General Probability Distribution Research Articles

On the Attainments of the van Trees and the Borovkov–Sakhanenko Bounds for the Escort Distribution

Some necessary and sufficient conditions for attaining equality for Bayesian information inequalities such as the van Trees and the Borovkov–Sakhanenko inequalities regard to the order of the escort distribution when the probability distribution of the data is modelled using an escort distribution, which is a generalized probability distribution constructed from an exponential family, and the prior distribution is either conjugate or Jeffreys, and the parameter of interest is a function of the order of the escort distribution. Examples of normal variance and logit models are also considered.

A Ranking-Based Cross-Entropy Loss for Early Classification of Time Series.

Early classification tasks aim to classify time series before observing full data. It is critical in time-sensitive applications such as early sepsis diagnosis in the intensive care unit (ICU). Early diagnosis can provide more opportunities for doctors to rescue lives. However, there are two conflicting goals in the early classification task-accuracy and earliness. Most existing methods try to find a balance between them by weighing one goal against the other. But we argue that a powerful early classifier should always make highly accurate predictions at any moment. The main obstacle is that the key features suitable for classification are not obvious in the early stage, resulting in the excessive overlap of time series distributions in different time stages. The indistinguishable distributions make it difficult for classifiers to recognize. To solve this problem, this article proposes a novel ranking-based cross-entropy () loss to jointly learn the feature of classes and the order of earliness from time series data. In this way, can help classifier to generate probability distributions of time series in different stages with more distinguishable boundary. Thus, the classification accuracy at each time step is finally improved. Besides, for the applicability of the method, we also accelerate the training process by focusing the learning process on high-ranking samples. Experiments on three real-world datasets show that our method can perform classification more accurately than all baselines at all moments.

Classical and Bayesian techniques for modelling engineering dataset using new generalized probability distribution with mathematical features

Classical and Bayesian techniques for modelling engineering dataset using new generalized probability distribution with mathematical features

Protecting oil storage tanks against floods: Natech risk assessment with imprecise probabilities

AbstractNatechs are technological accidents that are triggered by natural disasters. The increase in the frequency and severity of climatic natural disasters along with the growth of industrialization has accelerated the demand for development of dedicated methodologies for risk assessment and management of Natechs. Due to a lack of accurate and sufficient data, risk assessment of Natechs has largely been based on subjective assumptions and imprecise probabilities, making the assessed risks and the subsequent risk management strategies deficient in terms of cost‐effectiveness. In the present study, evidence theory, as an effective technique for dealing with imprecise probabilities, and Bayesian network, as an effective tool for reasoning under uncertainty, are combined to develop a methodology for risk analysis of Natechs based on imprecise probabilities with no attempt to increase the precision of the input data but the accuracy and cost‐effectiveness of the outcomes. Flotation of oil tanks during floods has been considered to exemplify the methodology. The methodology is demonstrated to outperform conventional approaches where average probabilities or generic probability distributions are used instead of interval probabilities for risk assessment and management.

Diff-MGR: Dynamic causal graph attention and pattern reproduction guided diffusion model for multivariate time series probabilistic forecasting

Time series probability forecasting provides insight into future evolution and its inherent uncertainty from past data. In order to obtain more accurate forecasting as the reliable basis for future decision-making and planning, a new probabilistic prediction model of multivariate time series Diff-MGR is proposed in this study. Diff-MGR innovatively proposes dynamic causal graph attention blocks and pattern reproduction guided prediction blocks to predict the future patterns. Compared with the existing methods, the former captures dynamic unidirectional information flow by using causal graph structure at different periods to provide a real representation of variable relationships. The latter completes a reliable mapping of historical patterns to the future based on the prior knowledge of pattern reproduction. Furthermore, Diff-MGR proposes a novel noise prediction network that can effectively capture dependencies in predicted future patterns and generate probability distributions of future sequences using a conditional diffusion model. Extensive experiments on several real datasets verify the effectiveness of Diff-MGR's components, and show it outperforms existing models in probabilistic forecasting performance.

