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# Loss function

In mathematical optimization, statistics, decision theory and machine learning, 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]

72 relations: Abraham Wald, Actuarial science, Bayesian inference, Bayesian probability, Cardinal utility, Closed-form expression, Death, Decision rule, Decision theory, Density estimation, Derivative test, Design of experiments, Deviation (statistics), Discounted maximum loss, Disease, Economic cost, Economics, Estimation theory, Event (probability theory), Expected utility hypothesis, Expected value, Fitness function, Frequentist inference, Function space, 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, Optimal control, Optimization problem, Ordinal utility, Pierre-Simon Laplace, Posterior probability, Prior probability, Probability density function, Probability measure, Profit maximization, ... Expand index (22 more) »

## Abraham Wald

Abraham Wald (Hungarian: Wald Ábrahám, –) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) 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 inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as evidence is acquired.

## Bayesian probability

Bayesian probability is one interpretation of the concept of probability.

## 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.

## Death

Death is the termination of all biological functions that sustain a living organism.

## Decision rule

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

## Decision theory

Decision theory or theory of choice in economics, psychology, philosophy, mathematics, computer science, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision.

## 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

In general usage, design of experiments (DOE) or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not.

## 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.

## 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 a particular abnormal condition, a disorder of a structure or function, that affects part or all of an organism.

## Economic cost

Economic cost is the gains and losses in money, time and resources of one course of action compared to another.

## Economics

Economics is the social science that seeks to describe the factors which determine 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 is a hypothesis concerning people's preferences with regard to choices that have uncertain outcomes (gambles).

## Expected value

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

## 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 one of a number of possible techniques of formulating generally applicable schemes for making statistical inference: drawing conclusions from sample data by the emphasis on the frequency or proportion of the data.

## Function space

In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It is called a space because in many applications it is a topological space (including metric spaces), a vector space, or both.

## 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.) 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 bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.

## 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 the approximate 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 an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression.

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.

## Machine learning

Machine learning is a subfield of computer sciencehttp://www.britannica.com/EBchecked/topic/1116194/machine-learning that evolved from the study of pattern recognition and computational learning theory in artificial intelligence.

## Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) 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) of an estimator measures the average of the squares of the "errors", that is, the difference between the estimator and what is estimated.

## Median

In statistics and probability theory, a median is the number 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.

## Optimal control

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies.

## 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.

## Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was an influential 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.

## Prior probability

In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence 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 that describes the relative likelihood for this random variable to take on a given value.

## 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 determines the price and output level that returns the greatest profit.

## Public health

Public health refers to "the science and art of preventing disease, prolonging life and promoting health through organized efforts and informed choices of society, organizations, public and private, communities and individuals." It is concerned with threats to health based on population health analysis.

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

## Random variable

In probability and statistics, a random variable, aleatory variable or stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense).

## Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

## Regression analysis

In statistics, regression analysis is a statistical process for estimating the relationships among variables.

## Regret (decision theory)

Regret is the negative emotion experienced when learning that an alternative course of action would have resulted in a more favorable outcome.

## Reinforcement learning

Reinforcement learning is an area of machine learning inspired by behaviorist 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, to attempt to reduce that uncertainty.

## Risk management

Risk management is the identification, assessment, and prioritization of risks (defined in ISO 31000 as the effect of uncertainty on objectives) followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities.

## Risk neutral

In economics and finance, risk neutral preferences 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.

## 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.

## Statistics

Statistics is the study of 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

A t-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution if the null hypothesis is supported.

## Subjective expected utility

In decision theory, subjective expected utility is the attractiveness of an economic opportunity as perceived by a decision-maker in the presence of risk.

## Supervised learning

Supervised learning is the machine learning task of inferring a function from labeled training data.

## Test set

In many areas of information science, finding predictive relationships from data is a very important task.

## Utility

In economics, utility is a measure of preferences over some set of goods and services.

## Variance

In probability theory and statistics, variance measures how far a set of numbers is spread out.

## References

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