3.2 Classification by Density Estimation in Machine Learning

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3.2 Classification by Density Estimation in Machine Learning

  • Classification is a machine learning where a model assigns data into different categories (classes).

Example:

  • Email → Spam / Not Spam

  • Student result → Pass / Fail

  • Medical report → Disease / No Disease

        The model studies past data and predicts which class a new data point belongs to.

Density Estimation:-

  • Density estimation means estimating how data points are distributed in a dataset.
  • In simple words, it answers this question: “How common is this type of data in a particular class?”
  • It calculates the probability density of data belonging to each class.


Classification by density estimation works :

  1. The model estimates the probability distribution of each class.

  2. For a new data point, it calculates how likely the data belongs to each class.

  3. The class with the highest probability density is selected.

Example

Suppose we classify students as:

  • Pass

  • Fail

Training data:

Now a new student score is 65.

The model calculates probability density.

  • Probability for Pass → High

  • Probability for Fail → Low

Prediction:    Pass

                     Because 65 is closer to the pass score distribution.


Method (Step-by-Step): -

Step 1: Collect training data

         Example: exam scores.

Step 2: Estimate probability density for each class

        Example:

  • Pass scores distribution

  • Fail scores distribution

Step 3: Input new data

            Example: score = 65.

Step 4: Compute probabilities

            Check which class distribution the data fits best.

Step 5: Choose highest probability class

            Prediction → Pass


In Mathematical density estimation classification, we compute:

P(x∣Class)

Where:

  • x = data value

  • P(x|Class) = probability of data belonging to that class

Then we choose the class with highest probability.


Some machine learning methods use this idea:

  • Naive Bayes Classifier

  • Gaussian Classifier

  • Kernel Density Estimation (KDE)

  • Bayesian Classifiers

These methods estimate probability distributions and classify based on them.




































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