Mixture Sampling Research Articles

An innovative mixture sampling strategy with uniform design: Application to global sensitivity analysis of mixture toxicity

Global sensitivity analysis combined with quantitative high-throughput screening (GSA-qHTS) uses random starting points of the trajectories in mixture design, which may lead to potential contingency and a lack of representativeness. Moreover, a scenario in which all factor levels were at stimulatory effects was not considered, thereby hindering a comprehensive understanding of GSA-qHTS. Accordingly, this study innovatively introduced an optimised experimental design, uniform design (UD), to generate non-random and representative sample points with smaller uniformity deviation as starting points of multiple trajectories. By combining UD with the previously optimised one-factor-at-a-time (OAT) method, a novel mixture design method was developed (UD-OAT). The single toxicity tests showed that three pyridinium and five imidazolium ionic liquids (ILs) exerted stimulatory effects on Vibrio qinghaiensis sp.-Q67; thus, four stimulatory effective concentrations of each IL were selected as factor levels. The UD-OAT generated 108 mixture samples with equal frequency and without repetition. High-throughput microplate toxicity analysis revealed that all 108 mixtures exhibited inhibitory effects. Among these, type B mixtures exhibited increasing toxicities that subsequently decreased, unlike type C mixtures, which consistently increased over time. GSA successfully identified three of the eight ILs as important factors influencing the toxicities of the mixtures. When individual ILs produced stimulatory effects, mixtures containing two to three ILs exhibited either stimulatory effects or none. In contrast, mixtures containing five to eight ILs exhibited inhibitory effects, while those containing four ILs showed a transition from stimulatory to inhibitory effects. This study provides a novel mixture design method for studying mixture toxicity and fills the application gap of GSA-qHTS. The phenomenon of individuals being beneficial while mixtures can be harmful challenges traditional mixture risk assessments.

Nonbonded Force Field Parameters from MBIS Partitioning of the Molecular Electron Density Improve Binding Affinity Predictions of the T4-Lysozyme Double Mutant.

The use of computer simulation for binding affinity prediction is growing in drug discovery. However, its wider use is constrained by the accuracy of the free energy calculations. The key sources of error are the force fields used to depict molecular interactions and insufficient sampling of the configurational space. To improve the quality of the force field, we developed a Python-based computational workflow. The workflow described here uses the minimal basis iterative stockholder (MBIS) method to determine atomic charges and Lennard-Jones parameters from the polarized molecular density. This is done by performing electronic structure calculations on various configurations of the ligand when it is both bound and unbound. In addition, we validated a simulation procedure that accounts for the protein and ligand degrees of freedom to precisely calculate binding free energies. This was achieved by comparing the self-adjusted mixture sampling and nonequilibrium thermodynamic integration methods using various protein and ligand conformations. The accuracy of predicting binding affinity is improved by using MBIS-derived force field parameters and a validated simulation procedure. This improvement surpasses the chemical precision for the eight aromatic ligands, reaching a root-mean-square error of 0.7 kcal/mol.

Rapid: Zero-shot Domain Adaptation for Code Search with Pre-trained Models

Code search, which refers to the process of identifying the most relevant code snippets for a given natural language query, plays a crucial role in software maintenance. However, current approaches heavily rely on labeled data for training, which results in performance decreases when confronted with cross-domain scenarios including domain-specific or project-specific situations. This decline can be attributed to their limited ability to effectively capture the semantics associated with such scenarios. To tackle the aforementioned problem, we propose a ze R o-shot dom A in ada P tion with pre-tra I ned mo D els framework for code search named RAPID. The framework first generates synthetic data by pseudo labeling, then trains the CodeBERT with sampled synthetic data. To avoid the influence of noisy synthetic data and enhance the model performance, we propose a mixture sampling strategy to obtain hard negative samples during training. Specifically, the mixture sampling strategy considers both relevancy and diversity to select the data that are hard to be distinguished by the models. To validate the effectiveness of our approach in zero-shot settings, we conduct extensive experiments and find that RAPID outperforms the CoCoSoDa and UniXcoder model by an average of 15.7% and 10%, respectively, as measured by the MRR metric. When trained on full data, our approach results in an average improvement of 7.5% under the MRR metric using CodeBERT. We observe that as the model’s performance in zero-shot tasks improves, the impact of hard negatives diminishes. Our observation also indicates that fine-tuning CodeT5 for generating pseudo labels can enhance the performance of the code search model, and using only 100-shot samples can yield comparable results to the supervised baseline. Furthermore, we evaluate the effectiveness of RAPID in real-world code search tasks in three GitHub projects through both human and automated assessments. Our findings reveal RAPID exhibits superior performance, e.g., an average improvement of 18% under the MRR metric over the top-performing model.

