Conditional Distribution Research Articles

Универсальный метод Монте-Карло для процессов Леви и его экстремумов

The article proposes a universal approach to constructing Monte Carlo methods for pricing options with payoffs depending on the joint distribution of the final position of the Lévy process X_T and its infimum J_T (or supremum S_T). We derive approximate formulas for the conditional cumulative distribution functions of the Lévy process "P"(X_T<x|S_T=y) (P(X_T<x|J_T=y)), which are expressed through the partial derivative with respect to y of the joint cumulative distribution function "P"(X_T<x,S_T<y) (P(X_T<x,J_T<y)) and the density of the infimum (or supremum) at the final moment of time. By applying the Laplace transform to the joint cumulative distribution function of the Lévy process and its extremum, we use the approximate Wiener–Hopf factorization to represent the image of its partial derivative. By inverting the Laplace transform using the Gaver–Stehfest algorithm, we find the desired conditional cumulative distribution function. The developed algorithm for simulating the joint position of the Lévy process and its extremum at a given point in time consists of two key stages. At the first stage, we simulate the extremum value of the L´evy process based on the approximation of its cumulative distribution function "P"(S_T<x) (or P(J_T<x)). In the second step, we simulate the final value of the Lévy process based on the approximation of the conditional cumulative distribution function of the final position of the Lévy process relative to its extremum. The universality of the Monte Carlo method we developed lies in the implementation of a uniform approach for a wide class of Lévy processes, in contrast to classical approaches, when simulations are essentially based on the features of the probability distribution associated with the simulated random process or its extrema. In our approach, it is enough to know the characteristic exponent of the Lévy process. The most time-consuming computational unit for simulating a random variable based on a known cumulative distribution function can be effectively implemented using neural networks and accelerated through parallel computing. Thus, on the one hand, the approach we propose is suitable for a wide class of Lévy models, on the other hand, it can be combined with machine learning methods.

Asymptotic Normality of Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

This work addresses the problem of the nonparametric estimation of the regression function, namely the conditional distribution and the conditional quantile in the single functional index model (SFIM) under the independent and identically distributed condition with randomly missing data. The main result of this study was the establishment of the asymptotic properties of the estimator, such as the almost complete convergence rates. Moreover, the asymptotic normality of the constructs was obtained under certain mild conditions. Lastly, the authors discussed how to apply the result to construct confidence intervals.

Semantic Correlation Transfer for Heterogeneous Domain Adaptation.

Heterogeneous domain adaptation (HDA) is expected to achieve effective knowledge transfer from a label-rich source domain to a heterogeneous target domain with scarce labeled data. Most prior HDA methods strive to align the cross-domain feature distributions by learning domain invariant representations without considering the intrinsic semantic correlations among categories, which inevitably results in the suboptimal adaptation performance across domains. Therefore, to address this issue, we propose a novel semantic correlation transfer (SCT) method for HDA, which not only matches the marginal and conditional distributions between domains to mitigate the large domain discrepancy, but also transfers the category correlation knowledge underlying the source domain to target by maximizing the pairwise class similarity across source and target. Technically, the domainwise and classwise centroids (prototypes) are first computed and aligned according to the feature embeddings. Then, based on the derived classwise prototypes, we leverage the cosine similarity of each two classes in both domains to transfer the supervised source semantic correlation knowledge among different categories to target effectively. As a result, the feature transferability and category discriminability can be simultaneously improved during the adaptation process. Comprehensive experiments and ablation studies on standard HDA tasks, such as text-to-image, image-to-image, and text-to-text, have demonstrated the superiority of our proposed SCT against several state-of-the-art HDA methods.

