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Concepts8

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
∑MathIntermediate

Law of Large Numbers

The Weak Law of Large Numbers (WLLN) says that the sample average of independent, identically distributed (i.i.d.) random variables with finite mean gets close to the true mean with high probability as the sample size grows.

#law of large numbers#weak law#sample mean+12
⚙️AlgorithmIntermediate

Distributed & Parallel Optimization

Data parallelism splits the training data across workers that compute gradients in parallel on a shared model.

#data parallelism
Advanced
Filtering by:
#variance reduction
#synchronous sgd
#asynchronous sgd
+12
⚙️AlgorithmIntermediate

Stratified & Latin Hypercube Sampling

Stratified sampling reduces Monte Carlo variance by dividing the domain into non-overlapping regions (strata) and sampling within each region.

#stratified sampling#latin hypercube sampling#variance reduction+11
⚙️AlgorithmIntermediate

Importance Sampling

Importance sampling rewrites an expectation under a hard-to-sample distribution p as an expectation under an easier distribution q, multiplied by a weight w = p/q.

#importance sampling#proposal distribution#self-normalized+12
⚙️AlgorithmIntermediate

Monte Carlo Estimation

Monte Carlo estimation approximates an expected value by averaging function values at random samples drawn from a probability distribution.

#monte carlo#expectation#variance reduction+12
⚙️AlgorithmIntermediate

Numerical Integration & Monte Carlo

Numerical integration approximates the area under a curve when an exact antiderivative is unknown, using deterministic quadrature rules or random sampling (Monte Carlo).

#numerical integration#quadrature#trapezoidal rule+11
⚙️AlgorithmIntermediate

Stochastic Gradient Descent (SGD)

Stochastic Gradient Descent (SGD) updates model parameters using small random subsets (mini-batches) of data, making learning faster and more memory-efficient.

#stochastic gradient descent#mini-batch#random shuffling+12
📚TheoryIntermediate

Bias-Variance Tradeoff

The bias–variance tradeoff explains how prediction error splits into bias squared, variance, and irreducible noise for squared loss.

#bias variance tradeoff#mse decomposition#polynomial regression+12