Probabilistic Perspective Research Articles

Using a 10-Year Radar Archive for Nowcasting Precipitation Growth and Decay: A Probabilistic Machine Learning Approach

AbstractMachine learning algorithms are trained on a 10-yr archive of composite weather radar images in the Swiss Alps to nowcast precipitation growth and decay in the next few hours in moving coordinates (Lagrangian frame). The hypothesis of this study is that growth and decay is more predictable in mountainous regions, which represent a potential source of practical predictability by machine learning methods. In this paper, artificial neural networks (ANN) are employed to learn the complex nonlinear dependence relating the growth and decay to the input predictors, which are geographical location, mesoscale motion vectors, freezing level height, and time of the day. The average long-term growth and decay patterns are effectively reproduced by the ANN, which allows exploring their climatology for any combination of predictors. Due to the low intrinsic predictability of growth and decay, its prediction in real time is more challenging, but is substantially improved when adding persistence information to the predictors, more precisely the growth and decay and precipitation intensity in the immediate past. The improvement is considerable in mountainous regions, where, depending on flow direction, the root-mean-square error of ANN predictions can be 20%–30% lower compared with persistence. Because large uncertainty is associated with precipitation forecasting, deterministic machine learning predictions should be coupled with a model for the predictive uncertainty. Therefore, we consider a probabilistic perspective by estimating prediction intervals based on a combination of quantile decision trees and ANNs. The probabilistic framework is an attempt to address the problem of conditional bias, which often characterizes deterministic machine learning predictions obtained by error minimization.

Formal Modeling and Verifying the TTCAN Protocol from a Probabilistic Perspective

The time-triggered CAN (TTCAN) protocol has been widely used in the automotive industry to fulfil the safety and real-time requirements of the application. As an extension of the standard CAN protocol, the TTCAN protocol aims to guarantee a safe and deterministic communication by introducing time-triggered messages with respect to a global synchronized time, which are scheduled in independent transmission windows within the system matrix. However, the new features bring more difficulties in designing and verifying the reliable applications in the TTCAN network. In this paper, we first present a formal probabilistic model of the TTCAN protocol with a consideration of its novel features. A TTCAN system consisting of three parts, i.e., a system matrix, an arbitration and some nodes, is modeled as discrete Markov chains model. Furthermore, five probabilistic properties are described and verified in the probabilistic model checker tool PRISM. Our work gives a quantitative analysis method for the given requirements, which facilitates the designers to a formal understanding of TTCAN protocol.

A framework for petrophysically and geologically guided geophysical inversion using a dynamic Gaussian mixture model prior

SUMMARYWe propose a new framework for incorporating petrophysical and geological information into voxel-based geophysical inversion. By developing the geophysical inverse problem from a probabilistic perspective, we redesign the objective function and the iteration steps as a suite of cyclic optimization problems in which three separate MAP optimization problems are solved using geophysical, petrophysical and geological data, respectively. By quantitatively linking these data into a single framework, we recover a final inverted model that reproduces the observed, or desired, petrophysical and geological features while fitting the geophysical data. To achieve our goal we replace the Gaussian prior, used in the Tikhonov inversion approach, by a Gaussian mixture model. After each geophysical model update, the mixture parameters (means, variances and proportions) are determined by the geophysical model and the expected characteristics of the lithologies through another optimization process using the expectation–maximization algorithm. We then classify the model cells into rock units according to the petrophysical and geological information. These two additional steps over the petrophysical and geological data result in a dynamic update of the reference model and associated weights and guide the inversion towards reproducing the expected petrophysical and geological characteristics. The resulting geophysical objective function does not require extra terms to include the additional petrophysical and geological information; this is an important distinction between our work and previous frameworks that carry out joint geophysical and petrophysical data inversion. We highlight different capabilities of our methodology by inverting magnetotelluric and direct-current resistivity data in 1-D and 2-D, respectively. Finally, we apply our framework to inverting airborne frequency domain data, acquired in Australia, for the detection and characterization of saline contamination of freshwater.

