Concepts64

📚TheoryAdvanced

Algorithmic Information Theory

Algorithmic Information Theory studies information content via the shortest programs that generate data, rather than via average-case probabilities.

#kolmogorov complexity#algorithmic probability#solomonoff induction+11
📚TheoryIntermediate

Online Algorithm Theory

Online algorithms make decisions step by step without seeing the future and are judged against an all-knowing offline optimum.

#online algorithms#competitive analysis#ski rental+12
📚TheoryIntermediate

Approximation Algorithm Theory

Approximation algorithms deliver provably near-optimal solutions for NP-hard optimization problems within guaranteed factors.

#approximation algorithms#ptas#fptas+12
📚TheoryIntermediate

Randomized Algorithm Theory

Randomized algorithms use random bits to make choices that simplify design, avoid worst cases, and often speed up computation.

#randomized algorithms#las vegas#monte carlo+12
📚TheoryIntermediate

Amortized Analysis

Amortized analysis measures the average cost per operation over a worst-case sequence, not over random inputs.

#amortized analysis#aggregate method#accounting method+12
📚TheoryIntermediate

Computability Theory

Computability theory studies the boundary between what can and cannot be computed by any algorithm.

#computability theory#turing machine#church-turing thesis+12
📚TheoryAdvanced

Optimal Transport Theory

Optimal Transport (OT) formalizes the cheapest way to move one probability distribution into another given a cost to move mass.

#optimal transport#wasserstein distance#kantorovich+12
📚TheoryIntermediate

Halting Problem

The Halting Problem asks whether a given program P will eventually stop when run on input x; there is no algorithm that correctly answers this for all P and x.

#halting problem#undecidable#diagonalization+12
📚TheoryAdvanced

Diffusion Models Theory

Diffusion models learn to reverse a simple noising process by estimating the score (the gradient of the log density) of data at different noise levels.

#diffusion models#ddpm#score matching+12
📚TheoryIntermediate

NP-Completeness

NP-completeness classifies decision problems that are both in NP and as hard as any problem in NP via polynomial-time reductions.

#np-complete#np-hard#polynomial-time reduction+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