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Concepts9

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📐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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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∑MathAdvanced

f-Divergences

An f-divergence measures how different two probability distributions P and Q are by averaging a convex function f of the density ratio p(x)/q(x) under Q.

#f-divergence#csiszar divergence#kullback–leibler+11
∑MathAdvanced

Evidence Lower Bound (ELBO)

The Evidence Lower Bound (ELBO) is a tractable lower bound on the log evidence log p(x) used to perform approximate Bayesian inference.

#elbo
Advanced
Filtering by:
#importance sampling
#variational inference
#vae
+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
⚙️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
📚TheoryIntermediate

ELBO (Evidence Lower Bound)

The Evidence Lower Bound (ELBO) is a tractable lower bound on the log evidence log p(x) that enables learning and inference in latent variable models like VAEs.

#elbo#variational inference#vae+12
📚TheoryAdvanced

Policy Gradient Theorem

The policy gradient theorem tells us how to push a stochastic policy’s parameters to increase expected return by following the gradient of expected rewards.

#policy gradient#reinforce#actor-critic+11
📚TheoryAdvanced

Measure Theory

Measure theory generalizes length, area, and probability to very flexible spaces while keeping countable additivity intact.

#measure theory#sigma-algebra#lebesgue integral+12