Probability box - A probability box, usually called a p-box, represents uncertainty about a probability distribution using lower and upper bounds on its cumulative...
Projected gradient descent - Projected gradient descent is an optimization method that combines a gradient step with a projection onto a feasible set.
Proximal algorithm - A proximal algorithm is an optimization method built around proximal operators, which balance reducing a function against staying near a supplied point.
Proximal operator - A proximal operator maps a point to the minimizer of a function plus a quadratic penalty for moving away from that point.
Pseudocontractive operator - A pseudocontractive operator is a mapping T on a Hilbert space, or a suitable subset, for which ||Tx−Ty||² ≤ ||x−y||² + ||(I−T)x−(I−T)y||² for every pair of...
Pseudoinverse - A pseudoinverse is a generalized matrix inverse that can be defined even when a matrix is rectangular or singular.
Quadratic function - A quadratic function is a function built from constant, linear and second-degree terms. For a real vector x, it can be written f(x)=xᵀQx+bᵀx+c.
Quasi-stationary distribution - A quasi-stationary distribution is a probability distribution over a process's nonabsorbing states that remains unchanged when the process starts with that...
Rademacher complexity - Rademacher complexity measures how strongly a class of functions can align with independent random positive and negative signs on sampled inputs.
Random optimization - Random optimization is an optimization approach that proposes random changes to a current solution and uses objective evaluations to decide whether to...
Random projection - Random projection is a dimensionality-reduction method that maps a feature vector into fewer coordinates using a suitably generated random matrix.
Rank - The rank of a matrix is the number of linearly independent columns it contains, equivalently the number of linearly independent rows.
Rank (Tensor) - Tensor rank, in TensorFlow and similar array-programming terminology, is the number of axes a tensor has.
Realization - A realization is a particular value taken by a random variable when an outcome of a random experiment is specified or observed.
Recurrence period density entropy - Recurrence period density entropy, or RPDE, is a time-series measure that summarizes how spread out the observed return times are when a signal's...
Regret - Regret is the difference between a decision-maker's loss and the loss of a specified comparison strategy.
Remez algorithm - The Remez algorithm is an iterative method for finding an approximation whose largest absolute error over a specified interval is as small as possible.
Rényi divergence - Rényi divergence is a family of measures for comparing two probability distributions, indexed by an order parameter α.
Rényi entropy - Rényi entropy is a family of measures of uncertainty or diversity in a probability distribution, controlled by an order parameter usually written α.
Revenue equivalence theorem - The revenue equivalence theorem states that, under specified auction-model assumptions, mechanisms with the same allocation probabilities and the same...
RMSNorm - RMSNorm, short for root mean square normalization, is a neural-network normalization operation that rescales a vector using the square root of its mean...
Robust optimization - Robust optimization is a way to choose decisions that remain feasible, or control worst-case cost, when uncertain inputs vary within a specified uncertainty...
Root finding - Root finding is the task of finding an input at which a function equals zero.
Ruzzo - Tompa algorithm - The Ruzzo - Tompa algorithm finds all maximal scoring contiguous subsequences in a sequence of real-valued scores, using linear time when implemented with...
Scale co-occurrence matrix - A scale co-occurrence matrix is an image-texture descriptor that counts how values at corresponding locations occur together across two image scales.
Scatterplot matrix - A scatterplot matrix is a grid of plots showing pairwise relationships among several variables.
Schur decomposition - Schur decomposition expresses a square complex matrix as A=QTQ*, where Q is unitary and T is upper triangular. The diagonal entries of T are A's eigenvalues.
Search-based software engineering - Search-based software engineering, or SBSE, applies optimization search to software-engineering problems.
Semidefinite embedding - Semidefinite embedding, or SDE, is a nonlinear dimensionality-reduction method that learns a matrix of inner products while preserving specified local...
Sequence - A sequence is an ordered collection of elements indexed by positions. Elements may repeat, and changing their order can change the sequence.
Sequential minimal optimization - Sequential minimal optimization, or SMO, is an algorithm for training support vector machines by repeatedly solving very small pieces of their quadratic...
Shape (Tensor) - A tensor's shape lists the lengths of its axes in order. For example, shape (4,7,3) describes three axes containing four, seven and three positions.
Shaping theorem - The shaping theorem is a reinforcement-learning result showing that a particular form of added reward can preserve the set of optimal policies.
Shear matrix - A shear matrix represents a transformation that slides points parallel to a fixed line or plane by amounts proportional to their distance from it.
Simple function - A simple function is a measurable function that takes only finitely many distinct values.
Simplex algorithm - The simplex algorithm is a method for solving linear programs: optimization problems with a linear objective and linear constraints.
Simulation-based optimization - Simulation-based optimization combines a simulation model with a procedure for searching for better decisions.
Singular matrix - A singular matrix is a square matrix that has no inverse.
Singular value - A singular value is a nonnegative number describing how much a matrix stretches a particular orthogonal input direction.
Singular value decomposition - Singular value decomposition, or SVD, factors a matrix into orthonormal input and output directions together with nonnegative scale factors.
Situation calculus - Situation calculus is a logical framework for describing actions and reasoning about how their effects change the world.
Skip connection - A skip connection is a neural-network connection that carries information past one or more intervening layers to a later part of the network.
Social cognitive optimization - Social cognitive optimization, or SCO, is a population-based optimization method inspired by learning from other people's examples.
Soft label - A soft label is a target that assigns weights or probabilities across classes instead of selecting only one class.
Sparse matrix - A sparse matrix is a two-dimensional numerical array in which most entries are zero.
Spherical contact distribution function - The spherical contact distribution function describes how far a location in space is from the nearest part of a random spatial pattern.
Spiral optimization algorithm - The spiral optimization algorithm is a multipoint search method for continuous optimization that moves candidate solutions through rotating, contracting...