Softmax is a mathematical function commonly used in machine learning, particularly in the context of classification problems. It transforms a vector of raw scores, often called logits, from a model into a vector of probabilities that sum to one. The probabilities generated by the softmax function represent the likelihood of each class being the correct classification. $$\sigma(\mathbf{z})_i = \frac{e^{z_i}}{\sum_{j=1}^K e^{z_j}}$$

Support Vector Machine (SVM) is a supervised learning algorithm used for classification and regression. It finds the best hyperplane that separates the data into different classes with the largest possible margin. SVM can work well with high-dimensional data and use different kernel functions to transform data for better separation when it is not linearly separable.$$f(x) = sign(w^T x + b)$$

Random Forest is an ensemble machine learning algorithm that builds multiple decision trees during training and merges their outputs to improve accuracy and reduce overfitting. It is commonly used for both classification and regression tasks. By averaging the predictions of several decision trees, Random Forest reduces the variance and increases model robustness, making it less prone to errors from noisy data. $$\text{Entropy}_{\text{after}} = \frac{|S_l|}{|S|}\text{Entropy}(S_l) + \frac{|S_r|}{|S|}\text{Entropy}(S_r)$$

The Taylor Series is a mathematical tool that approximates complex functions with polynomials, playing a crucial role in machine learning optimization. It enhances gradient descent by incorporating second-order information, leading to faster and more stable convergence. Additionally, it aids in linearizing non-linear models and informs regularization techniques. This post explores the significance of the Taylor Series in improving model training efficiency and understanding model behavior. $$\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n}$$

Multi-layer Neural Nets

Hidden Markov Model

Perceptron

Linear Regression

Learning Progress

Naive Bayes and Bayes NetWork

Artificial Intelligent

Evaluating the quality of classification

Navigating the world of sparse datasets is a fundamental skill in machine learning. This blog post delves into the challenges posed by sparse datasets, such as high dimensionality, overfitting, and computational inefficiency, offering insightful strategies to overcome them. With hands-on Python code snippets for visualization and implementation of solutions like dimensionality reduction, imputation, and regularization, this post is a comprehensive guide for anyone looking to harness the potential of sparse data in building robust machine learning models. Explore the intricacies of dealing with sparse datasets and equip yourself with the knowledge to turn challenges into opportunities!

Python GAM to fit

Fourier Transforms