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Polynomial regression

The term regression is used when you try to find the relationship between variables.

In Machine Learning, and in statistical modeling, that relationship is used to predict the outcome of future events.

Polynomial regression is a special case of linear regression where we fit a polynomial equation on the data with a curvilinear relationship between the target variable and the independent variables.

This line can be used to predict future values.

R-squared

It is important to know how the relationship between the values of the x-axis and the values of the y-axis is, if there are no relationship the linear regression can not be used to predict anything.

This relationship is measured with a value called r-squared.

The r2 value ranges from 0 to 1, where 0 means no relation and 1 means 100% relation

Overfitting

Overfitting refers to a model that models the training data too well.

Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data

Underfitting

Underfitting refers to a model that can neither model the training data nor generalize to new data.

An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

coefficient update

prediction function

guess(x) = a_nxⁿ + b_n-1x^n-1 +...+ a₀x⁰

n = degree of eqn

Mean squared error

E = (1/n)*∑(guess(x_i) - y_i)²

gradient calc..

updating k^th coefficient, where k ∈ [0, n]

∂E/∂a_k = 2*(1/n)*∑√E * ∂√E/∂a_k

∂√E/∂a_k = ∂(a_n(x_i)ⁿ + ... + a₀(x₀)⁰ - y_i)/ ∂a_k

∂√E/∂a_k = x^k * ∂a_k/∂a_k + 0+...+0

∂E/∂a_k = 2*(1/n)*∑√E * ∂√E/∂a_k*x^k

a_k = a_k - β*∂E/∂a_k

a_k = a_k - β * (2/n) * ∑ (guess(x_i) - y_i)*x^k

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polynomial regression | ML