Adaptive anchored inversion for Gaussian random fields using nonlinear data

A Bayesian approach to bandwidth selection for multivariate kernel density estimation

During the Late Triassic and Early Jurassic the Newark rift basin of the northeastern US accumulated in excess 5 km of continental, mostly lacustrine strata that show a profound cyclicity previousl...

In practical classification problems, imbalanced class distribution is very common. Traditional classification methods usually aim at optimizing the overall accuracy, which leads to classification decisions biased towards categories with a large number of samples. Similar to most traditional classifiers, Naive Bayes (NB) is sensitive to the class prior distribution and has poor recognition performance for minority class samples, which restricts its application in imbalanced classification. Therefore, we propose a Bayesian classifier based on distance-corrected multivariate kernel density estimation (BC-DMKDE). BC-DMKDE relaxes the assumptions regarding conditional independence and the normality of continuous variables in NB classifiers, by incorporating the multivariate kernel density estimation (MKDE). We also incorporate a distance-correction mechanism utilizing kernel density estimation, specifically to alleviate the impact of class imbalance and overlapping data samples. Across 18 real-world benchmarks, BC-DMKDE exhibits superior classification performance and robustness, outperforming existing methods at both the algorithm and data levels.

Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used, the bandwidth selection remains a challenging issue in terms of balancing algorithmic performance and statistical relevance. The purpose of this paper is to study a recently developed bandwidth selection method, called Penalized Comparison to Overfitting (PCO). We first provide new theoretical guarantees by proving that PCO performed with non-diagonal bandwidth matrices is optimal in the oracle and minimax approaches. PCO is then compared to other usual bandwidth selection methods (at least those which are implemented in the R-package) for univariate and also multivariate kernel density estimation on the basis of intensive simulation studies. In particular, cross-validation and plug-in criteria are numerically investigated and compared to PCO. The take home message is that PCO can outperform the classical methods without algorithmic additional cost.

The marginal likelihood has become an important tool for model selection in Bayesian analysis because it can be used to rank the models. We discuss the marginal likelihood for Poisson regression models that are potentially useful in small area estimation. Computation in these models is intensive and it requires an implementation of Markov chain Monte Carlo (MCMC) methods. Using importance sampling and multivariate density estimation, we demonstrate a computation of the marginal likelihood through an output analysis from an MCMC sampler.

An accurate solver for forward and inverse transport

The main modern construction methods of geological medium depth-velocity models are based on different solutions to the inverse kinematic problem of seismic prospecting. Unfortunately, solutions to the inverse problems are ill-posed. There are many algorithms for approximate solutions to the inverse problems. Its application and results comparison show the nonexistence of uniqueness and existence of structural instability of solutions to the inverse problems. The article presents an original seismic locating technology designed to computer modeling of seismic images with high-resolution and precision. The technology provides an accurate and consistent design of a computer depth-velocity medium model without inverse problems solutions. To eliminate obstacles inherent to traditional seismic images construction approaches, the technology applies radio locating methods ideas. The technology consequently solves three construction problems of computer models of qualitative seismic images. It begins with qualitative primary processing of field materials obtained with the reflected waves method, and continues with receiving computer images of the processing results. Next, it builds a high-resolution and precision model of the reflected waves hodograph series image. The technology completes with computer modeling of the configuration of the interface between the layers of the medium, linked in space to the observation profile. The concept of accurate and high-quality design of a computer image of the interface between two layers of the geological environment model is to find a line passing through an optimally selected set of wave reflection points. The seismic location technology uses algorithmic means providing an optimal location and estimation of the best reflecting point where the propagating wave has a minimal travel time. The virtual locating grid provides the spatial binding to the observation profile. Precision of the binding is achieved by a stochastic modification operation and the use of grid parameters variation.

K-means is the best known clustering algorithm, because of its usage simplicity, fast speed and efficiency.However, resultant clusters are influenced by the randomly selected initial centroids.Therefore, many techniques have been implemented to solve the mentioned issue. In this paper, a new version of the k-means clustering algorithm named as ImpKmeans shortly (An Improved Version of K-Means Algorithm by Determining Optimum InitialCentroids Based on Multivariate Kernel Density Estimation and Kd-tree) that uses kernel density estimation, to find the optimum initial centroids, is proposed.Kernel density estimation is used, because it is a nonparametric distribution estimation method, that can identify density regions.To understand the efficiency of the ImpKmeans, we compared it with some state-of-the-art algorithms.According to the experimental studies, the proposed algorithm was better than the compared versions of k-means.While ImpKmeans was the most successful algorithm in 46 tests of 60, the second-best algorithm, was the best on 34 tests.Moreover, experimental results indicated that the ImpKmeans is fast, compared to the selected k-means versions.

