Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Classification of interstitial lung disease patterns using local DCT features and random forest.

Over the last decade, a plethora of computer-aided diagnosis (CAD) systems have been proposed aiming to improve the accuracy of the physicians in the diagnosis of interstitial lung diseases (ILD). In this study, we propose a scheme for the classification of HRCT image patches with ILD abnormalities as a basic component towards the quantification of the various ILD patterns in the lung. The feature extraction method relies on local spectral analysis using a DCT-based filter bank. After convolving the image with the filter bank, q-quantiles are computed for describing the distribution of local frequencies that characterize image texture. Then, the gray-level histogram values of the original image are added forming the final feature vector. The classification of the already described patches is done by a random forest (RF) classifier. The experimental results prove the superior performance and efficiency of the proposed approach compared against the state-of-the-art.

Fully automatic segmentation of AP pelvis X-rays via random forest regression with efficient feature selection and hierarchical sparse shape composition

In clinical practice, traditional X-ray radiography is widely used, and knowledge of landmarks and contours in anteroposterior (AP) pelvis X-rays is invaluable for computer aided diagnosis, hip surgery planning and image-guided interventions. This paper presents a fully automatic approach for landmark detection and shape segmentation of both pelvis and femur in conventional AP X-ray images. Our approach is based on the framework of landmark detection via Random Forest (RF) regression and shape regularization via hierarchical sparse shape composition. We propose a visual feature FL-HoG (Flexible- Level Histogram of Oriented Gradients) and a feature selection algorithm based on trace radio optimization to improve the robustness and the efficacy of RF-based landmark detection. The landmark detection result is then used in a hierarchical sparse shape composition framework for shape regularization. Finally, the extracted shape contour is fine-tuned by a post-processing step based on low level image features. The experimental results demonstrate that our feature selection algorithm reduces the feature dimension in a factor of 40 and improves both training and test efficiency. Further experiments conducted on 436 clinical AP pelvis X-rays show that our approach achieves an average point-to-curve error around 1.2 mm for femur and 1.9 mm for pelvis.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.

Species interactions and random dispersal rather than habitat filtering drive community assembly during early plant succession

Theory on plant succession predicts a temporal increase in the complexity of spatial community structure and of competitive interactions: initially random occurrences of early colonising species shift towards spatially and competitively structured plant associations in later successional stages. Here we use long-term data on early plant succession in a German post mining area to disentangle the importance of random colonisation, habitat filtering, and competition on the temporal and spatial development of plant community structure. We used species co-occurrence analysis and a recently developed method for assessing competitive strength and hierarchies (transitive versus intransitive competitive orders) in multispecies communities. We found that species turnover decreased through time within interaction neighbourhoods, but increased through time outside interaction neighbourhoods. Successional change did not lead to modular community structure. After accounting for species richness effects, the strength of competitive interactions and the proportion of transitive competitive hierarchies increased through time. Although effects of habitat filtering were weak, random colonization and subsequent competitive interactions had strong effects on community structure. Because competitive strength and transitivity were poorly correlated with soil characteristics, there was little evidence for context dependent competitive strength associated with intransitive competitive hierarchies.

Preference Structure and Random Paths to Stability in Matching Markets

This paper examines how preference correlation and intercorrelation combine to influence the length of a decentralized matching market's path to stability. In simulated experiments, marriage markets with various preference specifications begin at an arbitrary matching of couples and proceed toward stability via the random mechanism proposed by Roth and Vande Vate (1990). The results of these experiments reveal that fundamental preference characteristics are critical in predicting how long the market will take to reach a stable matching. In particular, intercorrelation and correlation are shown to have an exponential impact on the number of blocking pairs that must be randomly satisfied before stability is attained. The magnitude of the impact is dramatically different, however, depending on whether preferences are positively or negatively intercorrelated.