Discretization and decoupled knowledge distillation for arbitrary oriented object detection

In recent years, lightweight object detection networks have been increasingly applied to remote sensing platforms due to their fast inference speed and flexible deployment advantages. Knowledge distillation methods have been widely used to reduce the performance gap between large and small models, and many studies have combined knowledge distillation with object detection. However, existing knowledge distillation methods often overlook the transfer of localization knowledge. Therefore, this paper proposes a method called Discretized Position Knowledge Distillation (DPKD) to improve the use of knowledge distillation in object detection. Specifically, the DPKD method incorporates a Discretization Algorithm Module (DAM), which leverages both general probability distribution and cross-Gaussian distribution to transfer high-quality bounding box position and pose information. Additionally, the Position Knowledge Distillation (PKD) method splits the target and non-target bounding boxes to form the distillation loss function, addressing the issue of missing background knowledge transfer during the distillation process. To further enhance the learning of high-quality bounding boxes, a Region Weighting Module (RWM) based on EIoU is introduced in DPKD, assigning weights to the various bounding boxes in the teacher's output. The effectiveness of DPKD in the field of remote sensing image object detection in multi-modal scenarios was verified through multi-modal training on the publicly available DOTA and HRSID datasets.

Quantum Monte Carlo simulations for financial risk analytics: scenario generation for equity, rate, and credit risk factors

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation – i.e. simulation of the risk factor evolution over time to generate probability distributions – into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.

Probabilistic linguistic prospect outranking risk decision making method based on stochastic dominance and application in emergency plan evaluation

In the decision-making process, probabilistic linguistic term sets (PLTSs) could represent decision-makers’ uncertain evaluation information. The combination of probabilistic and linguistic information assists decision-makers to depict their evaluation information more flexibly. In this paper, a prospect outranking decision-making method based on stochastic dominance is proposed for solving the multi-attribute risk decision-making problem under the probabilistic linguistic information environment. Firstly, to fully preserve the original probabilistic linguistic information, we give the definitions of the generalized probability distribution and the corresponding generalized cumulative distribution function of a PLTS for defining the distance measure between PLTSs. Secondly, based on the positive and negative ideal cumulative distribution functions, we propose the probabilistic linguistic prospect value functions. After that, considering the uncertainty of the relationship between alternatives, several kinds of novel prospect stochastic dominance and almost stochastic dominance relations are defined, which consider the decision makers’ distinction between gains and losses to measure the subtle relationship between alternatives. The stochastic dominance approach and the almost stochastic dominance approach under the probabilistic linguistic decision-making environment are put forward. Besides, we use the superiority and inferiority ranking method to solve the dominance ranking problem of the uncertainty relationship between any two alternatives. Finally, the proposed method is applied in the evaluation of emergency plans to show the accuracy and reliability, and comparative analyses are made to illustrate its availability.

Optimal ordering based on shortage scenarios under presence of a low-quality substitute and supply uncertainty

Global trade has shifted from short-distance supply chains within countries to long-distance supply chains between countries. As a result, delivery lead time has become a key operational factor, and uncertainty causes stock-outs, resulting in massive losses. An important solution for shortages is product substitutes, but they can affect the quality of the end products. Moreover, even when demand is expected and planned for, unexpected last-minute demand makes operational conditions challenging. This paper considers a single-period problem of replenishing a high-quality product under both lead time and demand-related uncertainty. Stock-outs during and at the end of the replenishment period can be handled only by providing a low-quality substitute product that requires repeated replacements, therefore affecting pending demand. We provide detailed modeling of possible stock-out scenarios and show that, in presence of these two types of uncertainty, the optimal order quantity of a high-quality product can be determined using an upper and lower threshold and a base stock level equal to anticipated (planned) demand over the replenishment period. In particular, we derive a closed-form solution for the optimal order quantity under general probability distributions of lead time and demand and explicit solutions for uniform distributions. We also show the conditions under which optimal order quantities can be insensitive to the cost of the high-quality product.

An Innovative Technique for Generating Probability Distributions: A Study on Lomax Distribution with Applications in Medical and Engineering Fields

An Innovative Technique for Generating Probability Distributions: A Study on Lomax Distribution with Applications in Medical and Engineering Fields

Probabilistic Keyphrase Generation From Copy and Generating Spaces.

Keyphrase generation is one of the most fundamental tasks in natural language processing (NLP). Most existing works on keyphrase generation mainly focus on using holistic distribution to optimize the negative log-likelihood loss, but they do not directly manipulate the copy and generating spaces, which may reduce the generability of the decoder. Additionally, existing keyphrase models are either unable to determine the dynamic numbers of keyphrases or produce the number of keyphrases implicitly. In this article, we propose a probabilistic keyphrase generation model from copy and generating spaces. The proposed model is built upon the vanilla variational encoder-decoder (VED) framework. On top of VED, two separate latent variables are adopted to model the distribution of data within the latent copy and generating spaces, respectively. Specifically, we adopt a von Mises-Fisher (vMF) distribution to obtain a condensed variable for modifying the generating probability distribution over the predefined vocabulary. Meanwhile, we utilize a clustering module, which is designed to promote Gaussian Mixture learning and subsequently extract a latent variable for the copy probability distribution. Moreover, we utilize a natural property of the Gaussian mixture network and use the number of filtered components to determine the number of keyphrases. The approach is trained based on latent variable probabilistic modeling, neural variational inference, and self-supervised learning. Experiments on social media and scientific article datasets outperform the state-of-the-art baselines in generating accurate predictions and controllable keyphrase numbers.