Utjecaj medija i vijesti o bolesti COVID-19 na burze i kripto tržišta

The entire world was significantly impacted by the COVID-19 pandemic,leading to confusion and turbulence in healthcare systems, as well as toextreme uncertainty in the financial realm. There was a profound distressin stock markets due to the enormously elevated levels of risk instigated bythe pandemic, which additionally inflated investors’ losses. The contagionwas supplemented by a surge of false stories that appear to be news (“fakenews”) that circulated throughout all media channels, thus additionally amplifyinguncertainty. This paper expands the previous literature by investigatingmedia impact on prominent indices of the stock and cryptocurrencymarkets. RavenPack Panic and Fake News indices were utilized to examinetheir influence on S&P 500 and crypto (Royalton CRIX) indices’ dailymovements by employing OLS and quantile regression. The results exhibitthat there are noteworthy dependencies over the conditional distribution,but they present only a small influence on observed indices. Fake news influencesthe cryptocurrencies’ daily movements in a bearish market, howeverthe effect is very weak. Furthermore, media-induced panic is significant inboth exceptionally bearish and bullish conditions considering S&P 500 dailyreturns, but is also exhibiting low impact.

Cross-Domain Social Rumor-Propagation Model Based on Transfer Learning.

Rumors in different topic domains have different text characteristics but similar emotional tendencies. To resolve the scarce-data problem in some rumor-topic domains, this study proposes a cross-domain rumor-propagation model, which is based on transfer learning. First, given the diversity and complexity of the rumor-propagation landscape, this study introduces a novel method, User-Retweet-Rumor2vec (URR2vec), which leverages the power of representation learning to uncover latent features within rumor topics. It also displays the forwarding relationship between users and rumors, user node information, and rumor-topic information in low-dimensional space. To capture the impact of human emotional cognition during rumor spreading, we also introduce a deep-learning model based on the natural language texts of rumor topics, which analyzes the sentiment in the text and uncovers the emotional correlations among users. Furthermore, a rumor-propagation prediction model based on the text-sentiment analysis-graph convolutional network (TSA-GCN) is proposed and pre-trained on existing rumor-topic data to ensure its prediction accuracy. Finally, considering the data sparsity at a rumor-topic outbreak, the trained propagation model is transferred to the rumor topic for prediction. Meanwhile, the rumor topic in different domains has different edges and conditional distribution, similar emotional characteristics, and network structure among the rumor topics. After fine-tuning the parameter and adding a domain adaptation layer in TSA-GCN, a domain adaptation model based on parameter and graph-structure migration is obtained.

Rejecting Unknown Gestures Based on Surface-Electromyography Using Variational Autoencoder.

The conventional surface electromyography (sEMG)-based gesture recognition systems exhibit impressive performance in controlled laboratory settings. As most systems are trained in a closed-set setting, the systems's performance may see significant deterioration when novel gestures are presented as imposter. In addition, the state-of-the-art generative and discriminative methods have achieved considerable performance on high-density sEMG signals. This can be seen as an unrealistic setting as the real-world muscle computer interface are mainly comprised of sparse multichannel sEMG signals. In this work, we propose a novel variational autoencoder based approach for open-set gesture recognition based on sparse multichannel sEMG signals. Using the predefined corresponding latent conditional distribution of known gestures, the conditional Gaussian distribution of each known gesture is learned. Those samples with low probability density are identified as unknown gestures. The sEMG signals of known gestures are classified using the Kullback-Leibler divergences between the predefined prior distributions and input samples. The proposed approach is evaluated using three benchmark sparse multichannel sEMG databases. The experimental results demonstrate that our approach outperforms the existing open-set sEMG-based gesture recognition approaches and achieves a better trade-off between classifying known gestures and rejecting unknown gestures.

Learning Many-to-Many Mapping for Unpaired Real-World Image Super-resolution and Downscaling.

Learning based single image super-resolution (SISR) for real-world images has been an active research topic yet a challenging task, due to the lack of paired low-resolution (LR) and high-resolution (HR) training images. Most of the existing unsupervised real-world SISR methods adopt a twostage training strategy by synthesizing realistic LR images from their HR counterparts first, then training the super-resolution (SR) models in a supervised manner. However, the training of image degradation and SR models in this strategy are separate, ignoring the inherent mutual dependency between downscaling and its inverse upscaling process. Additionally, the ill-posed nature of image degradation is not fully considered. In this paper, we propose an image downscaling and SR model dubbed as SDFlow, which simultaneously learns a bidirectional manyto- many mapping between real-world LR and HR images unsupervisedly. The main idea of SDFlow is to decouple image content and degradation information in the latent space, where content information distribution of LR and HR images is matched in a common latent space. Degradation information of the LR images and the high-frequency information of the HR images are fitted to an easy-to-sample conditional distribution. Experimental results on real-world image SR datasets indicate that SDFlow can generate diverse realistic LR and SR images both quantitatively and qualitatively.

