_3 = \omega_4 = 1.\]Furthermore, linear discriminant function \[g(x) = w^t x + b \]is adopted to learn from the training examples and the criterion function to be minimized is set as \[J(w, b) = -\sum_{i=1}^{4} \omega_i \cdot g(x_i).\]Given the initial model \[w_0 = (-2, 2)^t \quad \text{and} \quad b_0 = -3.\]If gradient descent techniques are utilized to minimize the criterion function, what is the resulting discriminant function after three gradient descent steps with learning rate \[\eta = 0.1 \]and threshold \[\epsilon = 10^{-6}?\]

In this scenario, tasked with employing gradient descent techniques to minimize a criterion function…

3. Suppose we have four training examples under the two-category case, i.e. D* = {(x₁,w₁) |1 ≤ i ≤ 4} where x₁ = (1, 2), x₂ = (2, 2), x3 = (1, 1)¹, x₁ = (2,0) and w₁ = 62 = -1, W3 = w₁ = 1. Furthermore, linear discriminant function g(x) = wx+b is adopted to learn from the training examples and the -5²,Wi. · g(x₁). criterion function to be minimized is set as (w. b) 11

3. Suppose we have four training examples under the two-category case, i.e. D* = {(x₁,w₁) |1 ≤ i ≤ 4} where x₁ = (1, 2), x₂ = (2, 2), x3 = (1, 1)¹, x₁ = (2,0) and w₁ = 62 = -1, W3 = w₁ = 1. Furthermore, linear discriminant function g(x) = wx+b is adopted to learn from the training examples and the -5²,Wi. · g(x₁). criterion function to be minimized is set as (w. b) 11

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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Concept explainers

Temporal difference learning

Temporal difference learning (TD learning) is a concept in machine learning that attributes to a class of model-free reinforcement learning methods. The technique predicts a reward or quantity depending on the future values of the value function.

Question

100%

The question is detailled and explained in the picture attached

**Problem Statement:**

Suppose we have four training examples under the two-category case, i.e.,

\[
D^* = \{(x_i, \omega_i) \mid 1 \leq i \leq 4\}
\]

where

\[
x_1 = (1, 2)^t, \quad x_2 = (2, 2)^t, \quad x_3 = (1, 1)^t, \quad x_4 = (2, 0)^t
\]

and

\[
\omega_1 = \omega_2 = -1, \quad \omega_3 = \omega_4 = 1.
\]

Furthermore, linear discriminant function

\[
g(x) = w^t x + b
\]

is adopted to learn from the training examples and the criterion function to be minimized is set as

\[
J(w, b) = -\sum_{i=1}^{4} \omega_i \cdot g(x_i).
\]

Given the initial model

\[
w_0 = (-2, 2)^t \quad \text{and} \quad b_0 = -3.
\]

If gradient descent techniques are utilized to minimize the criterion function, what is the resulting discriminant function after three gradient descent steps with learning rate

\[
\eta = 0.1
\]

and threshold

\[
\epsilon = 10^{-6}?
\]

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