Machine learning and deep learning are pretty much math wrapped in a fancy frame. It all comes down to the math behind everything. So let’s explore and understand the various mathematical concepts used majorly in deep learning. Mathematics is fundamental to understanding and working with machine learning algorithms. Here are some key areas of math that are relevant to machine learning, along with resources to learn them:
- Linear Algebra:
Linear algebra is crucial for understanding the mathematical representations of data and operations in machine learning algorithms. Used to represent and manipulate data in vectors and matrices, which are fundamental to machine learning operations. It is essential for tasks like feature engineering, dimensionality reduction, and solving systems of equations.
Resources:
- “Introduction to Linear Algebra” by Gilbert Strang (MIT OpenCourseWare): https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
- Khan Academy Linear Algebra: https://www.khanacademy.org/math/linear-algebra
2. Calculus:
Calculus is used by machine learning algorithms for model training. Crucial for understanding optimization techniques used in machine learning algorithms. Concepts like gradients, derivatives, and partial derivatives are extensively used in training models through techniques like gradient descent.
Resources:
- “Calculus” by Gilbert Strang (MIT OpenCourseWare): https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/
- Khan Academy Calculus: https://www.khanacademy.org/math/calculus-1
3. Probability and Statistics:
Probability and statistics play a significant role in understanding uncertainty, model evaluation, and decision-making in machine learning. These concepts for the foundation of probabilistic models and many machine learning algorithms. Concepts like probability distributions, statistical inference, and hypothesis testing are widely used in data analysis and model evaluation.
Resources:
- “Introduction to Probability and Statistics” by Joseph Blitzstein and Jessica Hwang (Harvard OpenCourseWare): https://projects.iq.harvard.edu/stat110/home
- Khan Academy Probability and Statistics: https://www.khanacademy.org/math/probability
4. Multivariate Calculus:
Multivariate calculus is essential for understanding advanced optimization algorithms and working with high-dimensional data. That is, it extends calculus to functions with multiple variables and is necessary for more complex optimization techniques, especially in deep learning.
Resources:
- “Multivariable Calculus” by Denis Auroux (MIT OpenCourseWare): https://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/
- Khan Academy Multivariable Calculus: https://www.khanacademy.org/math/multivariable-calculus
Want to dig deeper? check out : Optimization and Information Theory :
Optimization techniques are used to fine-tune machine learning models and find the best parameters.
Information theory provides insights into data compression, feature selection, and measuring uncertainty.
Resources:
- “Convex Optimization” by Stephen Boyd and Lieven Vandenberghe (Stanford): https://web.stanford.edu/class/ee364a/
- “An Introduction to Optimization” by Edwin K. P. Chong and Stanislaw H. Zak (Wiley)
- “Information Theory, Pattern Recognition, and Neural Networks” by David MacKay (Cambridge University Press): https://www.inference.org.uk/mackay/itila/book.html
- “Elements of Information Theory” by Thomas M. Cover and Joy A. Thomas (Wiley)
Remember that understanding the underlying math will give you a deeper appreciation and ability to fine-tune and develop new machine learning algorithms. While some of these resources may be more advanced, there are plenty of introductory-level materials available online to start building your math foundations for machine learning. As you progress, you can explore more specialized topics based on your specific interests and areas of focus in machine learning.
Thank you for reading through, happy learning!
FOllow and shower claps as encouragement?!!! :)
