Absolute Error Loss
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Bayes Estimator Under Absolute Error Loss
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Absolute Error Loss Median
of 3 Thread: Squared Error vs Absolute Error loss functions Thread Tools Show Printable Version Email this Page… Subscribe to this Thread… Display Linear Mode Switch to Hybrid Mode Switch absolute error formula to Threaded Mode 07-24-200802:29 PM #1 shrek View Profile View Forum Posts Give Away Points Posts 26 Thanks 0 Thanked 0 Times in 0 Posts Squared Error vs Absolute Error loss functions The two most popular types of loss functions are 1) squared error: (actual-estimate)^2 --> best estimate is the mean 2) absolute error: |actual-estimate| --> best estimate is the median absolute error calculator I have two questions. 1) Why do people use the squared error method? The absolute error method makes much more intuitive sense. You get the difference between the actual and the estimate. Plain and simple. If you square the difference, then won't you get "warped" values depending on the size of the difference? 2) This also got me thinking about what is "expected value." Expected value is defined as the mean. However, the best estimate under the absolute error loss function is the median. So is the "expected value" the median? I would very much appreciate it if someone can help me clarify my thinking. Thanks. Reply With Quote 07-24-200804:30 PM #2 Rounds View Profile View Forum Posts Posts 154 Thanks 0 Thanked 0 Times in 0 Posts I know when 'actual' and 'estimate' are vector quantities there are easier to explain reasons you might want one over the other. In the scalar situation it is less obvious but you captured a bit of it with: 'If you square the difference, then won't you get "warped" values depending on the size o
one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its negative (sometimes called a reward
Absolute Error Example
function, a profit function, a utility function, a fitness function, etc.), in which case how to find absolute error it is to be maximized. In statistics, typically a loss function is used for parameter estimation, and the event in question is some
Absolute Error Physics
function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century.[1] In the context http://www.talkstats.com/showthread.php/5085-Squared-Error-vs-Absolute-Error-loss-functions of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald CramĂ©r in the 1920s.[2] In optimal control the loss is the penalty for failing to achieve a desired value. In financial risk management the function is precisely mapped to https://en.wikipedia.org/wiki/Loss_function a monetary loss. Contents 1 Use in statistics 1.1 Definition 2 Expected loss 2.1 Frequentist expected loss 2.2 Bayesian expected loss 2.3 Economic choice under uncertainty 2.4 Examples 3 Decision rules 4 Selecting a loss function 5 Loss functions in Bayesian statistics 6 Regret 7 Quadratic loss function 8 0-1 loss function 9 See also 10 References 11 Further reading Use in statistics[edit] Parameter estimation for supervised learning tasks such as regression or classification can be formulated as the minimization of a loss function over a training set. The goal of estimation is to find a function that models its input well: if it were applied to the training set, it should predict the values (or class labels) associated with the samples in that set. The loss function quantifies the amount by which the prediction deviates from the actual values. Definition[edit] Formally, we begin by considering some family of distributions for a random variable X, that is indexed by some θ. More intuitively, we can think of X as our "data", perhaps X = ( X 1 , … , X n ) {\displaystyle X=(X_{1},\ldots ,X_{n})} , where X i ∼ F θ {\displaystyle X_{i}\sim F_{\theta }} i.i.d. The X is the set of things the decision rule will be making decisions on. There exists some number of possible ways F
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