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Sum Of Absolute Errors
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 (i.e., the Manhattan distance) 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. 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 predicted values that use different scales. The mean absolute error is a common measure of forecast error in time series analysis, sometimes used in co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), 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 statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median
The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, 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 Arithmetic mean, mean (often simply described as the "average") is that it is not Skewness, skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics. Median is a 2-quantile; it is the value that partitions a set into two equal parts. Finite set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are liste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Deviation And Dispersion
Statistics (from German: ', "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. When census data (comprising every member of the target population) 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 experimental study involves taking measurements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Estimation Performance
A point is a small dot or the sharp tip of something. Point or points may refer to: Mathematics * Point (geometry), an entity that has a location in space or on a plane, but has no extent; more generally, an element of some abstract topological space * Point, or Element (category theory), generalizes the set-theoretic concept of an element of a set to an object of any category * Critical point (mathematics), a stationary point of a function of an arbitrary number of variables * Decimal point * Point-free geometry * Stationary point, a point in the domain of a single-valued function where the value of the function ceases to change Places * Point, Cornwall, England, a settlement in Feock parish * 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, Inner Hebrides, Scotland * Points, West Virginia, an unincorporated community in the United States Business an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rob J
Rob or ROB may refer to: Places * Rob, Velike Lašče, a settlement in Slovenia * Republic of Belarus 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 Arts and entertainment * ''Rob'' (TV series), an American comedy show * ''Rob Riley'' (comic strip), a British comic strip named after its titular character * ''Rob the Robot'' (TV series), a TV series named after its titular character * Rob, a character from the Cartoon Network series ''The Amazing World of Gumball'' * ROB 64, a character in the ''Star Fox'' video game series * '' Castlevania: Rondo of Blood'', a 1993 video game nicknamed ''Castlevania: ROB'' * R.O.B., an accessory for the Nintendo Entertainment System Science and technology * Re-order buffer (ROB), used for out-of-order execution in microprocessors * Robertsonian translocati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Mean Absolute Percentage Error
The 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''. History The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was 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 un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (statistics), 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 residua ... [...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 = 100\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 aim at finding a good model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taxicab Geometry
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the ''taxicab distance'', ''Manhattan distance'', or ''city block distance''. The name refers to the island of Manhattan, or generically any planned city with a rectangular grid of streets, in which a taxicab can only travel along grid directions. In taxicab geometry, the distance between any two points equals the length of their shortest grid path. This different definition of distance also leads to a different definition of the length of a curve, for which a line segment between any two points has the same length as a grid path between those points rather than its Euclidean length. The taxicab distance is also sometimes known as ''rectilinear distance'' or distance (see ''Lp'' space). This geometry ha ... [...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 on minimizing the sum of absolute deviations (also ''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_ ... [...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, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-medians Clustering
K-medians clustering is a partitioning technique used in cluster analysis. It groups data into ''k'' clusters by minimizing the sum of distances—typically using the Manhattan (L1) distance—between data points and the median of their assigned clusters. This method is especially robust to outliers and is well-suited for discrete or categorical data. It is a generalization of the geometric median or 1-median algorithm, defined for a single cluster. ''k''-medians 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 2- norm distance metric, as opposed to the squared 2-norm distance metric (which ''k''-means does). This relates directly to the ''k''-median problem which is the problem of finding ''k'' centers such that the clusters formed by them are the most compact with respect to the 2-norm. Formally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