A novel mixture sampling strategy combining latin hypercube sampling with optimized one factor at a time method: A case study on mixtures of antibiotics and pesticides

Global sensitivity analysis in conjunction with quantitative high-throughput screening presents a novel technique for identifying the key components that induce the toxicities of mixtures. However, the mixtures currently designed with this method suffer from unequal frequency sampling, repeated mixtures, and only odd factor levels being considered. Accordingly, we use latin hypercube sampling to generate the starting points of the trajectories to achieve equal frequency sampling and non-repeated mixtures, as well as apply different one factor at a time methods for factors with odd and even levels to achieve suitability for factors with both odd and even levels. This method is called LHS-OAT. LHS-OAT was successfully applied to design 110 equal-frequency and non-repeated mixtures consisting of six antibiotics and four pesticides. It was found that four factors, roxithromycin (A5), tetracycline (A6), dichlorvos (P1), and demeton-S (P3), induce the toxicities of mixtures, and A5 and P1 in the Shaying River Basin have risk quotients ≥ 1. Additionally, we developed the toxicity deviation ratio to correct the risk quotients of interacting mixtures for effective risk assessments. This study provides a rational and effective method for mixture design that accurately identifies the important factors that induce the toxicities of mixtures.

Revisiting controlled mixture sampling for rendering applications

Monte Carlo rendering makes heavy use of mixture sampling and multiple importance sampling (MIS). Previous work has shown that control variates can be used to make such mixtures more efficient and more robust. However, the existing approaches failed to yield practical applications, chiefly because their underlying theory is based on the unrealistic assumption that a single mixture is optimized for a single integral. This is in stark contrast with rendering reality, where millions of integrals are computed---one per pixel---and each is infinitely recursive. We adapt and extend the theory introduced by previous work to tackle the challenges of real-world rendering applications. We achieve robust mixture sampling and (approximately) optimal MIS weighting for common applications such as light selection, BSDF sampling, and path guiding.

Using image-based machine learning and numerical simulation to predict pesticide inline mixing uniformity.

Accurate pesticide inline mixing uniformity (PIMU) evaluation for direct nozzle injection systems (DNIS) helps evaluate system performance and develop efficient inline mixers. Based on supervised machine learning (ML), inline mixing images and computational fluid dynamics (CFD) simulations are directly associated for realizing intelligent PIMU predictions. Image sets can be reduced to less than 3% of the data size at the same time as retaining 98% of information using principal component analysis (PCA). The CFD results, as referenced values for ML, were justified by mixture sampling experiments. Enhanced images for the long-mixing tube effectively trained models including generalized linear model (GLM), support vector regression (SVR), BP-neural network (NNW), and classification and regression trees (CART). By testing the re-collected images, the verification accuracy of GLM was less than 95% and it failed to recognize uniformity differences under varying working conditions, whereas NNW, CART and SVR realized it with an accuracy for NNW and CART higher than 97% and for SVR slightly lower than 97%. By testing images of the jet mixer, the prediction accuracy compared with the CFD results of NNW and CART was also higher than 97%, although that for SVR was relatively lower, and insignificant declines in accuracy were observed on comparing the results with mixture sampling experiments. PCA facilitates evaluations of CFD-referenced PIMU using image-based ML. Models trained by enhanced image sets of the long-mixing tube have satisfactory performance. NNW and CART performed slightly better than SVR, and they can be used as tools to improve the rationality when evaluating PIMU in DNIS. © 2022 Society of Chemical Industry.

