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# Loss function

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. [1]

80 relations: Abraham Wald, Actuarial science, Bayesian probability, Cardinal utility, Closed-form expression, Computational neuroscience, Continuous function, Decision rule, Decision theory, Density estimation, Derivative test, Design of experiments, Deviation (statistics), Differentiable function, Discounted maximum loss, Disease, Econometrics, Economic cost, Economics, Estimation theory, Event (probability theory), Expected utility hypothesis, Expected value, Financial risk management, Fitness function, Frequentist inference, Function space, Harald Cramér, Hinge loss, Independent and identically distributed random variables, Indicator function, Invariant estimator, Least squares, Leonard Jimmie Savage, Linear regression, Linear–quadratic regulator, Location parameter, Loss functions for classification, Machine learning, Mathematical optimization, Mean, Mean integrated squared error, Mean squared error, Median, Minimax, Mortality rate, Nassim Nicholas Taleb, Norm (mathematics), Optimal control, Optimization problem, ... Expand index (30 more) »

## Abraham Wald

Abraham Wald (Hungarian: Wald Ábrahám, –) was an American mathematician who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis.

## Actuarial science

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance and other industries and professions.

## Bayesian probability

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

## Cardinal utility

In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations.

## Closed-form expression

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.

## Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system.

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

## Decision rule

In decision theory, a decision rule is a function which maps an observation to an appropriate action.

## Decision theory

Decision theory (or the theory of choice) is the study of the reasoning underlying an agent's choices.

## Density estimation

In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function.

## Derivative test

In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point.

## Design of experiments

The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation.

## Deviation (statistics)

In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean.

## Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

## Discounted maximum loss

Discounted maximum loss, also known as worst-case risk measure, is the present value of the worst-case scenario for a financial portfolio.

## Disease

A disease is any condition which results in the disorder of a structure or function in an organism that is not due to any external injury.

## Econometrics

Econometrics is the application of statistical methods to economic data and is described as the branch of economics that aims to give empirical content to economic relations.

## Economic cost

Economic cost is the combination of gains and losses of any goods that have a value attached to them by any one individual.

## Economics

Economics is the social science that studies the production, distribution, and consumption of goods and services.

## Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component.

## Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

## Expected utility hypothesis

In economics, game theory, and decision theory the expected utility hypothesis, concerning people's preferences with regard to choices that have uncertain outcomes (gambles), states that if specific axioms are satisfied, the subjective value associated with an individual's gamble is the statistical expectation of that individual's valuations of the outcomes of that gamble.

## Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

## Financial risk management

Financial risk management is the practice of economic value in a firm by using financial instruments to manage exposure to risk: operational risk, credit risk and market risk, foreign exchange risk, shape risk, volatility risk, liquidity risk, inflation risk, business risk, legal risk, reputational risk, sector risk etc.

## Fitness function

A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims.

## Frequentist inference

Frequentist inference is a type of statistical inference that draws conclusions from sample data by emphasizing the frequency or proportion of the data.

## Function space

In mathematics, a function space is a set of functions between two fixed sets.

## Harald Cramér

Harald Cramér (25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory.

## Hinge loss

In machine learning, the hinge loss is a loss function used for training classifiers.

## Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

## Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

## Invariant estimator

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity.

## Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

## Leonard Jimmie Savage

Leonard Jimmie Savage (born Leonard Ogashevitz; 20 November 1917 – 1 November 1971) was an American mathematician and statistician.

## Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

The theory of optimal control is concerned with operating a dynamic system at minimum cost.

## Location parameter

In statistics, a location family is a class of probability distributions that is parametrized by a scalar- or vector-valued parameter x_0, which determines the "location" or shift of the distribution.

## Loss functions for classification

In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to).

## Machine learning

Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.

## Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

## Mean

In mathematics, mean has several different definitions depending on the context.

## Mean integrated squared error

In statistics, the mean integrated squared error (MISE) is used in density estimation.

## Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and what is estimated.

## Median

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

## Minimax

Minimax (sometimes MinMax or MM) is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario.

## Mortality rate

Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time.

## Nassim Nicholas Taleb

Nassim Nicholas Taleb (نسيم نقولا طالب., alternatively Nessim or Nissim, born 1960) is a Lebanese–American essayist, scholar, statistician, former trader, and risk analyst, whose work focuses on problems of randomness, probability, and uncertainty.

## Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

## Optimal control

Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.

## Optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.

## Ordinal utility

In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale.

## Outlier

In statistics, an outlier is an observation point that is distant from other observations.

## Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

## Posterior probability

In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.

## Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

## Probability measure

In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.

## Profit maximization

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input, and output levels that lead to the greatest profit.

## Public health

Public health is "the science and art of preventing disease, prolonging life and promoting human health through organized efforts and informed choices of society, organizations, public and private, communities and individuals".

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.

## Regret (decision theory)

In decision theory, on making decisions under uncertainty—should information about the best course of action arrive after taking a fixed decision—the human emotional response of regret is often experienced.

## Reinforcement learning

Reinforcement learning (RL) is an area of machine learning inspired by behaviourist psychology, concerned with how software agents ought to take actions in an environment so as to maximize some notion of cumulative reward.

## Risk aversion

In economics and finance, risk aversion is the behavior of humans (especially consumers and investors), when exposed to uncertainty, in attempting to lower that uncertainty.

## Risk neutral preferences

In economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking.

## Risk-seeking

In economics and finance, a risk-seeker or risk-lover is a person who has a preference for risk.

## Safety engineering

Safety engineering is an engineering discipline which assures that engineered systems provide acceptable levels of safety.

## Scoring rule

In decision theory, a score function, or scoring rule, measures the accuracy of probabilistic predictions.

## Statistic

A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value).

## Statistical classification

In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known.

## Statistical population

In statistics, a population is a set of similar items or events which is of interest for some question or experiment.

## Statistical risk

Statistical risk is a quantification of a situation's risk using statistical methods.

## Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

## Stochastic control

Stochastic control or stochastic optimal control is a subfield of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system.

## Student's t-test

The t-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis.

## Support (measure theory)

In mathematics, the support (sometimes topological support or spectrum) of a measure μ on a measurable topological space (X, Borel(X)) is a precise notion of where in the space X the measure "lives".

## Utility

Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

## W. Edwards Deming

William Edwards Deming (October 14, 1900 – December 20, 1993) was an American engineer, statistician, professor, author, lecturer, and management consultant.

## References

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