This repository contains Python scripts that implement various statistical and mathematical methods commonly used in Artificial Intelligence (AI) applications. These scripts cover fundamental concepts such as Gradient Descent, Maximum Likelihood Estimation (MLE), Maximum A Posteriori (MAP) estimation, Singular Value Decomposition (SVD), and Principal Component Analysis (PCA).
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Solution of Linear Systems with Direct Methods: Provides scripts for solving systems of linear equations using direct methods such as Gaussian elimination, LU decomposition, and other matrix factorization techniques.
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Singular Value Decomposition (SVD): Includes scripts for SVD, a matrix factorization technique that decomposes a matrix into the product of three matrices, which can be used for dimensionality reduction and feature extraction.
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Principal Component Analysis (PCA): Implements PCA, a dimensionality reduction technique used to identify patterns in data by transforming it into a new coordinate system aligned with the principal components.
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Gradient Descent: Implements the Gradient Descent algorithm, a first-order optimization algorithm used to minimize a function by iteratively moving in the direction of the steepest descent.
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Maximum Likelihood Estimation (MLE): Provides implementations of MLE, a method used to estimate the parameters of a statistical model given observations, under the assumption that the data follow a specific probability distribution.
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Maximum A Posteriori (MAP) Estimation: Demonstrates MAP estimation, a Bayesian method used to estimate the parameters of a probability distribution based on both prior knowledge and observed data.
Each script is self-contained and can be run independently. Simply execute the Python script of interest to see its functionality and usage examples.
- Python 3.x
- NumPy
- SciPy
- Andrea Fossà - andrea.fossa1801@gmail.com