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Mean Absolute Error
In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of ''Y'' versus ''X'' include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors divided by the sample size: \mathrm = \frac =\frac. It is thus an arithmetic average of the absolute errors , e_i, = , y_i - x_i, , where y_i is the prediction and x_i the true value. Note that alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series using different scales. The mean absolute error is a common measure of forecast error in time series analysis, sometimes used in confusion with the more standard de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
StackExchange
Stack Exchange is a network of question-and-answer (Q&A) websites on topics in diverse fields, each site covering a specific topic, where questions, answers, and users are subject to a reputation award process. The reputation system allows the sites to be self-moderating. As of August 2019, the three most actively-viewed sites in the network are Stack Overflow, Super User, and Ask Ubuntu. All sites in the network are modeled after the initial site Stack Overflow, a Q&A site for computer programming questions created by Jeff Atwood and Joel Spolsky. Further Q&A sites in the network are established, defined and eventually if found relevant brought to creation by registered users through a special site named Area 51. User contributions since May 2, 2018 are licensed under Creative Commons Attribution-ShareAlike 4.0 International. Older content, contributed while the site used the Creative Commons Attribution-ShareAlike 3.0 Unported license or the earlier Creative Com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Deviation And Dispersion
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Estimation Performance
Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Scotland, Lismore, Inner Hebrides, Scotland * Points, West Virginia, an unincorporated community in the United States Business and finance *Point (loyalty program), a type of virtual currency in common use among mercantile loyalty programs, globally *Point (mortgage), a percentage sometimes referred to as a form of pre-paid interest used to reduce interest rates in a mortgage loan * Basis point, 1/100 of one percent, denoted ''bp'', ''bps'', and ''‱'' * Percentage points, used to measure a change in percentage absolutely * Pivot point (technical analysis), a price level of significance in analysis of a financial market that is used as a predictive indicator of market movement * "Points", the term for profit sharing in the American film industry, where creatives involved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rob J
Rob or ROB may refer to: Places * Rob, Velike Lašče, a settlement in Slovenia * Roberts International Airport (IATA code ROB), in Monrovia, Liberia People * Rob (given name), a given name or nickname, e.g., for Robert(o), Robin/Robyn * Rob (surname) * ''Rob.'', taxonomic author abbreviation for William Robinson (gardener) (1838–1935), Irish practical gardener and journalist Fictional characters * Rob, a character from the Cartoon Network series ''The Amazing World of Gumball'' * ROB 64, a character in the ''Star Fox'' video game series Arts, entertainment, and media Gaming * '' Castlevania: Rondo of Blood'', a 1993 video game nicknamed ''Castlevania: ROB'' * R.O.B., an accessory for the Nintendo Entertainment System Reports * ''ISM Report On Business'' (informally, "The R.O.B."), an economic report issued by the Institute for Supply Management * ''Report on Business'', or "ROB", a section of the ''Globe and Mail'' newspaper Other uses in arts, entertainment, and med ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Mean Absolute Percentage Error
Symmetric mean absolute percentage error (SMAPE or sMAPE) is an accuracy measure based on percentage (or relative) errors. It is usually defined as follows: : \text = \frac \sum_^n \frac where ''A''''t'' is the actual value and ''F''''t'' is the forecast value. The absolute difference between ''A''''t'' and ''F''''t'' is divided by half the sum of absolute values of the actual value ''A''''t'' and the forecast value ''F''''t''. The value of this calculation is summed for every fitted point ''t'' and divided again by the number of fitted points ''n''. The earliest reference to similar formula appears to be Armstrong (1985, p. 348) where it is called "adjusted MAPE" and is defined without the absolute values in denominator. It has been later discussed, modified and re-proposed by Flores (1986). Armstrong's original definition is as follows: : \text = \frac 1 n \sum_^n \frac The problem is that it can be negative (if A_t + F_t < 0) or even undefined (if |
Mean Percentage Error
In statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast. The formula for the mean percentage error is: : \text = \frac\sum_^n \frac where ''a''''t'' is the actual value of the quantity being forecast, ''f''''t'' is the forecast, and ''n'' is the number of different times for which the variable is forecast. Because actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts. A disadvantage of this measure is that it is undefined whenever a single actual value is zero. See also *Percentage error * Mean absolute percentage error *Mean squared error *Mean squared prediction error *Minimum mean-square error *Squared deviations *Peak signal-to-noise ratio *Root mean square deviation *Errors and residu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Absolute Percentage Error
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: : \mbox = \frac\sum_^n \left, \frac\ where is the actual value and is the forecast value. Their difference is divided by the actual value . The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points . MAPE in regression problems Mean absolute percentage error is commonly used as a loss function for regression problems and in model evaluation, because of its very intuitive interpretation in terms of relative error. Definition Consider a standard regression setting in which the data are fully described by a random pair Z=(X,Y) with values in \mathbb^d\times\mathbb, and i.i.d. copies (X_1, Y_1), ..., (X_n, Y_n) of (X,Y). Regression models aims at finding a good model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Absolute Deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based minimizing the ''sum of absolute deviations'' (sum of absolute residuals or sum of absolute errors) or the ''L''1 norm of such values. It is analogous to the least squares technique, except that it is based on '' absolute values'' instead of squared values. It attempts to find a function which closely approximates a set of data by minimizing residuals between points generated by the function and corresponding data points. The LAD estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution. It was introduced in 1757 by Roger Joseph Boscovich. Formulation Suppose that the data set consists of the points (''x''''i'', ''y''''i'') with ''i'' = 1, 2, ..., ''n''. We want to find a function ''f'' such that f(x_i)\approx y_i. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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). Given \mathcal as the space of all possible inputs (usually \mathcal \subset \mathbb^d), and \mathcal = \ as the set of labels (possible outputs), a typical goal of classification algorithms is to find a function f: \mathcal \to \mathcal which best predicts a label y for a given input \vec. However, because of incomplete information, noise in the measurement, or probabilistic components in the underlying process, it is possible for the same \vec to generate different y. As a result, the goal of the learning problem is to minimize expected loss (also known as the risk), defined as :I = \displaystyle \int_ V(f(\vec),y) \, p(\vec,y) \, d\vec \, dy where V(f(\vec),y) is a given loss function, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-medians Clustering
In statistics, ''k''-medians clusteringP. S. Bradley, O. L. Mangasarian, and W. N. Street, "Clustering via Concave Minimization," in Advances in Neural Information Processing Systems, vol. 9, M. C. Mozer, M. I. Jordan, and T. Petsche, Eds. Cambridge, Massachusetts: MIT Press, 1997, pp. 368–374. is a cluster analysis algorithm. It is a variation of ''k''-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median. This has the effect of minimizing error over all clusters with respect to the 1-norm distance metric, as opposed to the squared 2-norm distance metric (which ''k''-means does.) This relates directly to the ''k''-median problem with respect to the 1-norm, which is the problem of finding ''k'' centers such that the clusters formed by them are the most compact. Formally, given a set of data points ''x'', the ''k'' centers ''c''''i'' are to be chosen so as to minimize the sum of the distances fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
