Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately.

Is there regime behavior in monsoon convection in the late 20th century?

Mixture model techniques are applied to a daily index of monsoon convection from ERA‐40 reanalysis to show regime behavior. The result is the existence of two significant regimes showing preferred locations of convection within the Asia/Western‐North Pacific domain, with some resemblance to active‐break events over India. Simple trend analysis over 1958–2001 shows that the first regime has become less frequent while the second becomes much more dominant. Both undergo a change in structure contributing to the total OLR trend over the ERA‐40 period. Stratifying the data according to a large‐scale dynamical index of monsoon interannual variability, we show the regime occurrence to be strongly perturbed by the seasonal condition, in agreement with conceptual ideas. This technique could be used to further examine predictability issues relating the seasonal mean and intraseasonal monsoon variability or to explore changes in monsoon behavior in centennial‐scale model integrations.

The experimetrics of public goods: inferring motivations from contributions

In public goods experiments, stochastic choice, censoring and motivational heterogeneity give scope for disagreement over the extent of unselfishness, and whether it is reciprocal or altruistic. We show that these problems can be addressed econometrically, by estimating a finite mixture model to isolate types, incorporating double censoring and a tremble term. Most subjects act selfishly, but a substantial proportion are reciprocal with altruism playing only a marginal role. Isolating reciprocators enables a test of Sugden’s model of voluntary contributions. We estimate that reciprocators display a self-serving bias relative to the model.

Late Quaternary highstands at Lake Chilwa, Malawi: frequency, timing and possible forcing mechanisms in the last 44ka

The extensive shoreline deposits of Lake Chilwa, southern Malawi, a shallow water body today covering 600 km2 of a basin of 7500 km2, are investigated for their record of late Quaternary highstands. OSL dating, applied to 36 samples from five sediment cores from the northern and western marginal sand ridges, reveal a highstand record spanning 44 ka. Using two different grouping methods, highstand phases are identified at 43.7–33.3 ka, 26.2–21.0 ka and 17.9–12.0 ka (total error method) or 38.4–35.5 ka, 24.3–22.3 ka, 16.2–15.1 ka and 13.5–12.7 ka (Finite Mixture Model age components) with two further discrete events recorded at 11.01 ± 0.76 ka and 8.52 ± 0.56 ka. Highstands are comparable to the timing of wet phases from other basins in East and southern Africa, demonstrating wet conditions in the region before the LGM, which was dry, and a wet Lateglacial, which commenced earlier in the southern compared to northern hemisphere in East Africa. We find no evidence that wet phases are insolation driven, but analysis of the dataset and GCM modelling experiments suggest that Heinrich events may be associated with enhanced monsoon activity in East Africa in both timing and as a possible causal mechanism.

Integrated visual vocabulary in latent Dirichlet allocation-based scene classification for IKONOS image

Scene classification based on latent Dirichlet allocation (LDA) is a more general modeling method known as a bag of visual words, in which the construction of a visual vocabulary is a crucial quantization process to ensure success of the classification. A framework is developed using the following new aspects: Gaussian mixture clustering for the quantization process, the use of an integrated visual vocabulary (IVV), which is built as the union of all centroids obtained from the separate quantization process of each class, and the usage of some features, including edge orientation histogram, CIELab color moments, and gray-level co-occurrence matrix (GLCM). The experiments are conducted on IKONOS images with six semantic classes (tree, grassland, residential, commercial/industrial, road, and water). The results show that the use of an IVV increases the overall accuracy (OA) by 11 to 12% and 6% when it is implemented on the selected and all features, respectively. The selected features of CIELab color moments and GLCM provide a better OA than the implementation over CIELab color moment or GLCM as individuals. The latter increases the OA by only ∼2 to 3%. Moreover, the results show that the OA of LDA outperforms the OA of C4.5 and naive Bayes tree by ∼20%. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.JRS.8.083690]

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

Analysis and clustering of residential customers energy behavioral demand using smart meter data

