A. J. Miller. Subset selection in regression. In Monographs on Statistics and Applied Probability 40. London: Chapman and Hall, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....points N as well as the number of predictor variables. This makes BMARS suitable for performing an ecient large scale data analysis often referred to as Data Mining. Now we would like to contrast the MARS and BMARS algorithms with a standard statistical forward subset selection procedure (FSS) [11]. MARS builds a model by adding basis functions one at a step and so does the FSS algorithm. However, the former selects a new basis function from a relatively small subset of all available tensor product basis functions. Speci cally, at each step such a subset is comprised of basis functions ....

Miller, A.J., Subset Selection in Regression, Chapman and Hall, 1990.

....of relevant attribute analysis and their scatter plot. A number of techniques have been developed to automatically select and rank models from a set of attributes, like t test, step wise regression. All of these methods are available in the popular statistical packages, like SAS, SPSS, S PLUS [24]. However, these model selection methods tend to favor those models that involve more attributes, which make them very vulnerable in the real modelling process [27] We adopt the approach proposed by Raftery [27] To assess a model, Raftery [27] introduced the Bayesian Information Criterion (BIC) ....

A. Miller, Subset Selection in Regression, Chapman & Hall, New York, 1990.

....to enter the model, the forward stepwise procedure is allowed to produce an excess number of basis functions. In order to get rid of suboptimal functions one has to apply the second module of the MARS algorithm. This is essentially just a standard statistical backward subset selection algorithm [7]. This part of MARS selects a submodel which minimizes an estimate of prediction error. The Generalized Cross Validation criterion (GCV) 5] is suggested. GCV (J) m=1 [y m Gamma f J (x m ) 1 Gamma C(J) # 2 (2.5) The numerator in GCV is the average residual squared error and ....

Miller, A.J., Subset Selection in Regression. Chapman and Hall, 1990.

.... is also very important to notice that variable suppression speeds up the acquisition process (i.e. the measurement of the real world in order to produce the input variables) A huge work has been done by statisticians in order to study variable selection when the regression tool is linear (e.g. [5]) The purpose of this article is not to # This work was performed on Mrs Kim K. PHAM s responsibility, at THOMSON CSF AIRSYS. Published in ICANNGA 97 Proceedings. Available at http: apiacoa.org publications 1997 icannaga97.pdf review these methods but to work on problems that cannot be ....

A. J. Miller. Subset Selection in Regression. Chapman and Hall, 1990.

....5.1.1.2 Sequential Search Algorithms Sequential Search algorithms have a complexity of O(n ) They add and or delete features to from the current subset sequentially. They usually use hill climbing strategy for the search. 104 5.1.1.2. 1 Sequential Forward Selection (SFS) In SFS [Miller, 1990, Devijver and Kittler, 1982] search starts with an empty set. First, feature subsets with only one feature are evaluated and the best feature (f is selected. Then two feature combinations of f with the other features are tested and the best feature subset is selected. The search goes on ....

Miller, A. J. (1990). Subset Selection in Regression. Chapman and Hall.

....real world applications. 3.2 Sequential Search Algorithms Sequential Search algorithms have a complexity of O(n ) They add and or delete features to from the current subset sequentially. They usually use hill climbing strategy for the search. 3.2. 1 Sequential Forward Selection (SFS) In SFS [9, 5] search starts with an empty set. First, feature subsets with only one feature are evaluated and the best feature (f # ) is selected. Then, two feature combinations of f # with the other features are tested and the best feature subset is selected. The search goes on like that by adding one more ....

A. J. Miller. Subset Selection in Regression. Chapman and Hall, 1990.

....a sparse coecient vector, is that the prior densities of the sources have zero mode. This assumption is discussed in section 3. 2 1. 1 Related research The principle of nding an economical description of data can be traced back to Occam s razor and has important applications in statistics [24, 41] The generative model formulation outlined in section 2 has two advantages: following a Bayesian framework, the economy of a code can be conveniently expressed as the prior probability distribution of source values; the Bayesian (subjective) interpretation of probabilities is unnecessary, ....

....pursuit reduces the number of false positives by removing the image components likely to arise from the background. Matching pursuit has also been applied to the processing of seismic data [37] The problem of nding sparse linear expansions is common in numerical linear algebra [45] statistics [24, 41], system identi cation [12] and control [64] Matching pursuit and related methods have found applications in these elds. 7.2 Biological implications Responses of simple cells in visual cortical area V1 can be described, to a rst approximation, as (halfwave recti ed) projections of the retinal ....

A.J. Miller, Subset selection in regression. London: Chapman and Hall, 1990.

....is always the possibility that any satisfactory results may simply be due to chance rather than to any merit inherent in the method yielding the results. 7.1. Variable Selection for Regression A classic example of data mining in this context occurs in variable selection for regression (e.g. [Mil90]) especially when applied to a relatively small training data set with no data used for holdout testing. Lets Data Mining At the Interface of Computer Science and Statistics 8 17 say we are trying to fit a simple linear regression model of the form Y = ff 0 ff 1 X i ff 2 X j e; 1 i; j ....

Miller, A. J. (1990) Subset Selection in Regression, London, Chapman and Hall.

