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ML (Methodologies, Taxonomy, What is it?, Hierarchical clustering, Feature…

- - - - Parameter tuning
- - - - Linear regression is used to predict the value of a continuous variable Y based on one or more input predictor variables X
      - Evoluation
        
        Root Mean Square Error
        \( E_{\text{rms}} = \sqrt{\frac{1}{N}\sum_{i=1}^N (y_i - \hat{y}_i)^2}) \)
        where \( y_i \) is the true value and \( \hat{y}_i\) is the predicted value.
        
        Mean absolute error
        \( E_{MAE} = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i| \)
        
        Mean Squared Error
        \(E_{MSE} = \frac{1}{N} \sum_{i=1}^N e_i^2 = \frac{1}{N} E_{SSE}\)
        
        R-Squared
        \( E_R = 1 - \frac{\sum e_i^2}{\sum(y_i - \bar{y})^2} \)
        where \( \bar y = \frac 1 N \sum y_i \)
        
        Sum of squared Errors
        \(E_{SSE} = \frac{e_1^2 + e_2^2 + \cdots + e_N^2} {N} = \frac{1}{N} \sum_{i=1}^N e_i^2\)
        \( e = y_i - \hat{y_i} \)
      - Problem
        
        Linear Solution
        
        Quadratic solution
        
        Cubic solution
        
        5-power solution
        
        n-th power solution
      - $$\hat{y}_i = f(x_i) = w_0 + w_1 x_i$$
      - Multiple Regression
        
        There are two or more predictors
        
        Problem
        
        Solution
        
        .
        
        \(f(\mathbf{x}_i) = \mathbf{w}^T \mathbf{x}_i = w_0 + w_1 x_{i1} + \cdots + w_K x_{iK}\)
        
        \(\mathbf{w} = [w_0, w_1, \cdots, w_K]^T\)
      - Models
        
        Linear
        
        Polynomial
        
        Sinusoids
        
        Radial basis functions
        
        Splines
        
        And many more! ...
      - Degrees of freedom
        
        A linear model \( y = w_0 + w_1x \) has two parameters and is inflexible, as it can only generate straight lines.
        
        A cubic model \(y = w_0 + w_1x + w_2x^2 + w_3x^3 \) has 4 parameters and is more flexible than a linear one.
      - Under-fitting
        
        Over-fitting
        
        Just Right
        
        .

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ML

ML

What is it?

Ability to acquire knowledge by extracting pattern from the raw data

Taxonomy

Supervised Learning

Un Supervised Learning

Classification

Regression

Density Estimation

Structure Analysis

Linear regression is used to predict the value of a continuous variable Y based on one or more input predictor variables X

Evoluation

Problem

$\hat{y}_i = f(x_i) = w_0 + w_1 x_i$

Linear Solution

Quadratic solution

Cubic solution

5-power solution

n-th power solution

Multiple Regression

There are two or more predictors

Problem

\(f(\mathbf{x}_i) = \mathbf{w}^T \mathbf{x}_i = w_0 + w_1 x_{i1} + \cdots + w_K x_{iK}\)

\(\mathbf{w} = [w_0, w_1, \cdots, w_K]^T\)

Solution

.

Models

Linear

Polynomial

Sinusoids

Radial basis functions

Splines

And many more! ...

Root Mean Square Error
\( E_{\text{rms}} = \sqrt{\frac{1}{N}\sum_{i=1}^N (y_i - \hat{y}_i)^2}) \)

where \( y_i \) is the true value and \( \hat{y}_i\) is the predicted value.

Mean absolute error
\( E_{MAE} = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i| \)

Mean Squared Error
\(E_{MSE} = \frac{1}{N} \sum_{i=1}^N e_i^2 = \frac{1}{N} E_{SSE}\)

R-Squared
\( E_R = 1 - \frac{\sum e_i^2}{\sum(y_i - \bar{y})^2} \)

where \( \bar y = \frac 1 N \sum y_i \)

Sum of squared Errors
\(E_{SSE} = \frac{e_1^2 + e_2^2 + \cdots + e_N^2} {N} = \frac{1}{N} \sum_{i=1}^N e_i^2\)
\( e = y_i - \hat{y_i} \)

Degrees of freedom

A linear model \( y = w_0 + w_1x \) has two parameters and is inflexible, as it can only generate straight lines.

A cubic model \(y = w_0 + w_1x + w_2x^2 + w_3x^3 \) has 4 parameters and is more flexible than a linear one.

Under-fitting

Over-fitting

Just Right

.

Methodologies

Sampling

Deployment performance

Optimisation theory

Error Surface

Gradient descent

\( w_{new} = w_{old} − \epsilon ∇E(w_{old}) \)

Parameter tuning

Hierarchical clustering

Feature Engineering