An efficient mixture sampling model for gaussian estimation of distribution algorithm

Estimation of distribution algorithm (EDA) is a stochastic optimization algorithm based on probability distribution model and has been widely applied in global optimization. However, the random sampling of Gaussian EDA (GEDA) usually suffers from the poor diversity and the premature convergence, which severely limits its performance. This paper analyzes the shortcomings of the random sampling and develops an efficient mixture sampling model (EMSM). EMSM can explore more promising regions and utilize the unsuccessful mutation vectors, which achieves a good tradeoff between the diversity and the convergence. Moreover, the feasibility analysis of EMSM is studied. A new GEDA variant named EMSM-EDA is developed, which combines EMSM with enhancing Gaussian estimation of distribution algorithm (EDA2). The experimental results on IEEE CEC2013 and IEEE CEC2014 test suites demonstrate that EMSM-EDA is efficient and competitive.

Customer Churn in Retail E-Commerce Business: Spatial and Machine Learning Approach

This study is a comprehensive and modern approach to predict customer churn in the example of an e-commerce retail store operating in Brazil. Our approach consists of three stages in which we combine and use three different datasets: numerical data on orders, textual after-purchase reviews and socio-geo-demographic data from the census. At the pre-processing stage, we find topics from text reviews using Latent Dirichlet Allocation, Dirichlet Multinomial Mixture and Gibbs sampling. In the spatial analysis, we apply DBSCAN to get rural/urban locations and analyse neighbourhoods of customers located with zip codes. At the modelling stage, we apply machine learning extreme gradient boosting and logistic regression. The quality of models is verified with area-under-curve and lift metrics. Explainable artificial intelligence represented with a permutation-based variable importance and a partial dependence profile help to discover the determinants of churn. We show that customers’ propensity to churn depends on: (i) payment value for the first order, number of items bought and shipping cost; (ii) categories of the products bought; (iii) demographic environment of the customer; and (iv) customer location. At the same time, customers’ propensity to churn is not influenced by: (i) population density in the customer’s area and division into rural and urban areas; (ii) quantitative review of the first purchase; and (iii) qualitative review summarised as a topic.

Do interest rate differentials drive the volatility of exchange rates? Evidence from an extended stochastic volatility model

We study the link between the volatility of exchange rates and interest rate differentials (IRD), motivated by the importance of currency carry trade activities in exchange rate dynamics. We examine this link by means of an extended stochastic volatility model, for which we detail an efficient estimation strategy based on Gaussian mixture sampling and a linearization of the volatility process. We apply this approach to six currency pairs over the period from January 1999 to December 2017. Our results suggest that changes in IRD affect volatility differently for low and high-interest-rate currencies. The volatility reacts strongly and positively to increases in the low interest rate, an effect consistent with the unwinding of carry trade positions. In contrast, the response to a raise in the high interest rate is negative and substantially smaller. In general, we find that the informational content of the interest rate differentials regarding the volatility of exchange rate is greater during and after the global financial crisis, compared to the pre-crisis period. • We study the link between exchange rate volatility and interest rate differentials. • This analysis is conducted by means of an extended stochastic volatility model. • We propose an efficient Bayesian estimation strategy. • A narrowing of absolute rate differentials implies an increase in volatility. • This result suggests the existence of a carry trade channel for developed economies.

Non-parametric construction of site-specific non-Gaussian multivariate joint probability distribution from sparse measurements

Construction of a joint probability distribution for correlated geotechnical properties is often needed in geotechnical reliability-based analysis and design. Geotechnical properties vary across sites and follow site-specific and non-Gaussian probability distribution, because of different geological processes that soils and rocks in different sites have undergone. In addition, site-specific measurements on geotechnical properties are usually sparse and correlated in geotechnical practice, leading to the difficulty in estimation of meaningful joint probability distribution when using conventional parametric statistical methods. To address this issue, this paper develops a non-parametric and data-driven approach for characterizing the site-specific non-Gaussian multivariate joint probability distribution without pre-selection of the marginal probability distribution type. Two key components for constructing a multivariate joint probability distribution (i.e., marginal probability distribution for each variable and correlation matrix for all variables) are estimated separately using Bayesian Gaussian mixture and Bayesian compressive sampling (BCS) and Karhunen-Loève (KL) expansion. The proposed method is illustrated using both simulated and real data in geotechnical site investigation. The results show that the proposed method performs well for both examples. The proposed method does not model spatial variability explicitly but is based on the assumption of independent measurement data along depth, and thus measurement records are required to be sufficiently spaced apart in depth (e.g., more than 1 scale of fluctuation) to satisfy this assumption.

