We describe the use of smoothing spline analysis of variance (SSANOVA) in the penalized log likelihood context, for learning (estimating) the probability p of a '1' outcome, given a training set with attribute vectors and outcomes. p is of the form pet) = eJ(t) /(1 + eJ(t)), where, if t is a vector of attributes, f is learned as a sum of smooth functions of one attribute plus a sum of smooth fu...

In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

We consider a problem of designing optimal smoothing spline curves using normalized uniform B-splines as basis functions. Assuming that the data for smoothing is obtained by sampling some curve with noises, an expression for optimal curves is derived when the number of data becomes infinity. It is then shown that, under certain condition, optimal smoothing splines converge to this curve as the ...

In a companion paper we characterized the class of scale-invariant convolution operators: the generalized fractional derivatives of order γ. We used these operators to specify regularization functionals for a series of Tikhonov-like least squares data fitting problems and proved that the general solution is a fractional spline of twice the order. We investigated the deterministic properties of ...

I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivativ...

1 I n t r o d u c t i o n The CBP method for tomographic reconstruction is derived from a mathemat i cal idealization of tomographic imaging without consideration of statistical measurement errors. This idealization leads to the well-known ramp filter [1], whose frequency response has the unfortunate effect of amplifying high-frequency measurement noise. The conventional approach to reducing th...

Nonparametric regression models are often used to check or suggest a parametric model. Several methods have been proposed to test the hypothesis of a parametric regression function against an alternative smoothing spline model. Some tests such as the locally most powerful (LMP) test by Cox et al. (Cox, D., Koh, E., Wahba, G. and Yandell, B. (1988). Testing the (parametric) null model hypothesis...

We propose a locally regularized snake based on smoothing-spline filtering. The proposed algorithm associates a regularization process with a force equilibrium scheme leading the snake’s deformation. In this algorithm, the regularization is implemented with a smoothing of the deformation forces. The regularization level is controlled through a unique parameter that can vary along the contour. I...

The problem of constructing and approximating control theoretic smoothing splines is considered in this paper. It is shown that the optimal approximating function can be given as the solution of a forced Hamiltonian system, that can be explicitly solved using the Riccati transform, and an explicit linear filter can be constructed. We show that the bandwidth of the filter can be naturally contro...

This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of mo...