Variational Autoencoder
A generative model that learns to encode input data into a latent space and then decode from that space to reconstruct the original data, often used for generating new data samples.
Category: Concepts
Lipschitz Function
A function is Lipschitz if there exists a constant such that the absolute difference between the function values is bounded by this constant times the distance between the inputs.
Convex Function
A function is convex if the line segment between any two points on the graph of the function lies above or on the graph.
Uniform Law of Large Numbers
A statistical principle stating that the average of a sequence of random variables converges to the expected value as the number of variables increases.
Subdifferential
A generalization of the derivative for convex functions that allows for the analysis of nonsmooth optimization problems.
High-Dimensional Optimization
High-dimensional optimization involves finding optimal solutions in spaces with a large number of dimensions, which poses unique computational challenges.
Adaptive Lower Bound
An adaptive lower bound is a dynamic threshold that adjusts to avoid vacuous acceptance regions during optimization.
Worst-m Memory Mechanism
A memory mechanism that restricts comparisons to a fixed-size subset of past evaluations to improve computational efficiency.
Every Call is Precious (ECP)
ECP is an optimization framework that ensures each accepted function evaluation is potentially informative to the optimization process.
Lipschitz Continuity
A function is Lipschitz continuous if there exists a constant such that the absolute difference in function values is bounded by this constant times the distance between input points.