Artificial neural networkArtificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.
Errors and residualsIn statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Mean squared errorIn 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.
Mean squared prediction errorIn statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors (PE), the square difference between the fitted values implied by the predictive function and the values of the (unobservable) true value g. It is an inverse measure of the explanatory power of and can be used in the process of cross-validation of an estimated model.
Residual sum of squaresIn statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection.
Studentized residualIn statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's t-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym Student. Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing.
Recurrent neural networkA recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.
Root-mean-square deviationThe 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.
Feedforward neural networkA feedforward neural network (FNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. Its flow is uni-directional, meaning that the information in the model flows in only one direction—forward—from the input nodes, through the hidden nodes (if any) and to the output nodes, without any cycles or loops, in contrast to recurrent neural networks, which have a bi-directional flow.
Least squaresThe method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
