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Mean Absolute Scaled Error
In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts. It is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast. It was proposed in 2005 by statistician Rob J. Hyndman and Professor of Decision Sciences Anne B. Koehler, who described it as a "generally applicable measurement of forecast accuracy without the problems seen in the other measurements." The mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation, and is therefore recommended for determining comparative accuracy of forecasts. Rationale The mean absolute scaled error has the following desirable properties: # Scale invariance: The mean absolute scaled error is independent of the scale of the data, so can be used to compare forecasts across data sets with different scales. # Predictable behavior as y_ \rightarrow 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "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.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 sample (statistics), samples. Representative sampling as ... [...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, 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 in making the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraction Of Variance Unexplained
In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable) ''Y'' which cannot be explained, i.e., which is not correctly predicted, by the explanatory variables ''X''. Formal definition Suppose we are given a regression function f yielding for each y_i an estimate \widehat_i = f(x_i) where x_i is the vector of the ''i''th observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: :\begin \text & = = = \left( = 1- , \text\right) \\ pt & = 1 - R^2 \end where ''R''2 is the coefficient of determination and ''VAR''err and ''VAR''tot are the variance of the residuals and the sample variance of the dependent variable. ''SS''''err'' (the sum of squared predictions errors, equivalently the residual sum of squares), ''SS''''tot'' (the total sum of squares), and ''SS''''reg'' (the sum of squares of the regression, equivalently the explai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Set
In machine learning, a common task is the study and construction of algorithms that can learn from and make predictions on data. Such algorithms function by making data-driven predictions or decisions, through building a mathematical model from input data. These input data used to build the model are usually divided in multiple data sets. In particular, three data sets are commonly used in different stages of the creation of the model: training, validation and test sets. The model is initially fit on a training data set, which is a set of examples used to fit the parameters (e.g. weights of connections between neurons in artificial neural networks) of the model. The model (e.g. a naive Bayes classifier) is trained on the training data set using a supervised learning method, for example using optimization methods such as gradient descent or stochastic gradient descent. In practice, the training data set often consists of pairs of an input vector (or scalar) and the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root-mean-square Deviation
The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed. The RMSD represents the square root of the second sample moment of the differences between predicted values and observed values or the quadratic mean of these differences. These deviations are called '' residuals'' when the calculations are performed over the data sample that was used for estimation and are called ''errors'' (or prediction errors) when computed out-of-sample. The RMSD serves to aggregate the magnitudes of the errors in predictions for various data points into a single measure of predictive power. RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent. RMSD is always non-negative, and a value of 0 (almost never achieved in practice) would ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the ''empirical'' risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average Absolute Deviation
The average absolute deviation (AAD) of a data set is the average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be a mean, median, mode, or the result of any other measure of central tendency or any reference value related to the given data set. AAD includes the mean absolute deviation and the median absolute deviation (both abbreviated as MAD). Measures of dispersion Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered a good practice to indicate the degree of uncertainty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accuracy
Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other. In other words, ''precision'' is a description of ''random errors'', a measure of statistical variability. ''Accuracy'' has two definitions: # More commonly, it is a description of only '' systematic errors'', a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this ''trueness''. # Alternatively, ISO defines accuracy as describing a combination of both types of observational error (random and systematic), so high accuracy requires both high precision and high trueness. In the first, more common definition of "accuracy" above, the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