....lines of research. II. Feature Subset Selection as a search problem Even if we locate our work as a Machine Learning or Data Mining approach, the FSS literature includes plenty of works in other fields such as Pattern Recognition (Jain and Chandrasekaran [27] Kittler [29] Statistic (Miller [40], Narendra and Fukunaga [46] or TextLearning (Mladeni c [41] In the Bayesian network community we have the example of the work of Provan and Singh [51] who, using a Bayesian network as a classifier, build it selecting in a greedy manner the variables that should maximize the predictive ....

Miller, A.J., Subset Selection in Regression, Chapman and Hall, Washington, DC, 1990.

....the model. 2. Estimation of the parameters of the selected model. Point predictions can then be made. 3. Assessment of the variability in the predictions. Conceivably we could split the data three ways and use a different part for each of the above tasks. This has been suggested in passing by Miller (1990, p. 13) and is, perhaps, what Mosteller and Tukey (1977) meant by double cross validation. I investigated this strategy and found it clearly inferior to any of those discussed below, so henceforth I restrict attention to splitting the data into two parts. Which parts of the data should be used ....

....model. This suggests a second data splitting strategy (B) where the first sample is used only to select the model and the second sample is used both to estimate the parameters of the model leading to predictions and to assess the variability in those predictions. This is the approach mentioned by Miller (1990, p. 13) and Hurvich and Tsai (1990) and actually implemented by Faraway (1992) Interestingly, none of the proponents of these two approaches seems to have considered the other. A third strategy (C) can also be motivated by the arrival of new data. One might retain the originally selected model, ....

Miller, A. (1990). Subset Selection in Regression. Chapman and Hall, London.

....(It needs to be pointed out that the IC criteria can be used to compare any models, not necessarily the nested models under stepwise regression analysis. For example, it can be shown that the likelihood ratio test statistic can be expressed as LR k 2 log(L k L k # ) n log(c(n) n 1) E c(n) (Miller, 1990, p. 208) The criterion is basically defined by c(n) if interpreted under BIC. Using AIC with c(n) 2 would yield a final LOD threshold of 043 In reference to QTL analysis on markers, Broman (1997) suggested using c(n) # log n and recommended that # be between 2 and 3. For n 100C 500, the LOD ....

....model selection can be inflated about 25 in our analysis. However, when the heritability is high, say 05 or higher, the estimate is usually close to the parameter value. Also, part of the bias can be corrected by using adjusted R# to estimate the total variance explained by QTL (Miller, 1990). To obtain the sampling variances of architectural parameter estimates, Kao Zeng (1997) described a Estimating the genetic architecture of quantitatie traits 287 procedure based on the Fisher information matrix allowing for missing data. The confidence intervals of parameter estimates can also ....

Miller, A. J. (1990). Subset Selection in Regression. London : Chapman and Hall.

.... by n 2 (EP f L r=n 2 ) 2 k : Therefore, a level 1 2 UCB for the expected risk is P 2 k (1 ) n 1 E S f L v n k ( If a greedy search for a subset of regression variables within some candidate set is performed, such as the forward or backward stepping procedures ([14]) then the search tree methodology can be applied to obtain a UCB for the risk of the resulting regression function. The following adaptation for Algorithm 2 calculates a level 1 4 UCB for the risk of the forward stepping procdure (as above, P i i ) The forward stepping procedure adds the ....

A.J. Miller. Subset selection in regression. Chapman and Hall, NY, 1990.

.... Subset Selection as a search problem Even if we locate our work as a Machine Learning or Data Mining approach, the FSS literature includes plenty of works in other fields such as Pattern Recognition (Jain and Chandrasekaran [27] Kittler [31] Stearns [61] Statistic (Boyce et al. 7] Miller [43], Narendra and Fukunaga [49] or TextLearning (Mladeni c [44] In the Bayesian network community we have the example of the work of Provan and Singh [55] who, using a Bayesian network as a classifier, build it selecting in a greedy manner the variables that should maximize the predictive ....

A.J. Miller, Subset Selection in Regression, Chapman and Hall, Washington, DC, 1990.

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A. J. Miller. Subset selection in regression. In Monographs on Statistics and Applied Probability 40. London: Chapman and Hall, 1990.

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A. J. Miller, Subset Selection in Regression, Chapman and Hall, 2002.

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Miller, A. (2002), Subset selection in regression, 2nd edn., Chapman & Hall/CRC, Florida.

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A. Miller. Subset Selection in Regression. Chapman and Hall, 1990.

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MILLER, A. J. Subset selection in regression, 2nd ed. Chapman and Hall, London, 2002.

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A.J. Miller. Subset Selection in Regression. Chapman and Hall, 1990.

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A.J. Miller. Subset Selection in Regression. Chapman and Hall, Washtington D.C., 1990. 44

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A. J. Miller. Subset Selection in Regression. Chapman & Hall, London, 2002.

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A. J. Miller, Subset Selection in Regression. Chapman & Hall, 1990.

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A. J. Miller, Subset selection in regression, Chapman and Hall, 1990.

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A. J. Miller. Subset Selection in Regression. Chapman and Hall, 1990.

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Miller, A. J. (1990) Subset Selection in Regression, New York, Chapman-Hall.

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