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https://github.com/LiteObject/Machine-Learning-Notebook

General notes on machine learning
https://github.com/LiteObject/Machine-Learning-Notebook

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General notes on machine learning

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# Machine Learning



## Model = Training (Algorithm + Data)

A machine learning model is a mathematical representation or algorithm that learns patterns and relationships from data to make predictions or take decisions without being explicitly programmed. It is the result of training a machine learning algorithm on a dataset to capture patterns, extract insights, and generalize to new, unseen data.



In essence, a machine learning model is a mapping from input data to output predictions or decisions. It takes input features or variables (also known as independent variables) and produces output predictions or labels (also known as dependent variables) based on the learned patterns from the training data.



The model's structure and parameters determine how it represents and processes the input data. The process of training a model involves adjusting these parameters to minimize the difference between the predicted outputs and the actual labels in the training data. The trained model can then be used to make predictions or classify new, unseen data.



Machine learning models can take various forms, depending on the problem and the algorithm used. Some common types of machine learning models include:

- Linear Regression: Models the relationship between independent variables and a continuous dependent variable using a linear equation.

- Logistic Regression: Models the probability of a binary outcome or class membership based on independent variables using a logistic function.

- Decision Trees: Models decisions or classifications by splitting the data based on a series of hierarchical rules or conditions.

- Random Forest: An ensemble model that combines multiple decision trees to make predictions by averaging or voting.

- Support Vector Machines (SVM): Models data by finding a hyperplane that best separates different classes or groups.

- Neural Networks: Deep learning models composed of interconnected layers of artificial neurons that can learn complex patterns and relationships.

- Naive Bayes: A probabilistic model based on Bayes' theorem that predicts the probability of different outcomes based on independent features.



These are just a few examples, and there are many other types of machine learning models available, each suitable for different types of data and problem domains.



Machine learning models enable automated decision-making, pattern recognition, and predictive capabilities across a wide range of applications, including image and speech recognition, natural language processing, recommendation systems, fraud detection, and more.



## Ordinary Least Squares (OLS)

It is a method used in statistics and econometrics to estimate the parameters of a linear regression model.



In the context of linear regression, the OLS model aims to find the best-fitting line that minimizes the sum of the squared differences between the observed dependent variable values and the predicted values based on the independent variables.



The "ordinary" in Ordinary Least Squares refers to the fact that the method assumes that the errors or residuals of the model are normally distributed and have constant variance (known as homoscedasticity). The "least squares" part of the name refers to the minimization of the sum of the squared errors.



The OLS model estimates the coefficients (slopes) and intercept of the linear regression equation, allowing you to explore the relationship between the dependent variable and one or more independent variables. The coefficients indicate the direction and magnitude of the relationship, while the intercept represents the estimated value of the dependent variable when all independent variables are zero.



The OLS method is widely used in various fields, including economics, finance, social sciences, and data analysis, to analyze and model the relationships between variables using linear regression.



## Objective functions

An objective function, also known as a cost function, loss function, or optimization function, is a mathematical function that defines the goal or objective of an optimization problem. In optimization, the objective function quantifies the performance or quality of a solution or a set of parameters.



The objective function is typically designed to be minimized or maximized based on the problem's requirements. For example, in a minimization problem, the objective function should be minimized, while in a maximization problem, the objective function should be maximized.



In various fields, such as mathematics, engineering, economics, and machine learning, objective functions play a crucial role in optimization problems. They help define the criteria for finding the optimal solution, which could be the solution that minimizes cost, maximizes profit, minimizes error, maximizes accuracy, or satisfies certain constraints.



For instance, in linear regression, the objective function could be the sum of squared differences between the observed values and the predicted values. In logistic regression, the objective function could be the negative log-likelihood of the model's predictions.



The choice of an objective function depends on the specific problem being solved and the desired outcome. It is essential to carefully define and design the objective function to accurately capture the problem's requirements and guide the optimization process towards the desired solution.



## Optimizer

In the context of machine learning, an optimizer is an algorithm or method used to adjust the parameters of a model in order to minimize the error or loss function during the training process. The optimizer plays a crucial role in the training phase of machine learning models, as it determines how the model's parameters are updated in response to the training data.



During the training phase, the model iteratively makes predictions on the training data and calculates the associated error or loss. The optimizer then adjusts the model's parameters based on the error, aiming to minimize the loss function and improve the model's performance.



Commonly used optimizers in machine learning include:

- Stochastic Gradient Descent (SGD): SGD is a widely used optimization algorithm that updates the model's parameters in the direction of the steepest gradient. It performs parameter updates based on a small batch of randomly selected training examples at each iteration.

- Adam: Adam (Adaptive Moment Estimation) is an adaptive learning rate optimization algorithm that combines ideas from both momentum and RMSProp. It adapts the learning rate for each parameter based on the first and second moments of the gradients.

- RMSProp: RMSProp (Root Mean Square Propagation) is an optimization algorithm that adapts the learning rate based on the average of the squared gradients. It helps to mitigate the vanishing or exploding gradient problem.

- Adagrad: Adagrad (Adaptive Gradient) is an optimization algorithm that adapts the learning rate based on the sum of the historical squared gradients. It gives more weight to less frequently occurring features by decreasing the learning rate for frequently occurring features.

- AdamW: AdamW is an extension of Adam that incorporates weight decay regularization, which helps prevent overfitting by penalizing large parameter values.

  

These optimizers, and many others, provide different strategies for updating the model's parameters and adjusting the learning rate during the training process. The choice of optimizer depends on the specific problem, the characteristics of the data, and the model architecture. Experimenting with different optimizers can help improve the model's convergence and overall performance.