Damage localisation using disparate damage states via domain adaptation

Abstract A significant challenge of structural health monitoring (SHM) is the lack of labeled data collected from damage states. Consequently, the collected data can be incomplete, making it difficult to undertake machine learning tasks, to detect or predict the full range of damage states a structure may experience. Transfer learning is a helpful solution, where data from (source) structures containing damage labels can be used to transfer knowledge to (target) structures, for which damage labels do not exist. Machine learning models are then developed that generalize to the target structure. In practical applications, it is unlikely that the source and the target structures contain the same damage states or experience the same environmental and operational conditions, which can significantly impact the collected data. This is the first study to explore the possibility of transfer learning for damage localisation in SHM when the damage states and the environmental variations in the source and target datasets are disparate. Specifically, using several domain adaptation methods, this article localizes severe damage states at a target structure, using labeled information from minor damage states at a source structure. By minimizing the distance between the marginal and conditional distributions between the source and the target structures, this article successfully localizes damage states of disparate severities, under varying environmental and operational conditions. The effect of partial and universal domain adaptation—where the number of damage states in the source and target datasets differ—is also explored in order to mimic realistic industrial applications of these methods.

Power enhancement in PV arrays under partial shaded conditions with different array configuration

Solar Photovoltaic systems are used for electrical power generation, and they provide an alternative source to non-renewable energy sources like coal, oil, natural gas and nuclear energy. Photovoltaic arrays used in PV systems may be subjected to partial shading conditions, thereby affecting power generation because of higher power mismatch losses. Due to an uneven distribution of irradiation condition, some of the bypass diodes turned on and affect the power generation in a photovoltaic array. The mismatch losses are due to the output from PV panels subjected to different irradiations because of non-uniform partial shading conditions. The power loss can be reduced by uniformly distributing the partially shaded condition over the entire PV array. In this work different shaped 4 × 4 array configuration is proposed to overcome the effect of partial shading condition, thereby providing lower mismatch losses. Simulations under different partial shading conditions are carried out using MATLAB Simulink, and the experimental setupis carried out for the proposed array configuration for 4 × 4 PV array and the results are discussed.

SiC Detector Thickness Optimization for Enhanced Response Variability

Neutron spectroscopy is a crucial point in several nuclear applications. Accurately measuring fast neutron energy distributions in high-flux conditions reveals a significant technology gap, hindering the acquisition of precise energy fluence distributions. This project investigates the potential of machine learning to bridge this gap, focusing on neutron energies from 100 keV to 20 MeV and fluence rates from 1010 n/cm2s to 1012 n/cm2s using solid detectors such as Silicon Carbide (SiC) and Chemical Vapor Deposition (CVD) diamonds. This paper details the simulation design phase of our project, emphasizing the exploration of optimal SiC solid detector thickness to introduce crucial variability for machine learning training.

System reliability calculation based on the run-time analysis of ladder program

Programmable logic controller (PLC) system, a typical member in the embedded family, is now widely applied in industry. For safety critical PLC systems, reliability is of top significance. However, due to subcomponents’ temporal correlations caused by the run-time execution of embedded ladder programs, the complexity of reliability analysis is greatly increased. In this paper, we propose a novel probabilistic model to analyze reliability of PLC systems, called run-time reliability model (RRM). RRM is automatically constructed based on the structure and run-time execution of the embedded ladder program. Moreover, it is also a dynamic bayesian network (DBN) capturing full dependencies in a PLC system. Then, according to execution semantics of RRM nodes, we present customized conditional probability distribution (CPD) tables to calculate final reliability of the system, with failure probability of every referenced component as refinement. The strength of this model is that not only does it explicitly specify the correlations between run-time execution of embedded software and system components, but also it serves as a computational mechanism for probabilistic inference. Besides, the proposed approach is superior to previous works in both accuracy and efficiency. Compared to monte carlo based simulation, the average error rate of reliability values inferred from RRM model is small.

