Lazy learning for local regression

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Description

By combining constant, linear, and quadratic local models, lazy estimates the value of an unknown multivariate function on the basis of a set of possibly noisy samples of the function itself. This implementation of lazy learning automatically adjusts the bandwidth on a query-by-query basis through a leave-one-out cross-validation.

Usage

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Arguments

formula

A formula specifying the response and some numeric predictors.

data

An optional data frame within which to look first for the response, predictors, and weights (the latter will be ignored).

weights

Optional weights for each case (ignored).

subset

An optional specification of a subset of the data to be used.

na.action

The action to be taken with missing values in the response or predictors. The default is to stop.

control

Control parameters: see lazy.control

.

...

Control parameters can also be supplied directly.

Details

For one or more query points, lazy estimates the value of an unknown multivariate function on the basis of a set of possibly noisy samples of the function itself. Each sample is an input/output pair where the input is a vector and the output is a number. For each query point, the estimation of the function is obtained by combining different local models. Local models considered for combination by lazy are polynomials of zeroth, first, and second degree that fit a set of samples in the neighborhood of the query point. The neighbors are selected according to either the Manhattan or the Euclidean distance. It is possible to assign weights to the different directions of the input domain for modifying their importance in the computation of the distance. The number of neighbors used for identifying local models is automatically adjusted on a query-by-query basis through a leave-one-out validations of models, each fitting a different numbers of neighbors. The local models are identified using the recursive least-squares algorithm, and the leave-one-out cross-validation is obtained through the PRESS statistic.

As the name lazy suggests, this function does not do anything... apart from checking the options and properly packing the data. All the actual computation is done when a prediction is request for a specific query point, or for a set of query points: see predict.lazy.

Value

An object of class lazy.

Author(s)

Mauro Birattari and Gianluca Bontempi

References

D.W. Aha (1997) Editorial. Artificial Intelligence Review, 11(1–5), pp. 1–6. Special Issue on Lazy Learning.

C.G. Atkeson, A.W. Moore, and S. Schaal (1997) Locally Weighted Learning. Artificial Intelligence Review, 11(1–5), pp. 11–73. Special Issue on Lazy Learning.

W.S. Cleveland, S.J. Devlin, and S.J. Grosse (1988) Regression by Local Fitting: Methods, Prospectives and Computational Algorithms. Journal of Econometrics, 37, pp. 87–114.

M. Birattari, G. Bontempi, and H. Bersini (1999) Lazy learning meets the recursive least squares algorithm. Advances in Neural Information Processing Systems 11, pp. 375–381. MIT Press.

G. Bontempi, M. Birattari, and H. Bersini (1999) Lazy learning for modeling and control design. International Journal of Control, 72(7/8), pp. 643–658.

G. Bontempi, M. Birattari, and H. Bersini (1999) Local learning for iterated time-series prediction. International Conference on Machine Learning, pp. 32–38. Morgan Kaufmann.

See Also

lazy.control, predict.lazy

Examples

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library("lazy")
data(cars)
cars.lazy <- lazy(dist ~ speed, cars)
predict(cars.lazy, data.frame(speed = seq(5, 30, 1)))

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