Construction risk analysis of cantilever casting mid-span closure of bridge in reservoir area

In order to assess the impact of frequent microseismic and cyclic water flow forces on the bridge cantilever casting construction in the Three Gorges reservoir area, a limited element-quantum-orthogonal experimental design-neural network-Monte Carlo simulation method was used to analyze the risk assessment of the construction. The orthogonal experimental design method is utilized to generate probability distribution samples of water velocity, water height, and microseismic acceleration. These samples are then combined with a finite element model and trained using a BP neural network. This approach aims to establish a nonlinear mapping relationship between each control parameter and the axial deviation value in the mid-span closure, and then the Monte Carlo simulation is used to generate the random influence parameter, which can be substituted into the trained BP neural network to predict the risk of the error in the mid-axial deviation. The results suggested that the risk probability of the medial axis deviation of the closure section due to the coupling effect of water flow force and high-frequency microseismicity had reached 5.06%, and the risk of line deviation of the cantilever casting construction of the bridge in the reservoir area needed to be paid sufficient attention and prevented. The risk of line deviation of the cantilever casting construction of the reservoir bridge needs to attract enough attention and precaution.

Asymptotic approximations of expectations of power means

In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general nonnegative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behavior depending on sample size contributes to interesting connections with the power mean of probability distribution.

Mathematical and statistical structures of a new generalized probability distribution for fitting different types of datasets

Mathematical and statistical structures of a new generalized probability distribution for fitting different types of datasets

Generating probability distributions on intervals and spheres: Convex decomposition

This work studies the convexity of a class of positive definite probability measures with density functionsρ=cλ∑n=0∞g(n)Cnλwλ, that are generated through the interval characteristic sequences. We discuss when such measures supported in an interval are convex and demonstrate how convexity is preserved under multiplication by certain multipliers and under the intertwining product. A key message to be delivered from this work is: any integrable function f on the interval with a polynomial expansion that has relatively fast absolute convergence, can be decomposed into a non-unique pair of positive convex interval probabilities (f+,f−)∈Eλ′×Eλ′ up to normalization, in the sense that f=f+−f−, where Eλ′ is a class of convex functions. Consequently not only the study of an interval distribution is reduced to the study of the properties of class Eλ′, but also the discontinuous probabilistic Galerkin schemes can be simplified. As concrete examples the decomposition of polynomials and truncated normal distribution are computed and graphically illustrated. Such interval measures lead to localized spherical probability measures, and as a convex expression of probability measure is a Jensen type inequality for spherical random variables. Based on the spherical information entropy models, one dependent on the domain partition and the other not, we propose three minimization formulations for the probabilistic finite element method, including one that mixes the least-squares and entropy models.

Half-wormholes and ensemble averages

Recently, the concept of half-wormholes is introduced to give a resolution to the factorization puzzle in holography and help understand better the relation between ensemble average theories and gravity in the bulk. Half-wormholes are proposed to be the contributions to the gravitational path integral that correspond to fluctuations of each individual theory around the average of the whole ensemble of theories. In this paper, we further explore the extent to which the half-wormhole interpretation is applicable. In particular, to further demonstrate that the half-wormhole interpretation is not merely a feature of a specific theory but is a general feature of ensemble average theories, we examine various models, including different enriched 0-dimensional SYK-like models, the 1-dimensional Brownian SYK model and its generalization. To further demonstrate that the half-wormhole interpretation applies to more general probability distributions apart from the zero-mean Gaussian distribution, we consider random couplings with other non-trivial moments. Specifically, introducing a non-trivial mean value to the random coupling renders the spectral correlators to exhibit both disconnected saddles and connected saddles. The inclusion of higher-order moments leads to new “multi-linked half-wormhole” saddles. We also clarify the distinctions between the unlinked half-wormhole and the linked half-wormhole in our modified Brownian SYK model.

General Nonlocal Probability of Arbitrary Order.