Ensemble Kalman inversion: a derivative-free technique for machine learning tasks

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, gradient-free algorithm for finding a solution to these problems using ensemble Kalman inversion (EKI). The method is inherently parallelizable and is applicable to problems with non-differentiable loss functions, for which back-propagation is not possible. Applications of our approach include offline and online supervised learning with deep neural networks, as well as graph-based semi-supervised learning. The essence of the EKI procedure is an ensemble based approximate gradient descent in which derivatives are replaced by differences from within the ensemble. We suggest several modifications to the basic method, derived from empirically successful heuristics developed in the context of SGD. Numerical results demonstrate wide applicability and robustness of the proposed algorithm.

Bivariate probabilistic quantification of drought impacts on terrestrial vegetation dynamics in mainland China

Frequent droughts in a warming climate may exert more negative influences on ecosystems. Unlike previous studies that have investigated the vegetation response to drought generally in a deterministic way, a copula-based model is developed for quantifying drought impacts on terrestrial vegetation and identifying drought-vulnerable regions for mainland China from a probabilistic perspective in this study. The Normalized Difference Vegetation Index (NDVI) is firstly correlated with the Standardized Precipitation Evapotranspiration Index (SPEI) at varying timescales from 1 month to 24 months to determine the response time of vegetation to water variability. Then, the dependence structure of vegetation vigor and water availability is modeled through the bivariate copula analysis. Furthermore, conditional probabilities of vegetation decline under moderate, severe and extreme drought scenarios are systematically estimated using copula-based conditional probability distributions. Results indicate that spatial patterns of vegetation response time present distinct seasonality, with faster response to water variation in the southern part than in the northern proportion of mainland China during the non-growing season while the inverse pattern is observed for the growing season. The higher conditional probabilities of the below-average vegetation status in the dry condition evidence that water deficits overwhelming water surplus play a more profound role in diminishing vegetation vigor across more than 80% of mainland China. Specifically, when moderate droughts develop into extreme ones, the average probability of vegetation status below the 50th percentile escalates by 6.9%. Moreover, extreme droughts are noted to exaggerate probabilities of vegetation activity falling below the increasingly lower (40th, 30th, 20th and 10th) percentiles by 8.8%, 10.8%, 12.7% and 13.7% in comparison with moderate counterparts, thereby suggesting higher likelihood of the deteriorating drought conditions inducing vegetation losses, especially major vegetation decline. As for the drought-vulnerable region, North China, particularly the central Inner Mongolia, is recognized with vegetation decline probabilities being 28.1% and 68.8% greater than the mainland average given drought conditions (quantified as SPEI ≤ −1), respectively. Results of the study may improve our understanding of climatic extreme influence on vegetation status and benefit the effective drought preparedness and mitigation.

Probabilistic assessment of remote sensing-based terrestrial vegetation vulnerability to drought stress of the Loess Plateau in China

Quantitative understanding of vegetation vulnerability under drought stress is essential to initiating drought preparedness and mitigation. In this study, a bivariate probabilistic framework is developed for assessing vegetation vulnerability and mapping drought-prone ecosystems more informatively, which is different from previous studies conducted in a deterministic way. The Normalized Difference Vegetation Index (NDVI) is initially correlated to the Standardized Precipitation Index (SPI) at contrasting timescales to evaluate the degree of vegetation dependence on water availability and screen out the vegetation response time. Afterward, the monthly NDVI series is connected with the most correlated SPI to derive joint distributions using a copula method. On such basis, conditional probabilities of vegetation losses are estimated under multiple drought scenarios and used for revealing tempo-spatial patterns of vegetation vulnerability. Particular focus is directed to the Loess Plateau (LP), China, which is a world-famous environmentally fragile area. Results indicate that the proposed framework is valid for vegetation vulnerability assessment as the pair-wise SPI-NDVI observations fall within high-density areas of the estimated NDVI distributions. From a probabilistic perspective, roughly 95% of the LP exhibits greater probability of vegetation losses when suffering from water deficits rather than water surplus. Vegetation loss probabilities reaching their peak (39.7%) in summer indicate the highest vegetation vulnerability to drought stress in summer months sequentially followed by autumn (32.9%) and spring (31.0%), which is linked to marked variations in water requirement at different stages of vegetation growth. Spatially, drought-vulnerable regions are identified in the western edge with vegetation loss probability 20.6% higher than the LP mean value, suggesting higher vulnerability in more arid areas. Irrigation practices and large-scale vegetation restoration, as two important sources of anthropogenic disturbance in the LP, benefit the decreased vegetation vulnerability over the majority of affected areas. Results may increase our knowledge about climatic controls on vegetation health and support the ecosystem restoration planning in the LP.