Although density‐based clustering algorithms can successfully define clusters in arbitrary shapes, they encounter issues if the dataset has varying densities or neck‐typed clusters due to the requirement for precise distance parameters, such as eps parameter of DBSCAN. These approches assume that data density is homogenous, but this is rarely the case in practice. In this study, a new clustering algorithm named ANDClust (Adaptive Neighborhood Distance‐based Clustering Algorithm) is proposed to handle datasets with varying density and/or neck‐typed clusters. The algorithm consists of three parts. The first part uses Multivariate Kernel Density Estimation (MulKDE) to find the dataset's peak points, which are the start points for the Minimum Spanning Tree (MST) to construct clusters in the second part. Lastly, an Adaptive Neighborhood Distance (AND) ratio is used to weigh the distance between the data pairs. This method enables this approach to support inter‐cluster and intra‐cluster density varieties by acting as if the distance parameter differs for each data of the dataset. ANDClust is tested on synthetic and real datasets to reveal its efficiency. The algorithm shows superior clustering quality in a good run‐time compared to its competitors. Moreover, ANDClust could effectively define clusters of arbitrary shapes and process high‐dimensional, imbalanced datasets may have outliers.

With the advent of the Legacy Survey of Space and Time, time-domain astronomy will be faced with an unprecedented volume and rate of data. Real-time processing of variables and transients detected by such large-scale surveys is critical to identifying the more unusual events and allocating scarce follow-up resources efficiently. We develop an algorithm to identify these novel events within a given population of variable sources. We determine the distributions of magnitude changes (dm) over time intervals (dt) for a given passband f, , and use these distributions to compute the likelihood of a test source being consistent with the population or being an outlier. We demonstrate our algorithm by applying it to the DECam multiband time-series data of more than 2000 variable stars identified by Saha et al. in the Galactic Bulge that are largely dominated by long-period variables and pulsating stars. Our algorithm discovers 18 outlier sources in the sample, including a microlensing event, a dwarf nova, and two chromospherically active RS CVn stars, as well as sources in the blue horizontal branch region of the color–magnitude diagram without any known counterparts. We compare the performance of our algorithm for novelty detection with the multivariate Kernel Density Estimator and Isolation Forest on the simulated PLAsTiCC data set. We find that our algorithm yields comparable results despite its simplicity. Our method provides an efficient way for flagging the most unusual events in a real-time alert-broker system.

This paper presents fabrication of complex surficial micro-features employing a cross-innovative hybrid process inspired from lithography and Jet-ECM. The process is referred here as mask electrolyte jet machining (MEJM). MEJM is a non-contact machining process which combines high resolution of lithography and greater flexibility of Jet-ECM. It is a non-contact process which can fabricate variety of microstructures on difficult-to-machine materials without need of expensive tooling. The presented work demonstrates the process performance of this technology by statistical analysis and multivariate kernel density estimation (KDE) based on probabilistic density function. Micro-letters are fabricated as an example of complex surficial structure comprising of multiple intersecting, straight and curved grooves. The processing response is characterized in terms of geometrical size, similarity ratio, and cumulative shape deviation. Experimental results demonstrated that micro letters with good repeatability (minimum SD of shape error ratio 0.297%) and shape accuracy (minimum shape error of 0.039%) can be fabricated with this technology. The results suggest MEJM could be a promising technology for batch manufacturing of surface microstructures with high productivity.

A novel maximum a posteriori (MAP) method for dynamic single-photon emission computed tomography image reconstruction is proposed. The prior probability is modeled as a multivariate kernel density estimator (KDE), effectively modeling the prior probability non-parametrically, with the aim of reducing the effects of artifacts arising from inconsistencies in projection measurements in low-count regimes where projections are dominated by noise. The proposed prior spatially and temporally limits the variation of time-activity functions (TAFs) and attracts similar TAFs together. The similarity between TAFs is determined by the spatial and range scaling parameters of the KDE-like prior. The resulting iterative image reconstruction method is evaluated using two simulated phantoms, namely the extended cardiac-torso (XCAT) heart phantom and a simulated Mini-Deluxe Phantom. The phantoms were chosen to observe the effects of the proposed prior on the TAFs based on the vicinity and abutments of regions with different activities. Our results show the effectiveness of the proposed iterative reconstruction method, especially in low-count regimes, which provides better uniformity within each region of activity, significant reduction of spatiotemporal variations caused by noise, and sharper separation between different regions of activity than expectation maximization and an MAP method employing a more traditional Gibbs prior.

Publication in the conference proceedings of EUSIPCO, Lisbon, Portugal, 2014

A metabolomics approach to characterise and identify various Mycobacterium species

With the rapid increase in distributed wind generation, considerable efforts have been devoted to the microgrid day-ahead scheduling. The effectiveness of those methods will highly depend on the selection of the uncertainty sets. We propose a distribution-free approach for wind power scenario generation, using sequence generative adversarial networks. To capture the temporal correlation, the model adopts the long short-term memory architecture and uses generative adversarial networks coupled with reinforcement learning, which, in contrast to the existing methods, avoids manual labeling and captures the complex dynamics of the weather. We conduct case studies based on the data from the Bonneville Power Administration and the National Renewable Energy Laboratory, and show that the generated scenarios can better characterize the variability of wind power and reduce the risk of uncertainties, compared with those produced by Gaussian distribution, vanilla long short-term memory, and multivariate kernel density estimation. Moreover, the proposed method achieves better performance when applied to the day-ahead scheduling of microgrids.