Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

Minimum stable convergence criteria for stochastic diffusion search

An analysis of Stochastic Diffusion Search (SDS), a novel and efficient optimisation and search algorithm, is presented, resulting in a derivation of the minimum acceptable match resulting in a stable convergence within a noisy search space. The applicability of SDS can therefore be assessed for a given problem.

Evaluation of agri-environmental and forestry schemes with multiple objectives

The evaluation of EU policy in the area of rural land use management often encounters problems of multiple and poorly articulated objectives. Agri-environmental policy has a range of aims, including natural resource protection, biodiversity conservation and the protection and enhancement of landscape quality. Forestry policy, in addition to production and environmental objectives, increasingly has social aims, including enhancement of human health and wellbeing, lifelong learning, and the cultural and amenity value of the landscape. Many of these aims are intangible, making them hard to define and quantify. This article describes two approaches for dealing with such situations, both of which rely on substantial participation by stakeholders. The first is the Agri-Environment Footprint Index, a form of multi-criteria participatory approach. The other, applied here to forestry, has been the development of ‘multi-purpose’ approaches to evaluation, which respond to the diverse needs of stakeholders through the use of mixed methods and a broad suite of indicators, selected through a participatory process. Each makes use of case studies and involves stakeholders in the evaluation process, thereby enhancing their commitment to the programmes and increasing their sustainability. Both also demonstrate more ‘holistic’ approaches to evaluation than the formal methods prescribed in the EU Common Monitoring and Evaluation Framework.

Tin–osmium cluster formation with a monomeric tin(II) alkyl: the formation, crystal structure and reactivity of [Os3(µ-H)SnR(CO)10], a formal stannyne complex of the osmium triangle {R = C(SiMe3)2C5H4N-2}

The monomeric tin(II) species SnR2{R = C(SiMe3)2C5H4N-2} reacts with [Os3(H)2(CO)10] in hexane to give [Os3(µ-H)SnR(CO)10]1 quantitatively; 1 is the first formal stannyne complex of the triosmium nucleus, in which the picoline nitrogen is coordinated to the tin atom, and which is itself also reactive, being a potential precursor to high nuclearity SnOs clusters.

μ-Peroxo-μ-oxo-bis[bis(trimethylsilylmethyl)tin]: the first structurally characterised main-group metal η2-peroxide, a formal tin analogue of an ozonide

The title compound is the first µ-η2-peroxodimetallic species to be characterised for a main group metal, possessing a long peroxo O–O bond, and large C–Sn–C angles, and is an unexpected product from the oxidation of [SnR2][R = CH(SiMe3)2], with a structure analogous to an organic ozonide.

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling.