Mathematics and optimization

447 terms

# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

  • Spot instance - A spot instance is a cloud computing instance offered from spare capacity under terms that allow the provider to reclaim it.
  • Squared error loss - Squared error loss measures the mismatch between a numerical prediction and its target by squaring their difference.
  • Stability - Stability describes how little an output changes under specified disturbances.
  • Staleness - Staleness is the degree to which information used by a distributed computation lags behind the relevant current state.
  • State-value function - A state-value function assigns each state the expected future return obtained by starting there and following a specified policy.
  • Stochastic algorithm - A stochastic algorithm uses random choices as part of its execution.
  • Stochastic gradient descent - Stochastic gradient descent, or SGD, is an optimization method that updates parameters using a randomly sampled estimate of the objective's gradient.
  • Stochastic gradient Langevin dynamics - Stochastic gradient Langevin dynamics, or SGLD, is a method for approximately sampling a Bayesian posterior distribution using mini-batch gradients and...
  • Stochastic matrix - A stochastic matrix is a matrix of nonnegative numbers whose rows or columns sum to one, depending on the convention.
  • Stochastic process - A stochastic process is an indexed collection of random variables defined on a common probability space.
  • Stratification - Stratification divides a population or dataset into defined subgroups, called strata, using selected characteristics.
  • Subgradient - A subgradient is a vector that defines a supporting linear lower bound to a function at a specified point.
  • Subgradient descent - Subgradient descent is an iterative optimization method that replaces an ordinary gradient with a subgradient.
  • Subspace - A subspace is a subset of a vector space that is itself a vector space under the same addition and scalar multiplication.
  • Sum-of-squares optimization - Sum-of-squares optimization, or SOS optimization, uses representations of polynomials as sums of squared polynomials to obtain tractable certificates of...
  • Superiority and inferiority ranking method - The superiority and inferiority ranking method, usually abbreviated SIR, is a family of methods for comparing alternatives across several criteria.
  • Supporting hyperplane - A supporting hyperplane is a flat boundary that passes through a boundary point of a set while leaving the entire set on one side.
  • Supremum (or least upper bound) - The supremum of a set of real numbers is its least upper bound: the smallest number that is at least as large as every member of the set.
  • Symbolic-numeric computation - Symbolic-numeric computation combines algebraic manipulation with numerical calculation in one mathematical workflow.
  • Symmetric matrix - A real symmetric matrix is a square matrix that equals its transpose.
  • Tabular data - Tabular data organize observations into rows and shared attributes into columns.
  • Tall matrix - A tall matrix has more rows than columns. If its shape is m by d, it is tall when m > d.
  • Tensor size - Tensor size, in the Google/TensorFlow glossary sense, is the total number of scalar elements in a tensor.
  • Term-document matrix - A term-document matrix represents a collection of documents using numerical associations between terms and documents.
  • Ternary search - Ternary search is an interval-reduction method for finding the minimum or maximum of a one-dimensional unimodal function.
  • Theil index - The Theil index is an entropy-based measure of inequality in nonnegative quantities such as income or resource allocations.
  • Theorem proving - Theorem proving is the process of establishing that a statement follows logically from specified assumptions, definitions, and inference rules.
  • Toeplitz matrix - A Toeplitz matrix is a matrix whose entries stay constant along each diagonal running from the upper left toward the lower right.
  • Total correlation - Total correlation measures statistical dependence among several random variables by comparing the sum of their individual entropies with their joint entropy.
  • Total variation - Total variation measures accumulated change across a specified structure.
  • Trace - The trace of a square matrix is the sum of its main-diagonal entries, written tr(A). Those entries run from the upper-left corner to the lower-right corner.
  • Training error - Training error is a model's measured loss on the examples used to fit it.
  • Trajectory optimization - Trajectory optimization chooses a time-varying sequence of states and controls that minimizes a specified cost while satisfying dynamics and other constraints.
  • Transpose - The transpose of a matrix is formed by swapping its row and column positions. An entry originally in row i, column j moves to row j, column i.
  • Triangle inequality - The triangle inequality says that the distance directly between two points is no greater than the sum of their distances through a third point.
  • Triangular network coding - Triangular network coding is a packet-coding approach that combines suitably shifted and zero-padded binary payloads using XOR operations.
  • Truncated Newton method - A truncated Newton method approximately solves the Newton equations inside each optimization iteration, stopping the inner solve before full accuracy when...
  • Trust region - A trust region is a neighborhood around the current point within which an optimization algorithm uses a local model to propose a step.
  • Tsallis entropy - Tsallis entropy is a parameterized entropy measure defined for probabilities pi by Sq=k(1−Σpiᑫ)/(q−1), for q≠1.
  • Unconstrained minimization - Unconstrained minimization is the task of finding input values that make an objective function as small as possible without imposing separate equality...
  • Unit vector - A unit vector is a vector whose length is one under the chosen norm.
  • Unitary matrix - A unitary matrix is a square complex-valued matrix whose conjugate transpose is its inverse.
  • Universal approximator theorem - The universal approximator theorem, more commonly called the universal approximation theorem, describes the expressive capacity of certain neural-network...
  • User matrix - A user matrix is the collection of learned user representations in a matrix-factorization recommendation model.
  • Value iteration - Value iteration is a dynamic-programming method for finding optimal state values in a Markov decision process.
  • Vanishing gradient - A vanishing gradient is a training signal that becomes very small as derivatives are propagated backward through many computational steps.
  • Variable-order Bayesian network - A variable-order Bayesian network is a probabilistic model in which the conditioning information needed for a variable can depend on the observed context.
  • Variable-order Markov model - A variable-order Markov model predicts the next symbol in a sequence using a context whose length depends on the recent history.

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