55,692 research outputs found
The CIFF Proof Procedure for Abductive Logic Programming with Constraints: Theory, Implementation and Experiments
We present the CIFF proof procedure for abductive logic programming with
constraints, and we prove its correctness. CIFF is an extension of the IFF
proof procedure for abductive logic programming, relaxing the original
restrictions over variable quantification (allowedness conditions) and
incorporating a constraint solver to deal with numerical constraints as in
constraint logic programming. Finally, we describe the CIFF system, comparing
it with state of the art abductive systems and answer set solvers and showing
how to use it to program some applications. (To appear in Theory and Practice
of Logic Programming - TPLP)
Model Selection for High Dimensional Quadratic Regression via Regularization
Quadratic regression (QR) models naturally extend linear models by
considering interaction effects between the covariates. To conduct model
selection in QR, it is important to maintain the hierarchical model structure
between main effects and interaction effects. Existing regularization methods
generally achieve this goal by solving complex optimization problems, which
usually demands high computational cost and hence are not feasible for high
dimensional data. This paper focuses on scalable regularization methods for
model selection in high dimensional QR. We first consider two-stage
regularization methods and establish theoretical properties of the two-stage
LASSO. Then, a new regularization method, called Regularization Algorithm under
Marginality Principle (RAMP), is proposed to compute a hierarchy-preserving
regularization solution path efficiently. Both methods are further extended to
solve generalized QR models. Numerical results are also shown to demonstrate
performance of the methods.Comment: 37 pages, 1 figure with supplementary materia
Invariant Discretization Schemes Using Evolution-Projection Techniques
Finite difference discretization schemes preserving a subgroup of the maximal
Lie invariance group of the one-dimensional linear heat equation are
determined. These invariant schemes are constructed using the invariantization
procedure for non-invariant schemes of the heat equation in computational
coordinates. We propose a new methodology for handling moving discretization
grids which are generally indispensable for invariant numerical schemes. The
idea is to use the invariant grid equation, which determines the locations of
the grid point at the next time level only for a single integration step and
then to project the obtained solution to the regular grid using invariant
interpolation schemes. This guarantees that the scheme is invariant and allows
one to work on the simpler stationary grids. The discretization errors of the
invariant schemes are established and their convergence rates are estimated.
Numerical tests are carried out to shed some light on the numerical properties
of invariant discretization schemes using the proposed evolution-projection
strategy
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