M1. Likelihood Estimation

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Likelihood estimation in the context of machine learning and statistics is a method used to estimate the parameters of a statistical model. It's based on the principle of finding the parameters that make the observed data most probable.

Components

To understand likelihood estimation, let's break it down into simpler terms:

1. Statistical Model: 

This is a mathematical representation of a process or phenomenon. 

Example

For example, if you're studying the height of people in a population, your statistical model might assume that height is normally distributed (a bell curve shape).

2. Parameters: 

These are the values in the model that determine its behavior. 

Example

In our height example, the parameters would be the mean (average height) and the standard deviation (how much variation there is).

3. Observed Data: 

This is the actual data you've collected. 

Example

For instance, the heights of 100 people.

4. Likelihood: 

This refers to how probable the observed data is, given certain parameters. 

Example

If your model says the average height is 5 feet but all your data points are over 6 feet, the likelihood of your model given the data is low.

Likelihood Estimation

Now, likelihood estimation involves:

- Starting with a model (like a normal distribution for height).

- Plugging in your observed data.

- Adjusting the parameters (mean and standard deviation, in our case) to find the values that make the observed data most likely.

MLE

There are different methods of likelihood estimation, with Maximum Likelihood Estimation (MLE) being the most common. MLE searches for the parameter values that maximize the likelihood, making the observed data as probable as possible under the model.

In summary, likelihood estimation is a key concept in statistics and machine learning for determining the best parameters for a model based on the data at hand. It's about finding the most likely explanation for the data you see.

 


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