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ANOVA decomposition
, 2010
"... This paper studies the ANOVA decomposition of a dvariate function f defined on the whole of R d, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions al ..."
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This paper studies the ANOVA decomposition of a dvariate function f defined on the whole of R d, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions
The smoothing effect of the ANOVA decomposition
, 2008
"... We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component of x, where ..."
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Cited by 10 (2 self)
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We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component of x
The Smoothing Effect of the ANOVA Decomposition
"... We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f in general belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component ..."
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We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f in general belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component
Hierarchical array priors for ANOVA decompositions
, 2012
"... ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matri ..."
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Cited by 4 (1 self)
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ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors
Support Vector Regression with ANOVA Decomposition Kernels
, 1997
"... Support Vector Machines using ANOVA Decomposition Kernels (SVAD) [Vapng] are a way of imposing a structure on multidimensional kernels which are generated as the tensor product of onedimensional kernels. This gives more accurate control over the capacity of the learning machine (VCdimension) . SVA ..."
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Cited by 38 (1 self)
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Support Vector Machines using ANOVA Decomposition Kernels (SVAD) [Vapng] are a way of imposing a structure on multidimensional kernels which are generated as the tensor product of onedimensional kernels. This gives more accurate control over the capacity of the learning machine (VCdimension
Estimating mean dimensionality of ANOVA decompositions
 Journal of the American Statistical Association
"... The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy t ..."
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Cited by 2 (0 self)
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The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy
Element I: ANOVA Decomposition Multivariate Decomposition
, 2015
"... f (x)dx Applications: e.g., in finance d = 360 = 12 × 30. Some integration problems are easier than others, e.g., f (x) = d∑ i=1 fi(xi). ..."
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f (x)dx Applications: e.g., in finance d = 360 = 12 × 30. Some integration problems are easier than others, e.g., f (x) = d∑ i=1 fi(xi).
HOEFFDINGANOVA DECOMPOSITIONS FOR SYMMETRIC STATISTICS OF EXCHANGEABLE OBSERVATIONS
, 2004
"... Consider a (possibly infinite) exchangeable sequence X = {Xn:1 ≤ n < N}, where N ∈ N ∪ {∞}, with values in a Borel space (A, A), and note Xn = (X1,...,Xn). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written ..."
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Cited by 8 (7 self)
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Consider a (possibly infinite) exchangeable sequence X = {Xn:1 ≤ n < N}, where N ∈ N ∪ {∞}, with values in a Borel space (A, A), and note Xn = (X1,...,Xn). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n Ustatistics with degenerated and symmetric kernels of increasing order. The only two examples of Hoeffding decomposable sequences studied in the literature are i.i.d. random variables and extractions without replacement from a finite population. In the first part of the paper we establish a necessary and sufficient condition for an exchangeable sequence to be Hoeffding decomposable, that is, called weak independence. We show that not every exchangeable sequence is weakly independent, and, therefore, that not every exchangeable sequence is Hoeffding decomposable. In the second part we apply our results to a class of exchangeable and weakly independent random vectors X (α,c) n = (X (α,c)
Visualization And Exploration Of HighDimensional Functions Using The Functional Anova Decomposition
, 1995
"... In recent years the statistical and engineering communities have developed many highdimensional methods for regression (e.g. MARS, feedforward neural networks, projection pursuit). Users of these methods often wish to explore how particular predictors affect the response. One way to do so is by dec ..."
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Cited by 6 (0 self)
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is by decomposing the model into loworder components through a functional ANOVA decomposition and then visualizing the components. Such a decomposition, with the corresponding variance decomposition, also provides information on the importance of each predictor to the model, the importance of interactions
Results 1  10
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