Improving surface quality in microcutting of 10B/Al composite

Purpose The microcutting performance of the 10B/Al composite is significantly poor because of the existence of hard boron particles. The effects of cutting parameters, including uncut chip thickness and cutting speed, on the material removal mechanism and surface generation are investigated to improve the surface quality. Design/methodology/approach The 2D finite element model, which includes a rigid cutting tool, a reinforced phase, a matrix and a dense layer, is established. The effects of uncut chip thickness on material removal mechanism and surface generation are analyzed from a probabilistic perspective. The relationship between the uncut chip thickness and the probability in which the machined surface will have a better surface quality is constructed. A Gaussian distribution formula is applied to describe the machined surface quality. Findings Two representative particle-removal modes, namely, cutting-through and pulling-out modes, are observed. For cutting-through mode, when the relative cutting location is small, better surface quality is obtained. For pulling-out mode, the quality of the machined surface gradually improves because the further increase of the relative cutting location reduces the height of the generated pit and scratches. The microcutting at high cutting speed tends to suppress the scratch phenomenon. The best surface quality will be obtained at small uncut chip thickness and high cutting speed. Originality/value The surface quality generated in microcutting of the 10B/Al composite can be improved by optimizing the cutting parameters and controlling the particle-removal modes based on the proposed Gaussian distribution formula.

Time course of the subjective visual vertical during sustained optokinetic and galvanic vestibular stimulation

The brain is thought to use rotation cues from both the vestibular and optokinetic system to disambiguate the gravito-inertial force, as measured by the otoliths, into components of linear acceleration and gravity direction relative to the head. Hence, when the head is stationary and upright, an erroneous percept of tilt arises during optokinetic roll stimulation (OKS) or when an artificial canal-like signal is delivered by means of galvanic vestibular stimulation (GVS). It is still unknown how this percept is affected by the combined presence of both cues or how it develops over time. Here, we measured the time course of the subjective visual vertical (SVV), as a proxy of perceived head tilt, in human participants (n = 16) exposed to constant-current GVS (1 and 2 mA, cathodal and anodal) and constant-velocity OKS (30°/s clockwise and counterclockwise) or their combination. In each trial, participants continuously adjusted the orientation of a visual line, which drifted randomly, to Earth vertical. We found that both GVS and OKS evoke an exponential time course of the SVV. These time courses have different amplitudes and different time constants, 4 and 7 s respectively, and combine linearly when the two stimulations are presented together. We discuss these results in the framework of observer theory and Bayesian state estimation.NEW & NOTEWORTHY While it is known that both roll optokinetic stimuli and galvanic vestibular stimulation affect the percept of vertical, how their effects combine and develop over time is still unclear. Here we show that both effects combined linearly but are characterized by different time constants, which we discuss from a probabilistic perspective.

Multi-failure probabilistic design for turbine bladed disks using neural network regression with distributed collaborative strategy

The performance and reliability of aircraft engine are seriously affected by multiple failures induced by multi-physical loads. Multi-failure probabilistic design is an effective measure to estimate the multi-failure response traits and quantify the multi-failure risk for the improvement of component reliability. In this paper, we propose a neural network regression-distributed collaborative strategy (NNR-DCS) based on a developed two-step error control technique, to improve the efficiency and accuracy of multi-failure probabilistic analysis. We firstly mathematically model NNR-DCS and then introduce the corresponding multi-failure probabilistic framework. With respect to various failure modes such as deformation failure, stress failure and strain failure, the multi-failure probabilistic analysis of a turbine bladed disk is conducted to evaluate the proposed method. From this simulation, we gain the probabilistic distribution features, reliability degree and sensitivity degree of each failure mode and overall failure modes on turbine bladed disk, which provides a useful reference for improving the reliability and performance of aircraft engine. The comparison of methods (Monte Carlo method, RSM, DCRSM, DCFRM, NNR and NNR-DCS) shows that the proposed NNR-DCS holds high efficiency and accuracy for multi-failure probabilistic analysis. The efforts of this study offer an effective way for multi-failure evaluation from a probabilistic perspective and shed light on the multi-objective reliability-based design optimization of complex structures besides turbine bladed disk.

Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Abstract In the light of regularized dynamic time warping kernels, this paper re-considers the concept of a time elastic centroid for a set of time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expresses the averaging process in terms of stochastic alignment automata. It uses an iterative agglomerative heuristic method for averaging the aligned samples, while also averaging the times of their occurrence. By comparing classification accuracies for 45 heterogeneous time series data sets obtained by first nearest centroid/medoid classifiers, we show that (i) centroid-based approaches significantly outperform medoid-based ones, (ii) for the data sets considered, our algorithm, which combines averaging in the sample space and along the time axes, emerges as the most significantly robust model for time-elastic averaging with a promising noise reduction capability. We also demonstrate its benefit in an isolated gesture recognition experiment and its ability to significantly reduce the size of training instance sets. Finally, we highlight its denoising capability using demonstrative synthetic data. Specifically, we show that it is possible to retrieve, from few noisy instances, a signal whose components are scattered in a wide spectral band.

A spatial-aware joint optic disc and cup segmentation method

When dealing with the optic disc and cup in the optical nerve head images, their joint segmentation confronts two critical problems. One is that the spatial layout of the vessels in the optic nerve head images is variant. The other is that the landmarks for the optic cup boundaries are spatially sparse and at small spatial scale. To solve these two problems, we propose a spatial-aware joint segmentation method by explicitly considering the spatial locations of the pixels and learning the multi-scale spatially dense features. We formulate the joint segmentation task from a probabilistic perspective, and derive a spatial-aware maximum conditional probability framework and the corresponding error function. Accordingly, we provide an end-to-end solution by designing a spatial-aware neural network. It consists of three modules: the atrous CNN module to extract the spatially dense features, the pyramid filtering module to produce the spatial-aware multi-scale features, and the spatial-aware segmentation module to predict the labels of pixels. We validate the state-of-the-art performances of our spatial-aware segmentation method on two public datasets, i.e., ORIGA and DRISHTI. Based on the segmentation masks, we quantify the cup-to-disk values and apply them to the glaucoma screening. High correlation between the cup-to-disk values and the risks of the glaucoma is validated on the dataset ORIGA.

Probabilistic assessment of axial force–biaxial bending capacity domains of reinforced concrete sections

Capacity domains of reinforced concrete elements, computed according to Eurocode 2 provisions, have been investigated from a probabilistic perspective in order to examine the variability of the failure probability over different regions of the domain boundary. To this end, constitutive parameters, such as limit stresses and strains, have been defined as random variables. Discretized ultimate limit state domains have been computed by a fiber-free approach for a set of cross sections. In addition, the failure probability relevant to each point of the domain’s boundary has been evaluated by means of Monte Carlo simulations. The numerical results prove that the failure probability presents a significant variability over the domain boundary; it attains its maximum nearby pure axial force while it drastically decreases in presence of significant bending contributions. Finally, the iso-probability surface, i.e. the locus of the internal forces corresponding to a fixed value of the failure probability, is presented. It permits to establish a probabilistic interpretation of the axial force–biaxial bending capacity check consistently with the underlying philosophy of recent structural codes.

Attention to the Variation of Probabilistic Events: Information Processing with Message Importance Measure.

Different probabilities of events attract different attention in many scenarios such as anomaly detection and security systems. To characterize the events’ importance from a probabilistic perspective, the message importance measure (MIM) is proposed as a kind of semantics analysis tool. Similar to Shannon entropy, the MIM has its special function in information representation, in which the parameter of MIM plays a vital role. Actually, the parameter dominates the properties of MIM, based on which the MIM has three work regions where this measure can be used flexibly for different goals. When the parameter is positive but not large enough, the MIM not only provides a new viewpoint for information processing but also has some similarities with Shannon entropy in the information compression and transmission. In this regard, this paper first constructs a system model with message importance measure and proposes the message importance loss to enrich the information processing strategies. Moreover, the message importance loss capacity is proposed to measure the information importance harvest in a transmission. Furthermore, the message importance distortion function is discussed to give an upper bound of information compression based on the MIM. Additionally, the bitrate transmission constrained by the message importance loss is investigated to broaden the scope for Shannon information theory.