Using the Luchko's general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (CF) extensions of probability density functions (PDFs), cumulative distribution functions (CDFs) and probability are defined and its properties are described. Examples of general nonlocal probability distributions of AO are considered. An application of the multi-kernel GFC allows us to consider a wider class of operator kernels and a wider class of nonlocality in the probability theory.

Event-Based Distributed Secondary Control for AC Islanded Microgrid With Semi-Markov Switched Topology Under Cyber-Attacks

The operation of a microgrid (MG) is easily affected by the environment, which leads to the change of communication topology among distributed generations (DGs). Most of the existing results on secondary control of MG consider that the topology connection is fixed, or just simply switched by arbitrary form. In this article, a more general semi-Markov process is introduced to describe such switching, i.e., the switching of communication topology is regarded as a random change process of system mode under general probability distribution. Then, out of the comprehensive consideration of inevitable network constraints, this article proposes distributed resilient secondary control method for AC islanded MG. In our control strategy, the network security, communication burden, and transmission delay are all considered in the controller design. An event detection mechanism is used as the transmission protocol for information interaction among DGs, reducing the communication burden effectively. And a cyber-attack model is introduced to follow the Bernoulli distribution, and the neighbors' information of each DG may be attacked with possible probability. Based on feedback linearization, the studied secondary control problem is cast into distributed tracking synchronization of first-order multiagent systems. The Lyapunov functional method is used to prove the proposed strategy theoretically, and its effectiveness is verified by a modified IEEE 34 bus test system. The result shows that the proposed method can reduce the communication numbers by over 80% under the premise of realizing frequency restoration and accurate real power sharing of AC islanded MG, and the transmission rate is also reduced by about 40% compared with the existing general method.

RegRL-KG: Learning an L1 regularized reinforcement agent for keyphrase generation

Keyphrase generation (KG) aims at condensing the content from the source text to the target concise phrases. Though many KG algorithms have been proposed, most of them are tailored into deep learning settings with various specially designed strategies and may fail in solving the bias exposure problem. Reinforcement Learning (RL), a class of control optimization techniques, are well suited to compensate for some of the limitations of deep learning methods. Nevertheless, RL methods typically suffer from four core difficulties in keyphrase generation: environment interaction and effective exploration, complex action control, reward design, and task-specific obstacle. To tackle this difficult but significant task, we present RegRL-KG, including actor-critic based-reinforcement learning control and L1 policy regularization under the first principle of minimizing the maximum likelihood estimation (MLE) criterion by a sequence-to-sequence (Seq2Seq) deep learnining model, for efficient keyphrase generation. The agent utilizes an actor-critic network to control the generated probability distribution and employs L1 policy regularization to solve the bias exposure problem. Extensive experiments show that our method brings improvement in terms of the evaluation metrics on five scientific article benchmark datasets.

Estimating annual average daily traffic (AADT) data on low-volume roads with the cokriging technique and census/population data

Background: Geostatistics focuses on spatial or spatiotemporal datasets. Geostatistics was initially developed to generate probability distribution predictions of ore grade in the mining industry; however, it has been successfully applied in diverse scientific disciplines. This technique includes univariate, multivariate, and simulations. Kriging geostatistical methods, simple, ordinary, and universal Kriging, are not multivariate models in the usual statistical function. Notwithstanding, simple, ordinary, and universal kriging techniques utilize random function models that include unlimited random variables while modeling one attribute. The coKriging technique is a multivariate estimation method that simultaneously models two or more attributes defined with the same domains as coregionalization. Objective: This study investigates the impact of populations on traffic volumes as a variable. The additional variable determines the strength or accuracy obtained when data integration is adopted. In addition, this is to help improve the estimation of annual average daily traffic (AADT). Methods Procedures, Process: The investigation adopts the coKriging technique with AADT data from 2009 to 2016 from Montana, Minnesota, and Washington as primary attributes and population as a controlling factor (second variable). CK is implemented for this study after reviewing the literature and work completed by comparing it with other geostatistical methods. Results, Observations, and Conclusions: The Investigation employed two variables. The data integration methods employed in CK yield more reliable models because their strength is drawn from multiple variables. The cross-validation results of the model types explored with the CK technique successfully evaluate the interpolation technique's performance and help select optimal models for each state. The results from Montana and Minnesota models accurately represent the states' traffic and population density. The Washington model had a few exceptions. However, the secondary attribute helped yield an accurate interpretation. Consequently, the impact of tourism, shopping, recreation centers, and possible transiting patterns throughout the state is worth exploring.