Given a dataset, (1,+), (7, - ), (2, +), (6, -), (5, +), (9, -), (11, +) You are supposed to find a threshold function that minimizes the error in the given dataset. Threshold functions look like this: f( x | a,b ) = sign(a-x).b where a is a real number and b is in {1,-1}. How many possible values should you consider to solve this problem? What is the value of a and b in the case that minimizes the error? What is the minimum error? Show how you found it.
This is a Machine Learning question :
Given a dataset,
(1,+), (7, - ), (2, +), (6, -), (5, +), (9, -), (11, +)
You are supposed to find a threshold function that minimizes the error in the given dataset. Threshold functions look like this:
f( x | a,b ) = sign(a-x).b where a is a real number and b is in {1,-1}.
How many possible values should you consider to solve this problem? What is the value of a and b in the case that minimizes the error? What is the minimum error? Show how you found it.
Note: Please first sort the dataset, and use the mid-point between two adjacent points as the threshold value to identify the misclassified points. Explain in detail how you have identified the misclassified points using the threshold value and the values of b.
To find the threshold function that minimizes the error in the given dataset, we will follow these steps:
- Sort the dataset in ascending order based on the x-values.
- Calculate the midpoint between each adjacent pair of points and use it as the threshold value.
- For each threshold value, identify the misclassified points using the threshold value and the values of 'b' (1 or -1).
Let's go through each step:
Step 1: Sort the dataset:
Original Dataset: (1, +), (7, -), (2, +), (6, -), (5, +), (9, -), (11, +)
Sorted Dataset: (1, +), (2, +), (5, +), (6, -), (7, -), (9, -), (11, +)
Step 2: Calculate the midpoint between each adjacent pair of points:
Threshold Values: Threshold 1: (1 + 2) / 2 = 1.5 Threshold 2: (2 + 5) / 2 = 3.5 Threshold 3: (5 + 6) / 2 = 5.5 Threshold 4: (6 + 7) / 2 = 6.5 Threshold 5: (7 + 9) / 2 = 8.0 Threshold 6: (9 + 11) / 2 = 10.0
Step 3: Identify the misclassified points for each threshold value using 'b' (1 or -1):
Step by step
Solved in 3 steps