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Concepts356

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
📚TheoryIntermediate

KL Divergence

KL divergence measures how much information is lost when using model Q to approximate the true distribution P.

#kl divergence#relative entropy#cross-entropy+12
∑MathIntermediate

Confidence Intervals & Prediction Intervals

A confidence interval estimates a fixed but unknown parameter (like a population mean) with a range that would capture the true value in a long run of repeated samples.

#confidence interval
89101112
Advanced
#prediction interval
#t distribution
+12
📚TheoryIntermediate

Empirical Risk Minimization

Empirical Risk Minimization (ERM) chooses a model that minimizes the average loss on the training data.

#empirical risk minimization#expected risk#loss function+12
∑MathIntermediate

Sufficient Statistics

A sufficient statistic compresses all information in the sample about a parameter into a lower-dimensional summary without losing inferential power.

#sufficient statistic#fisher neyman factorization#exponential family+12
⚙️AlgorithmIntermediate

Bootstrap & Resampling Methods

Bootstrap is a resampling method that estimates uncertainty by repeatedly sampling with replacement from the observed data.

#bootstrap#resampling#confidence intervals+12
∑MathIntermediate

Hypothesis Testing

Hypothesis testing is a decision-making process to evaluate claims about a population using sample data.

#hypothesis testing#null hypothesis#alternative hypothesis+12
📚TheoryIntermediate

Bayesian Inference

Bayesian inference updates prior beliefs with observed data to produce a posterior distribution P(\theta\mid D).

#bayesian inference#posterior#prior+12
∑MathIntermediate

Maximum A Posteriori (MAP) Estimation

Maximum A Posteriori (MAP) estimation chooses the parameter value with the highest posterior probability after seeing data.

#map estimation#posterior mode#bayesian inference+12
∑MathIntermediate

Maximum Likelihood Estimation (MLE)

Maximum Likelihood Estimation (MLE) chooses parameters that make the observed data most probable under a chosen model.

#maximum likelihood#log-likelihood#bernoulli mle+12
∑MathIntermediate

Exponential Family Distributions

Exponential family distributions express many common probability models in a single template p(x|η) = h(x) exp(η^T T(x) − A(η)).

#exponential family#natural parameter#sufficient statistics+12
∑MathIntermediate

Markov Chains

A Markov chain models a system that moves between states where the next step depends only on the current state, not the past.

#markov chain#transition matrix#stationary distribution+11
∑MathIntermediate

Multivariate Gaussian Distribution

A multivariate Gaussian (normal) distribution models a vector of real-valued variables with a bell-shaped probability hill in many dimensions.

#multivariate normal#gaussian distribution#covariance matrix+11