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Prediction by partial matching (PPM) is an adaptive statistical data compression technique based on context modeling and prediction. PPM models use a set of previous symbols in the uncompressed symbol stream to predict the next symbol in the stream. PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Matching is a statistical technique that evaluates the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned).
In the least squares method of data modeling, the objective function to be minimized, S, is a quadratic form: S = r T W r , {\displaystyle S=\mathbf {r^{T}Wr} ,} where r is the vector of residuals and W is a weighting matrix.
The results of a formula (example "=A1*B1") applies only to a single cell (that is, the cell the formula is located in—in this case perhaps C1), even though it can "extract" data from many other cells, and even real-time dates and actual times.
The Theory of Functional Connections (TFC) is a mathematical framework specifically developed for functional interpolation.Given any interpolant that satisfies a set of constraints, TFC derives a functional that represents the entire family of interpolants satisfying those constraints, including those that are discontinuous or partially defined.
This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted.
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