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Concepts22

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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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📚TheoryAdvanced

PAC-Bayes Theory

PAC-Bayes provides high-probability generalization bounds for randomized predictors by comparing a data-dependent posterior Q to a fixed, data-independent prior P through KL(Q||P).

#pac-bayes#generalization bound#kl divergence+12
📚TheoryIntermediate

Concentration Inequalities

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

#concentration inequalities
12
Advanced
Filtering by:
#kl divergence
#hoeffding inequality
#chernoff bound
+12
📚TheoryAdvanced

Information-Theoretic Lower Bounds

Information-theoretic lower bounds tell you the best possible performance any learning algorithm can achieve, regardless of cleverness or compute.

#information-theoretic lower bounds#fano inequality#le cam method+12
📚TheoryAdvanced

Variational Inference Theory

Variational Inference (VI) replaces an intractable posterior with a simpler distribution and optimizes it by minimizing KL divergence, which is equivalent to maximizing the ELBO.

#variational inference#elbo#kl divergence+12
📚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

Information Bottleneck Theory

Information Bottleneck (IB) studies how to compress an input X into a representation Z that still preserves what is needed to predict Y.

#information bottleneck#mutual information#variational information bottleneck+12
📚TheoryIntermediate

Mutual Information

Mutual Information (MI) measures how much knowing one random variable reduces uncertainty about another.

#mutual information#entropy#kl divergence+12
📚TheoryIntermediate

KL Divergence (Kullback-Leibler Divergence)

Kullback–Leibler (KL) divergence measures how one probability distribution P devotes probability mass differently from a reference distribution Q.

#kl divergence#kullback-leibler#cross-entropy+12
📚TheoryIntermediate

Shannon Entropy

Shannon entropy quantifies the average uncertainty or information content of a random variable in bits when using base-2 logarithms.

#shannon entropy#information gain#mutual information+12
📚TheoryIntermediate

Information Theory

Information theory quantifies uncertainty and information using measures like entropy, cross-entropy, KL divergence, and mutual information.

#entropy#cross-entropy#kl divergence+12