A place to compile all my notes for various classes. This exists since reviewing my notes has started to become a pain.
- Trying to figure out which notebook holds what
- Attempting to decipher my messy handwriting
- The stacks of 3 subject notebooks takes up a lot of space
All of the above is mitigated if I publish my notes online. That way, I can quickly find what I want, the notes don’t take up physical space, and I don’t need to read my god-awful handwriting. I can also access my notes from anywhere.
Feel free to browse. Any errata is of my own accord, and many of these are works in progress. The notes are also quite messy because I type them in class.
Here is a compendium of my notes that I took to review for Machine Learning. This was meant to be a quick refresher on concepts and to put everything in one place. For a less cursory version, see the background section under Resources at the course website.
Probability and Statistics Basic Concepts Axioms of Probability Definitions Baye’s Rule Expectation Common Probability Distributions Bernoulli Distribution Binomial Distribution Poisson Distribution Categorical Distribution Multinomial Distribution Guassian(Normal) Distribution Multivariate Gaussian Distribution Laplace distribution Dirac Delta Distribution Mixtures of Distributions Common Functions Logistic sigmoid $\sigma(x)$ Softplus Function $\Zeta(x)$ Information Theory Self-Information Shannon Entropy Kullback-Leibler (KL) divergence Cross-entropy Exponential Distribution Chi-squared Distribution Basics Goodness of Fit (GOF) Independence T-test One Sample Two Sample Paired Unpaired Linear Algebra Types of Objects in Linear Algebra Matrix Operations Central Problem of Linear Algebra Gaussian Elimination Reduced Row Echelon Form (RREF) Reading of Solutions of Ax=b from RREF LU Decomposition LDU Decomposition Identity and Inverses Vector Spaces Subspaces Orthogonal Complements Linear Transformations Diagonalization Change of Basis Linear Dependence and Span Basis and Dimension Norms Orthogonal Bases Gram-Schmidt and Orthogonal Complements Eigendecomposition Singular Value Decomposition (SVD) Moore-Penrose Pseudoinverse QR Decomposition Gram-Schmidt Trace Determinant Kernel, Range, Nullity,Rank Mapping definitions Kernel Rank and Nullity Least Squares Probability and Statistics Basic Concepts Axioms of Probability Probability Measure $P: \mathbb{F} \rightarrow \mathbb{{R}}$ such that $P(A) \geq 0$ for all $A \in \mathbb{F}$ $P(\Omega) = 1$ If $A_{1},A_{2}…$ are disjoint events, then $P(\cup A_{i}) = \Sigma_{i} P(A_{i})$ Definitions Sample space $\Omega$: The set of all possible outcomes Event space $\mathbb{F}:A$ is a subset of $\Omega$ a random variable quantity that has an uncertain value....