Concepts37
Category
Concentration Inequalities
Concentration inequalities give high-probability bounds that random outcomes stay close to their expectations, even without knowing the full distribution.
Markov Chain Theory
A Markov chain is a random process where the next state depends only on the current state, not the full history.
Spectral Graph Theory
Spectral graph theory studies graphs by looking at eigenvalues and eigenvectors of matrices like the adjacency matrix A and Laplacians L and L_norm.
Parallel Algorithm Theory
Parallel algorithm theory studies how to solve problems faster by coordinating many processors that share work and memory.
Online Algorithm Theory
Online algorithms make decisions step by step without seeing the future and are judged against an all-knowing offline optimum.
Approximation Algorithm Theory
Approximation algorithms deliver provably near-optimal solutions for NP-hard optimization problems within guaranteed factors.
Randomized Algorithm Theory
Randomized algorithms use random bits to make choices that simplify design, avoid worst cases, and often speed up computation.
Amortized Analysis
Amortized analysis measures the average cost per operation over a worst-case sequence, not over random inputs.
Computability Theory
Computability theory studies the boundary between what can and cannot be computed by any algorithm.
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.
NP-Completeness
NP-completeness classifies decision problems that are both in NP and as hard as any problem in NP via polynomial-time reductions.
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.