Welcome to the "Deep Learning Math" tutorial! This page is designed to help you understand the fundamental mathematical concepts required for deep learning. If you are looking for a comprehensive guide, be sure to check out our Deep Learning Basics Tutorial.
Table of Contents
Linear Algebra
Linear algebra is the foundation of many machine learning and deep learning algorithms. It deals with vectors, matrices, and linear transformations. Here are some key concepts:
- Vectors: A mathematical object that has both magnitude and direction.
- Matrices: A rectangular array of numbers that can represent linear transformations.
- Determinants: A scalar value that can be computed from a matrix and encapsulates certain properties of the matrix.
For a deeper understanding, you might want to read our Linear Algebra Basics.
Calculus
Calculus is essential for understanding how neural networks learn and optimize their parameters. Here are some fundamental concepts:
- Derivatives: A measure of how a function changes as its input changes.
- Integrals: A way to sum up infinitely small parts of a function.
- Gradients: The vector of partial derivatives of a function.
If you're looking to improve your calculus skills, our Calculus Tutorial is a great resource.
Probability and Statistics
Probability and statistics provide the theoretical framework for understanding and building machine learning models. Here are some key terms:
- Probability: The likelihood that a specific event will occur.
- Statistics: The practice of collecting, analyzing, and interpreting data.
- Bayesian Inference: A method of statistical inference that applies to cases where the probability of a hypothesis is updated as more evidence or information becomes available.
To delve deeper into these topics, explore our Probability and Statistics Tutorial.
Optimization
Optimization is the process of finding the best solution among a set of possible solutions. In deep learning, optimization is used to find the weights and biases of a neural network that minimize a loss function. Here are some commonly used optimization algorithms:
- Stochastic Gradient Descent (SGD): An iterative optimization algorithm that updates parameters in the direction of the negative gradient.
- Adam: An optimization algorithm that combines the best properties of Momentum and RMSprop.
Learn more about optimization techniques in our Optimization Tutorial.