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Concepts9

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
⚙️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
⚙️AlgorithmAdvanced

Langevin Dynamics & Score-Based Sampling

Langevin dynamics is a noisy gradient-ascent method that moves particles toward high probability regions while adding Gaussian noise to ensure proper exploration.

Advanced
Group:
Sampling & Monte Carlo Methods
#langevin dynamics
#mala
#ula
+12
⚙️AlgorithmAdvanced

Hamiltonian Monte Carlo (HMC)

Hamiltonian Monte Carlo (HMC) uses gradients of the log-density to propose long-distance moves that still land in high-probability regions.

#hamiltonian monte carlo#hmc#mcmc+11
⚙️AlgorithmIntermediate

Gibbs Sampling

Gibbs sampling is an MCMC method that generates samples by repeatedly drawing each variable from its conditional distribution given the others.

#gibbs sampling#mcmc#markov chain+12
⚙️AlgorithmIntermediate

Metropolis-Hastings Algorithm

Metropolis–Hastings is a clever accept/reject method that lets you sample from complex probability distributions using only an unnormalized density.

#metropolis-hastings#mcmc#acceptance ratio+12
⚙️AlgorithmIntermediate

Markov Chain Monte Carlo (MCMC)

MCMC builds a random walk (a Markov chain) whose long-run visiting frequency matches your target distribution, even when the target is only known up to a constant.

#mcmc#metropolis-hastings#gibbs sampling+12
⚙️AlgorithmIntermediate

Rejection Sampling

Rejection sampling draws from a hard target distribution by using an easier proposal and accepting with probability p(x)/(M q(x)).

#rejection sampling#accept-reject#proposal distribution+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