The Most Important Machine Learning Equations: A Comprehensive Guide
13 days ago
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- #machine-learning
- #mathematics
- Machine learning (ML) is a field driven by mathematics, with core equations essential for building models and optimizing algorithms.
- Probability and information theory provide the foundation for reasoning about uncertainty and measuring differences between distributions.
- Bayes’ Theorem is a cornerstone of probabilistic reasoning, used in tasks like classification and inference.
- Entropy measures uncertainty in a probability distribution and is fundamental in decision trees and information gain calculations.
- Joint and conditional probability are building blocks of Bayesian methods and probabilistic models.
- Kullback-Leibler Divergence (KLD) measures how much one probability distribution diverges from another, used in variational autoencoders (VAEs).
- Cross-entropy quantifies the difference between true and predicted distributions, widely used as a loss function in classification.
- Linear algebra powers transformations and structures in ML models, with linear transformations being core operations in neural networks.
- Eigenvalues and eigenvectors describe how a matrix scales and rotates space, crucial for understanding data variance in PCA.
- Singular Value Decomposition (SVD) breaks down a matrix into orthogonal matrices and a diagonal matrix, revealing intrinsic data structure.
- Gradient descent updates parameters by moving opposite to the gradient of the loss function, scaled by a learning rate.
- Backpropagation applies the chain rule to compute gradients of the loss with respect to weights in neural networks.
- Mean Squared Error (MSE) calculates the average squared difference between true and predicted values, common in regression tasks.
- The diffusion process describes a forward diffusion process where data is gradually noised over time, key in generative AI.
- Convolution combines two functions by sliding one over the other, extracting features in data like images, core to CNNs.
- Softmax converts raw scores into probabilities, ideal for multi-class classification in neural network outputs.
- Attention computes a weighted sum of values based on the similarity between queries and keys, powering transformers in NLP.