Foreign Aid and Economic Growth in the Sub-Saharan African Countries

ABSTRACT: Official Development Assistance (ODA) remains an important tool for nurturing economic growth in Sub-Saharan African (SSA) countries. This is evidenced by numerous studies that have investigated the ODA-growth nexus in SSA region. However the existing studies on the relationship between ODA and economic growth is subject to identification issues. More specifically, the issue of distributional heterogeneity has not been given the attention it deserves in this field. In other words, the issue of whether ODA-growth nexus differ among developing nations with different economic growth levels has not been meticulously explored. This study aims to examine the heterogeneous impact of ODA on economic growth across 24 SSA countries over a 38-year period. To achieve this, an attempt is made in this study to investigate how the effect of ODA varies along the conditional economic growth distribution by employing the Moment of Moments Quantile Regression (MM-QR) approach, an approach that is able to capture the diverse effects of ODA across different levels of growth distribution. Moreover, this study explores the role of social infrastructure and institutional quality in shaping this relationship. The results suggest that ODA has a positive impact on economic growth in the SSA region, with a larger positive impact in countries with high levels of economic growth. This finding is key as it underlines the important idea that though ODA positively influence growth, it doesn’t homogeneously affect all nations; but instead, it remarkably enhance it in areas with relatively robust and healthy economic conditions. The study also finds a positive and significant relationship between social infrastructures and institutions quality and economic growth, particularly in the 50th, 75th, and 95th quantiles, thereby highlighting the fact that well-developed social infrastructures and high-quality institutions play a pivotal role in nurturing economic progress, particularly at the mid to higher percentiles of economic development. The inclusion of institutions quality and interaction terms in the model influences the effect of aid on economic growth, with ODA being effective in countries located within the 25th and 50th quantiles. The findings suggest that aid can be strategically used to stimulate economic growth in SSA countries, particularly low-income countries.

Unsupervised Joint Domain Adaptation for Decoding Brain Cognitive States From tfMRI Images.

Recent advances in large model and neuroscience have enabled exploration of the mechanism of brain activity by using neuroimaging data. Brain decoding is one of the most promising researches to further understand the human cognitive function. However, current methods excessively depends on high-quality labeled data, which brings enormous expense of collection and annotation of neural images by experts. Besides, the performance of cross-individual decoding suffers from inconsistency in data distribution caused by individual variation and different collection equipments. To address mentioned above issues, a Join Domain Adapative Decoding (JDAD) framework is proposed for unsupervised decoding specific brain cognitive state related to behavioral task. Based on the volumetric feature extraction from task-based functional Magnetic Resonance Imaging (tfMRI) data, a novel objective loss function is designed by the combination of joint distribution regularizer, which aims to restrict the distance of both the conditional and marginal probability distribution of labeled and unlabeled samples. Experimental results on the public Human Connectome Project (HCP) S1200 dataset show that JDAD achieves superior performance than other prevalent methods, especially for fine-grained task with 11.5%-21.6% improvements of decoding accuracy. The learned 3D features are visualized by Grad-CAM to build a combination with brain functional regions, which provides a novel path to learn the function of brain cortex regions related to specific cognitive task in group level.

DECISION THEORETIC BOOTSTRAPPING

The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution and (2) the testing data distribution. Although these two distributions are identical and identifiable when the data set is infinite, they are imperfectly known when the data are finite (and possibly corrupted), and this uncertainty must be taken into account for robust uncertainty quantification (UQ). An important case is when the test distribution is coming from a modal or localized area of the finite sample distribution. We present a general decision theoretic bootstrapping solution to this problem: (1) partition the available data into a training subset and a UQ subset; (2) take m subsampled subsets of the training set and train m models; (3) partition the UQ set into n sorted subsets and take a random fraction of them to define <i>n</i> corresponding empirical distributions μ<sub>j</sub>; (4) consider the adversarial game where Player I selects a model i ∈ {1,.....,m}, Player II selects the UQ distribution μ<sub>j</sub>, and Player I receives a loss defined by evaluating the model <i>i</i> against data points sampled from μ<sub>j</sub>; (5) identify optimal mixed strategies (probability distributions over models and UQ distributions) for both players. These randomized optimal mixed strategies provide optimal model mixtures, and UQ estimates given the adversarial uncertainty of the training and testing distributions represented by the game. The proposed approach provides (1) some degree of robustness to in-sample distribution localization/concentration and (2) conditional probability distributions on the output space forming aleatory representations of the uncertainty on the output as a function of the input variable.