Empirical predictive model for generating synthetic non-stationary stochastic accelerogram of the Iranian plateau: including far- and near-field effects as well as mainshock and aftershock categorization

This work proposes comprehensive empirical predictive equations for generating stochastic synthetic 3-dimensional accelerograms for the Iranian plateau based on the existing database. First, the databank of Iranian accelerograms is collected, sorted, processed, declustered and categorized into the pulse-like and non-pulse-like data. To simulate the artificial accelerograms, a stochastic model capable of handling both the temporal and spectral non-stationarity of accelerograms is adopted. By implementing nonlinear curve fitting, parameters of the stochastic model are estimated. Then, the recorded events are categorized into eight distinct groups based on the existence of pulse-like components, and whether the recorded accelerogram is a mainshock or aftershock. Next, for each group, a Bayesian linear regression analysis is performed to obtain empirical predictive equations with probabilistic perspective. This proposed set of equations can estimate parameters of the stochastic model by using input seismological properties including event magnitude, focal depth, epicentral distance and average shear wave velocity of top 30 m of the subsurface profile. Finally, the validity of model is successfully assessed using the existing ground motion prediction equations for the Iranian plateau.

Constrained Covariance Matrices With a Biologically Realistic Structure: Comparison of Methods for Generating High-Dimensional Gaussian Graphical Models

High-dimensional data from molecular biology possess an intricate correlation structure that is imposed by the molecular interactions between genes and their products forming various different types of gene networks. This fact is particularly well known for gene expression data, because there is a sufficient number of large-scale data sets available that are amenable for a sensible statistical analysis confirming this assertion. The purpose of this paper is two fold. First, we investigate three methods for generating constrained covariance matrices with a biologically realistic structure. Such covariance matrices are playing a pivotal role in designing novel statistical methods for high-dimensional biological data, because they allow to define Gaussian graphical models (GGM) for the simulation of realistic data; including their correlation structure. We study local and global characteristics of these covariance matrices, and derived concentration/partial correlation matrices. Second, we connect these results, obtained from a probabilistic perspective, to statistical results of studies aiming to estimate gene regulatory networks from biological data. This connection allows to shed light on the well-known heterogeneity of statistical estimation methods for inferring gene regulatory networks and provides an explanation for the difficulties inferring molecular interactions between highly connected genes.

An information-theoretic approach to machine-oriented music summarization

Music summarization allows for higher efficiency in processing, storage, and sharing of datasets. Machine-oriented approaches, being agnostic to human consumption, optimize these aspects even further. Such summaries have already been successfully validated in some MIR tasks. We now generalize previous conclusions by evaluating the impact of generic summarization of music from a probabilistic perspective. We estimate Gaussian distributions for original and summarized songs and compute their relative entropy, in order to measure information loss incurred by summarization. Our results suggest that relative entropy is a good predictor of summarization performance in the context of tasks relying on a bag-of-features model. Based on this observation, we further propose a straightforward yet expressive summarizer, which minimizes relative entropy with respect to the original song, that objectively outperforms previous methods and is better suited to avoid potential copyright issues.

Probability Analysis and Control of River Runoff–sediment Characteristics based on Pair-Copula Functions: The Case of the Weihe River and Jinghe River

