Math implementations in Python

Hi! This repository contains implementations of some mathematical topics, that often uses in "Machine Learning" area. I am writing it for myself just to get better understanding of some topics, that I'm currently learning. All implementations are written in Python.

For now this repository contains the following topics:

• Linear algebra
• Statistics
• Probability theory
• Machine learning

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Implemented:

Linear algebra:

Functions:

• Scalar product
• Matrix product
• Matrix transpose
• Vector norm
• Minor
• Determinant
• Inverse matrix
• Matrix rank

Solving equations:

• Gaussian method
• QR method

Statistics:

Functions:

• Mean
• Variance
• Standard Deviation
• Standard Error
• Percentile
• Median
• QQ plot
• Covariance
• Correlation

Student's t-test:

• One sample t-test (independent)
• Two sample t-test (independent)
• Paired t-test (dependent test)

ANOVA test:

• One-way ANOVA
• Two-way ANOVA

Pearson's chi-squared test:

• Chi squared distance between 2 groups
• Chi2 test
• Coin toss simulation distribution
• Simulate distribution with specified degree of freedom

Probability theory:

Probability functions:

• Intersection probability
• Union probability
• A\B and B\A probabilities

Combination functions:

• Factorial
• Permutations
• Accommodations with and without repetitions
• Combinations with and without repetitions

Machine learning:

Functions:

• Sum of squares
• Residuals
• Determination coefficient
• Regression prediction

Preprocessing

• Min-Max Scaler
• Standard Scaler

Regression:

• Linear regression with one feature

Distance metrics:

• Euclidean metric
• Manhattan metric
• Max-metric

Anomaly detection:

• Anomaly detection using Chauvenet's criterion
• Anomaly detection using Z Score
• Outlier detection using Interquartile Range (IQR)

Clustering:

• K Means Clustering