Nonparametric Bayesian modeling for non-normal data through a transformation

<abstract><p>In many applications, modeling based on a normal kernel is preferred because not only does the normal kernel belong to the family of stable distributions, but also it is easy to satisfy the stationary condition in the stochastic process. However, the characteristic of the data, such as count or proportion, is a major obstacle to complete modeling based on a normal distribution. To solve a limited boundary or non-normal distribution problem, we provided a novel transformation method and proposed a nonparametric Bayesian approach based on a normal kernel of the transformed variable. In particular, the provided transformation transforms any probability space into a real space and is free from the constraints of the previous transformation, such as skewness, presence of power, and bounded domains. Another advantage was that it was possible to use the Dirichlet process mixture model with full conditional posterior distributions for all parameters, leading to a fast convergence rate in the Markov chain Monte Carlo. The proposed methodology was illustrated with simulated datasets and two real datasets with non-normal distribution problems. In addition, to demonstrate the superiority of the proposed methodology, the comparison with the transformed Bernstein polynomial model was made in the real data analysis.</p></abstract>

Modelo linear misto para a previsão de taxas de infiltração em pavimentos de concreto permeáveis urbanos em parques densamente arborizados

Abstract Clogging of porous concrete pavements is understood as a performance pathology within this peculiar concrete component. Albeit the clogging performance of porous concrete pavements is a sensitive topic in technical literature, most studies refer to laboratory investigations on concrete samples using different kinds of apparatus for the simulation of loss of permeability due to debris insertion on porous interstices. However, infiltration rate measurements are the basis for defining maintenance needs in actual pavements and shall be carried out periodically to measure and endorse infiltration rate adequacy as the kern of a clogging management protocol. This study dealt with a field experiment in a pervious concrete sidewalk surrounded by a wooded garden with tropical native and a variety of exotic trees. Over four years, eleven monitoring measurements were carried out using the ASTM C1701 infiltration ring test. The main contribution of this paper is a proposition of a mixed linear prediction model considering conditioned exponential distribution and a random normal intercept for the infiltration rate. From residual analysis and diagnosis plots, it can be seen that the proposed model presents a goodness of fit, allowing anticipation of infiltration rates reduction due to clogging by dense organic matter. Minimum infiltration rate is taken as 0.1 cm/s and such condition was achieved in a couple of months, awakening consciously to consider three to four intensive cleaning maintenance per year in dense wooded areas like public parks.

Deep Drug Synergy Prediction Network Using Modified Triangular Mutation-Based Differential Evolution.

Drug combination therapy is crucial in cancer treatment, but accurately predicting drug synergy remains a challenge due to the complexity of drug combinations. Machine learning and deep learning models have shown promise in drug combination prediction, but they suffer from issues such as gradient vanishing, overfitting, and parameter tuning. To address these problems, the deep drug synergy prediction network, named as EDNet is proposed that leverages a modified triangular mutation-based differential evolution algorithm. This algorithm evolves the initial connection weights and architecture-related attributes of the deep bidirectional mixture density network, improving its performance and addressing the aforementioned issues. EDNet automatically extracts relevant features and provides conditional probability distributions of output attributes. The performance of EDNet is evaluated over two well-known drug synergy datasets, NCI-ALMANAC and deep-synergy. The results demonstrate that EDNet outperforms the competing models. EDNet facilitates efficient drug interactions, enhancing the overall effectiveness of drug combinations for improved cancer treatment outcomes.

