44 docs tagged with "mathematics-for-ml"

Introduction to the fundamental pillars of statistics in ML: Populations vs. Samples, Descriptive vs. Inferential statistics, and Data Types.

An intuitive introduction to probability theory, sample spaces, events, and the fundamental axioms that govern uncertainty in Machine Learning.

A deep dive into Bayes' Theorem: the formula for updating probabilities based on new evidence, and its massive impact on Machine Learning.

Understanding the foundations of binary outcomes: The Bernoulli trial and the Binomial distribution, essential for classification models.

Mastering the Chain Rule, the fundamental calculus tool for differentiating composite functions, and its direct application in the Backpropagation algorithm for training neural networks.

Mastering permutations, combinations, and counting principles essential for understanding probability, feature engineering, and model complexity.

Understanding how the probability of an event changes given the occurrence of another event, and its role in predictive modeling.

Mastering If, Else, and Elif statements to control program flow and handle logic in Machine Learning pipelines.

Mastering Python's built-in collections: Lists, Tuples, Dictionaries, and Sets, and their specific roles in data science pipelines.

Exploring the essential plots and charts used in statistical analysis to identify patterns, distributions, and outliers in Machine Learning datasets.

Mastering the art of data visualization in Python: from basic line plots to complex statistical heatmaps.

An introduction to derivatives, their definition, rules, and their crucial role in calculating the slope of the loss function, essential for optimization algorithms like Gradient Descent.

Mastering measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation, range) to summarize and understand data distributions.

Understanding the determinant of a matrix, its geometric meaning (scaling factor), and its crucial role in checking for matrix invertibility in ML.

Understanding matrix diagonalization, its geometric meaning as a change of basis, and how it simplifies matrix computations, especially in complex systems and Markov chains.

A beginner-friendly explanation of Eigenvalues and Eigenvectors, their geometric meaning, and their critical role in dimensionality reduction (PCA) and data analysis.

Learning to handle errors gracefully in Python to build robust and fault-tolerant Machine Learning pipelines.

Mastering reusable code blocks in Python: defining functions, handling arguments, and understanding global vs. local scope in ML workflows.

Defining the Gradient vector, its mathematical composition from partial derivatives, its geometric meaning as the direction of maximum increase, and its role as the central mechanism for learning in Machine Learning.

Exploring the fundamentals of graph theory, including nodes, edges, adjacency matrices, and their applications in neural networks and Knowledge Graphs.

Understanding how to make predictions and inferences about populations using samples, hypothesis testing, and p-values.

Defining the inverse of a matrix, its calculation, the condition for invertibility (non-singular), and its essential role in solving linear equations in ML.

Mastering For loops, While loops, and the logic of iteration in Machine Learning pipelines.

An introduction to matrices, their definition, structure (rows and columns), and their essential role in representing entire datasets and system transformations in ML.

Mastering the fundamental matrix operations: addition, subtraction, scalar multiplication, matrix transpose, and the crucial matrix multiplication used in all neural networks.

Mastering N-dimensional arrays, vectorization, and broadcasting: the foundational tools for numerical computing in ML.

Understanding Classes, Objects, and the four pillars of OOP in the context of Machine Learning model development.

Mastering DataFrames, Series, and data cleaning techniques: the essential toolkit for exploratory data analysis (EDA).

Defining partial derivatives, how they are calculated in multi-variable functions (like the Loss Function), and their role in creating the Gradient vector for optimization.

A deep dive into Probability Mass Functions (PMF) for discrete data and Probability Density Functions (PDF) for continuous data.

Understanding the Poisson distribution: modeling the number of events occurring within a fixed interval of time or space.

Mastering the Python essentials required for ML: from data structures to vectorization and the scientific ecosystem.

Understanding Discrete and Continuous Random Variables, Probability Mass Functions (PMF), and Probability Density Functions (PDF).

Understanding scalars, the fundamental single-number quantities in linear algebra and machine learning.

Mastering high-level statistical plotting: visualizing distributions, regressions, and categorical relationships.

Exploring the fundamentals of Set Theory and Relations, and how these discrete structures underpin data categorization and recommendation systems in Machine Learning.

A detailed explanation of Singular Value Decomposition (SVD), why it is the most general matrix decomposition, its geometric meaning, and its critical applications in dimensionality reduction and recommender systems.

Defining tensors as generalized matrices, their ranks (order), and their crucial role in representing complex data types like images and video in Deep Learning frameworks (PyTorch, TensorFlow).

Understanding the Hessian matrix, second-order derivatives, and how the curvature of the loss surface impacts optimization and model stability.

Understanding the Jacobian matrix, its role in vector-valued functions, and its vital importance in backpropagation and modern deep learning frameworks.

A deep dive into the Normal Distribution, the Central Limit Theorem, and why Gaussian assumptions are the backbone of many Machine Learning algorithms.

Exploring the Discrete and Continuous Uniform distributions: the foundation of random sampling and model initialization.

Understanding Python's dynamic typing system, memory management, and the core data types essential for data science.

A comprehensive guide to vectors, their representation, key properties (magnitude, direction), and fundamental operations in Machine Learning.