Clustering methods are increasingly being applied to residential smart meter data, providing a number of important opportunities for distribution network operators (DNOs) to manage and plan the low voltage networks. Clustering has a number of potential advantages for DNOs including, identifying suitable candidates for demand response and improving energy profile modelling. However, due to the high stochasticity and irregularity of household level demand, detailed analytics are required to define appropriate attributes to cluster. In this paper we present in-depth analysis of customer smart meter data to better understand peak demand and major sources of variability in their behaviour. We find four key time periods in which the data should be analysed and use this to form relevant attributes for our clustering. We present a finite mixture model based clustering where we discover 10 distinct behaviour groups describing customers based on their demand and their variability. Finally, using an existing bootstrapping technique we show that the clustering is reliable. To the authors knowledge this is the first time in the power systems literature that the sample robustness of the clustering has been tested.

Using laboratory and field measurements to constrain a single habit shortwave optical parameterization for cirrus

A single habit parameterization for the shortwave optical properties of cirrus is presented. The parameterization utilizes a hollow particle geometry, with stepped internal cavities as identified in laboratory and field studies. This particular habit was chosen as both experimental and theoretical results show that the particle exhibits lower asymmetry parameters when compared to solid crystals of the same aspect ratio. The aspect ratio of the particle was varied as a function of maximum dimension, D, in order to adhere to the same physical relationships assumed in the microphysical scheme in a configuration of the Met Office atmosphere-only global model, concerning particle mass, size and effective density. Single scattering properties were then computed using T-Matrix, Ray Tracing with Diffraction on Facets (RTDF) and Ray Tracing (RT) for small, medium, and large size parameters respectively. The scattering properties were integrated over 28 particle size distributions as used in the microphysical scheme. The fits were then parameterized as simple functions of Ice Water Content (IWC) for 6 shortwave bands. The parameterization was implemented into the GA6 configuration of the Met Office Unified Model along with the current operational long-wave parameterization. The GA6 configuration is used to simulate the annual twenty-year short-wave (SW) fluxes at top-of-atmosphere (TOA) and also the temperature and humidity structure of the atmosphere. The parameterization presented here is compared against the current operational model and a more recent habit mixture model.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Neurofuzzy mixture of experts network parallel learning and model construction algorithms

A connection between a fuzzy neural network model with the mixture of experts network (MEN) modelling approach is established. Based on this linkage, two new neuro-fuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm. These two construction methods are equivalent in their effectiveness in overcoming the curse of dimensionality by reducing the dimensionality of the regression vector, but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

A Filter for Visual Tracking Based on a Stochastic Model for Driver Behaviour

A driver controls a car by turning the steering wheel or by pressing on the accelerator or the brake. These actions are modelled by Gaussian processes, leading to a stochastic model for the motion of the car. The stochastic model is the basis of a new filter for tracking and predicting the motion of the car, using measurements obtained by fitting a rigid 3D model to a monocular sequence of video images. Experiments show that the filter easily outperforms traditional filters.

Measuring and modelling mixture toxicity of imidacloprid and thiacloprid on Caenorhabditis elegans and Eisenia fetida

While the standard models of concentration addition and independent action predict overall toxicity of multicomponent mixtures reasonably, interactions may limit the predictive capability when a few compounds dominate a mixture. This study was conducted to test if statistically significant systematic deviations from concentration addition (i.e. synergism/antagonism, dose ratio- or dose level-dependency) occur when two taxonomically unrelated species, the earthworm Eisenia fetida and the nematode Caenorhabditis elegans were exposed to a full range of mixtures of the similar acting neonicotinoid pesticides imidacloprid and thiacloprid. The effect of the mixtures on C. elegans was described significantly better (p<0.01) by a dose level-dependent deviation from the concentration addition model than by the reference model alone, while the reference model description of the effects on E. fetida could not be significantly improved. These results highlight that deviations from concentration addition are possible even with similar acting compounds, but that the nature of such deviations are species dependent. For improving ecological risk assessment of simple mixtures, this implies that the concentration addition model may need to be used in a probabilistic context, rather than in its traditional deterministic manner. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.