Ultra-high-dimensional feature screening of binary categorical response data based on Jensen-Shannon divergence

<abstract><p>Currently, most of the ultra-high-dimensional feature screening methods for categorical data are based on the correlation between covariates and response variables, using some statistics as the screening index to screen important covariates. Thus, with the increasing number of data types and model availability limitations, there may be a potential problem with the existence of a class of unimportant covariates that are also highly correlated with the response variable due to their high correlation with the other covariates. To address this issue, in this paper, we establish a model-free feature screening procedure for binary categorical response variables from the perspective of the contribution of features to classification. The idea is to introduce the Jensen-Shannon divergence to measure the difference between the conditional probability distributions of the covariates when the response variables take on different values. The larger the value of the Jensen-Shannon divergence, the stronger the covariate's contribution to the classification of the response variable, and the more important the covariate is. We propose two kinds of model-free ultra-high-dimensional feature screening methods for binary response data. Meanwhile, the methods are suitable for continuous or categorical covariates. When the numbers of covariate categories are the same, the feature screening is based on traditional Jensen-Shannon divergence. When the numbers of covariate categories are different, the Jensen-Shannon divergence is adjusted using the logarithmic factor of the number of categories. We theoretically prove that the proposed methods have sure screening and ranking consistency properties, and through simulations and real data analysis, we demonstrate that, in feature screening, the approaches proposed in this paper have the advantages of effectiveness, stability, and less computing time compared with an existing method.</p></abstract>

New Bounds on the Accuracy of Majority Voting for Multiclass Classification.

Majority voting is a simple mathematical function that returns the most frequently occurring value within a given set. As a popular decision fusion technique (DFT), the majority voting function (MVF) finds applications in resolving conflicts, where several independent voters report their opinions on a classification problem. Despite its importance and its various applications in ensemble learning, data crowdsourcing, remote sensing, and data oracles for blockchains, the accuracy of the MVF for the general multiclass classification problem has remained unknown. In this article, we derive a new upper bound on the accuracy of the MVF for the multiclass classification problem. More specifically, we show that under certain conditions, the error rate of the MVF exponentially decays toward 0 as the number of independent voters increases. Conversely, the error rate of the MVF exponentially grows with the number of voters if these conditions are not met. We first explore the problem for voters with independent and identically distributed (i.i.d.) outputs, where we assume that, given the true classification of the data point, every voter follows the same conditional probability distribution of voting for different classes. Next, we extend our results to encompass independent but nonidentically distributed votes. Using the derived results, we then provide a discussion on the accuracy of the truth discovery algorithms. We show that in the best-case scenarios, truth discovery algorithms operate as an amplified MVF and thereby achieve a small error rate only when the MVF achieves a small error rate too, and vice versa, achieve a large error rate when the MVF also achieves a large error rate. However, in the worst case scenario, the truth discovery algorithms may exhibit a significantly higher error rate than the MVF. Finally, we confirm our theoretical results using numerical simulations.

Probability distributions for dynamic and extreme responses of linear elastic structures under quasi-stationary harmonizable loads

The non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to ambiguous structural responses. Quasi-stationary harmonizable processes with non-negative Wigner-Ville spectra are suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, random environmental loads are modeled as quasi-stationary harmonizable processes. The Loève spectrum of a harmonizable load process contains several random physical parameters. An explicit approach to calculate the probability distributions for the dynamic and extreme responses of a linear elastic structure subjected to a quasi-stationary harmonizable load is proposed. Conditioned on the specific values of the load spectral parameters, the harmonizable load process is assumed to be Gaussian. The conditional joint probability density function (PDF) of structural dynamic responses at any finite time instants and the conditional cumulative distribution function (CDF) of the structural extreme response are provided. By multiplying these two conditional probability distributions with the joint PDF of the load spectral parameters, and then integrating these two products over the parameter sample space, the joint PDF of structural dynamic responses at any finite time instants and the CDF of the structural extreme response can be calculated. The efficacy of the proposed approach is numerically validated using two linear elastic systems, which are subjected to non-stationary and non-Gaussian wind and seismic loads, respectively. The merit of the harmonizable load process model is highlighted through a comparative analysis with the EPSD load model.