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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts10

Groups

๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

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๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

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AllBeginnerIntermediate
โˆ‘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
โˆ‘MathIntermediate

Exponential Family Distributions

Exponential family distributions express many common probability models in a single template p(x|ฮท) = h(x) exp(ฮท^T T(x) โˆ’ A(ฮท)).

#exponential family
Advanced
Group:
Probability Theory
#natural parameter
#sufficient statistics
+12
โˆ‘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
โˆ‘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
โˆ‘MathIntermediate

Expectation, Variance & Moments

Expectation is the long-run average value of a random variable and acts like the balance point of its distribution.

#expectation#variance#moments+12
โˆ‘MathIntermediate

Random Variables & Distributions

A random variable maps uncertain outcomes to numbers and is described by a distribution that assigns likelihoods to values or ranges.

#random variable#pmf#pdf+12
โˆ‘MathIntermediate

Probability Axioms & Rules

Kolmogorovโ€™s axioms define probability as a measure on events: non-negativity, normalization, and countable additivity.

#kolmogorov axioms#probability measure#sample space+12
๐Ÿ“šTheoryIntermediate

Concentration Inequalities

Concentration inequalities give high-probability bounds that random outcomes stay close to their expectations, even without knowing the full distribution.

#concentration inequalities#hoeffding inequality#chernoff bound+12
๐Ÿ“šTheoryIntermediate

Central Limit Theorem

The Central Limit Theorem (CLT) says that the sum or average of many independent, identically distributed variables with finite variance becomes approximately normal (Gaussian).

#central limit theorem#berry-esseen#lindeberg+12
โˆ‘MathIntermediate

Bayes' Theorem

Bayes' Theorem tells you how to update the probability of a hypothesis after seeing new evidence.

#bayes' theorem#posterior probability#prior probability+11