Analyzing the encounter frequency of high–low runoff and sediment yield is important for the appropriate dispatching of runoff–sediment resources, as well as river regulation. However, there have been no reports on the utilization of the pair-copula function in analyzing the runoff–sediment characteristics from a probabilistic perspective and conducting probability control on the runoff–sediment yields of different hydrologic stations. This paper builds marginal distribution functions on the basis of kernel distribution theory. In addition, this paper builds the joint distribution functions through pair-copula functions in order to analyze the encounter probability and the compensation characteristics of high–low runoff and sediment at different stations on the Weihe River in China, as well as the origins of runoff–sediment, to conduct probability control of river runoff–sediment resource allocation. The results show that, in different periods, the synchronous probability of high–low runoff of the Weihe River’s Xianyang and Huaxian Stations, and the Jinghe River’s Zhangjiashan Station differ, while that of high–low sediment at the three stations changes little—remaining at around 54%. Therefore, the sediment and runoff of the Weihe River apparently have different origins. In years of high and low runoff, if the runoffs of the Xianyang and Zhangjiashan Stations can be kept within a certain range, then the runoff of the Huaxian Station will be in a particular range, at a certain probability. Sediment at the Huaxian Station can be controlled, in a similar way. These results are of great significance for the water and sediment management department of the Weihe river, in order to reasonably allocate water and sediment resources.

A probabilistic argumentation framework for reinforcement learning agents

A bounded-reasoning agent may face two dimensions of uncertainty: firstly, the uncertainty arising from partial information and conflicting reasons, and secondly, the uncertainty arising from the stochastic nature of its actions and the environment. This paper attempts to address both dimensions within a single unified framework, by bringing together probabilistic argumentation and reinforcement learning. We show how a probabilistic rule-based argumentation framework can capture Markov decision processes and reinforcement learning agents; and how the framework allows us to characterise agents and their argument-based motivations from both a logic-based perspective and a probabilistic perspective. We advocate and illustrate the use of our approach to capture models of agency and norms, and argue that, in addition to providing a novel method for investigating agent types, the unified framework offers a sound basis for taking a mentalistic approach to agent profiles.

Multi-focus image fusion using boosted random walks-based algorithm with two-scale focus maps

In conventional fusion methods for multi-focus images, the focus map generated by a focus measure would usually be sensitive to mis-registration and noise, or produce badly-aligned boundaries. While many state-of-the-art algorithms use more complex strategies or procedures to address this problem, in this paper we propose to estimate a focus map directly from the two-scale imperfect observations (focus maps) obtained using a small and large-scale focus measures. This would contribute to a more robust fusion by taking advantage of the complementary properties of the two-scale observed focus maps, i.e., robustness to mis-registration (and noise) and the better aligned boundaries. The estimation is firstly modeled in a probabilistic perspective using random walks-based algorithm, in which we try to solve the probabilities that each pixel of the focus map is associated with the observed ones. Then we found that this method is equivalent to solving an alternate objective function, enabling a great boost both in computational efficiency and estimation result. Experimental results demonstrate that the proposed method is robust yet efficient compared with state-of-the-art fusion methods.

Exposure to ≤15 cGy of 600 MeV/n 56Fe Particles Impairs Rule Acquisition but not Long-Term Memory in the Attentional Set-Shifting Assay.

On future missions into deep space, astronauts will be required to work more autonomously than on previous missions, and thus their ability to perform executive functions could be critical to mission success. In this study, we determined the effect that ≤15 cGy of 600 MeV/n 56Fe particles has on attentional set-shifting (ATSET) performance of ∼10 month-old (at the time of irradiation) male Wistar rats that had been prescreened for their ability to perform the task. Exposure to 1-15 cGy of 56Fe particles leads to a significant impairment in compound discrimination (CD) performance. Should similar effects occur in astronauts, an impaired ability to execute CD would result in a decreased ability to identify and maintain focus on relevant aspects of the task being performed. The use of rats that had been prescreened for ATSET performance helped to establish that working memory of the rules for the food reward remained intact (for at least 100 days) even after 15 cGy irradiation with 600 MeV/n 56Fe particles, but that 56Fe radiation exposure affected associative cue learning/acquisition rather than an intrinsic inability to perform the CD tasks. Our data suggest that declarative memory, and the ability to transitively infer established rules, also remained intact in the irradiated rats. Thus, should similar effects occur in astronauts, 56Fe-induced CD performance deficits may only be manifested in scenarios where astronauts are required to transitively apply their knowledge to solve problems that they have not previously encountered; nevertheless, potentially one-third of astronauts may not be able to perform event-critical tasks correctly. The implication of this data, from a probabilistic risk assessment perspective, is that cognitive performance studies that use naïve rodents, thus requiring task rule acquisition as well as task performance, are likely to overestimate the risk of 56Fe-induced cognitive deficits.