Statistical technique for smoothing categorical data
For the image processing technique, see Laplacian smoothing.
In statistics, additive smoothing, also called Laplace smoothing[1] or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts from a -dimensional multinomial distribution with trials, a "smoothed" version of the counts gives the estimator
where the smoothed count , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) and the uniform probability Invoking Laplace's rule of succession, some authors have argued[citation needed] that α should be 1 (in which case the term add-one smoothing[2][3] is also used)[further explanation needed], though in practice a smaller value is typically chosen.
From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution.
^C. D. Manning, P. Raghavan and H. Schütze (2008). Introduction to Information Retrieval. Cambridge University Press, p. 260.
^Jurafsky, Daniel; Martin, James H. (June 2008). Speech and Language Processing (2nd ed.). Prentice Hall. p. 132. ISBN 978-0-13-187321-6.
^Russell, Stuart; Norvig, Peter (2010). Artificial Intelligence: A Modern Approach (2nd ed.). Pearson Education, Inc. p. 863.
and 26 Related for: Additive smoothing information
In statistics, additivesmoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused...
smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing....
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function...
iterative smoothing of partial residuals and provides a very general modular estimation method capable of using a wide variety of smoothing methods to...
0} (no smoothing), the smoothing spline converges to the interpolating spline. As λ → ∞ {\displaystyle \lambda \to \infty } (infinite smoothing), the roughness...
C\simeq 9/m} ensures a 99% confidence interval has width about 2m. Additivesmoothing "Bayesian Average Ratings". www.evanmiller.org. Retrieved 2016-05-21...
Newcomb's paradox Unsolved problems in statistics Additivesmoothing (also called Laplace smoothing) "LII. An essay towards solving a problem in the doctrine...
3D printing or additive manufacturing is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety...
science Adapted process Adaptive estimator Additive Markov chain Additive model AdditivesmoothingAdditive white Gaussian noise Adjusted Rand index –...
regression) A quadratic or a polynomial curve Local regression Smoothing splines The smoothing curve is chosen so as to provide the best fit in some sense...
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an...
Additive synthesis example A bell-like sound generated by additive synthesis of 21 inharmonic partials Problems playing this file? See media help. Additive...
probabilities of a multinomial distribution given a set of observations. Additivesmoothing Evans, Morton; Hastings, Nicholas; Peacock, Brian (2000). Statistical...
matrix of explanatory variables in the optimal direction before applying smoothing functions to these explanatory variables. The model consists of linear...
subjective to some extent (dependent upon the analyst and analysis used). Additivesmoothing Krichevsky–Trofimov estimator Principle of indifference Laplace, Pierre-Simon...
scores. The Continuously Additive Model (CAM) assumes additivity in the time domain. The functional predictors are assumed to be smooth across the time domain...
mutations are additive, they can be acquired in any order and still give a continuous uphill trajectory. The landscape is perfectly smooth, with only one...
which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative integer, which is how often...
assumed to be affine. Some authors use a slightly stronger assumption of additive noise: Y = m ( X ) + U , {\displaystyle Y=m(X)+U,} where the random variable...
substances (and so are both hydrophilic and lipophilic), and are used for smoothing food textures, emulsifying, homogenizing liquid mixtures, and repelling...
Dodge blend mode simply sums the values in the two layers (also known as additive blending). Blending with white gives white. Blending with black does not...
half the smoothing. The t values for each portion of the smoothing (poles, zeros, forward and backward multiple applications, etc.) are additive, in accordance...
Natural American Spirit products in the year 2000 were advertised as "100% Additive-Free Tobacco".[citation needed] California Attorney General Jerry Brown...
since the 1980s; the first mats were cut from carpet underlay. As a food additive, azodicarbonamide is used as a flour bleaching agent and a dough conditioner...
Global Information