Consensus Monte Carlo for Random Subsets Using Shared Anchors

We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records. Supplementary materials for this article are available online.

Optimal multiple importance sampling

Multiple Importance Sampling (MIS) is a key technique for achieving robustness of Monte Carlo estimators in computer graphics and other fields. We derive optimal weighting functions for MIS that provably minimize the variance of an MIS estimator, given a set of sampling techniques. We show that the resulting variance reduction over the balance heuristic can be higher than predicted by the variance bounds derived by Veach and Guibas, who assumed only non-negative weights in their proof. We theoretically analyze the variance of the optimal MIS weights and show the relation to the variance of the balance heuristic. Furthermore, we establish a connection between the new weighting functions and control variates as previously applied to mixture sampling. We apply the new optimal weights to integration problems in light transport and show that they allow for new design considerations when choosing the appropriate sampling techniques for a given integration problem.

Tracing sediment sources in a mountainous forest catchment under road construction in northern Iran: comparison of Bayesian and frequentist approaches

Development and land use change lead to accelerated soil erosion as a serious environmental problem in river catchments in Iran. Reliable information about the sources of sediment in catchments is therefore necessary to design effective control strategies. This study used a composite sediment source tracing procedure to determine the importance of forest road cuttings as a sediment source in a mountainous catchment located in northern Iran. A fallout radionuclide (137Cs) and 12 geochemical tracers (Ca, Cu, Fe, K, Mg, Mn, Na, Ni, OC, Pb, Sr and TN) were used to determine the relative contributions of three sediment source types (hillslopes, road cuttings and channel banks) to both suspended and bed sediment samples. Two mixing models based on different mathematical concepts were used to apportion the sediment sources: the mixture sampling importance resampling Bayesian model which incorporates the mass-balance matrix and a distribution model using normal and summed probability of normal distributions. The results of both mixing models indicated that sub-soil erosion from road cuttings and channel banks dominated the sources of river bed and suspended sediment samples, respectively. These results therefore highlight that conservation that works in the study area to remedy the sediment problem should initially focus on stabilisation and rehabilitation of road cuttings and channel banks. This successful application of a composite (radionuclide and geochemical) tracing technique for discriminating source end members characterised by different erosion processes underscores the importance of sub-soil erosion in this case study.

Learning Trans-Dimensional Random Fields with Applications to Language Modeling.

To describe trans-dimensional observations in sample spaces of different dimensions, we propose a probabilistic model, called the trans-dimensional random field (TRF) by explicitly mixing a collection of random fields. In the framework of stochastic approximation (SA), we develop an effective training algorithm, called augmented SA, which jointly estimates the model parameters and normalizing constants while using trans-dimensional mixture sampling to generate observations of different dimensions. Furthermore, we introduce several statistical and computational techniques to improve the convergence of the training algorithm and reduce computational cost, which together enable us to successfully train TRF models on large datasets. The new model and training algorithm are thoroughly evaluated in a number of experiments. The word morphology experiment provides a benchmark test to study the convergence of the training algorithm and to compare with other algorithms, because log-likelihoods and gradients can be exactly calculated in this experiment. For language modeling, our experiments demonstrate the superiority of the TRF approach in being computationally more efficient in computing data probabilities by avoiding local normalization and being able to flexibly integrate a richer set of features, when compared with n-gram models and neural network models.

Optimally Adjusted Mixture Sampling and Locally Weighted Histogram Analysis

ABSTRACTConsider the two problems of simulating observations and estimating expectations and normalizing constants for multiple distributions. First, we present a self-adjusted mixture sampling method, which accommodates both adaptive serial tempering and a generalized Wang–Landau algorithm. The set of distributions are combined into a labeled mixture, with the mixture weights depending on the initial estimates of log normalizing constants (or free energies). Then, observations are generated by Markov transitions, and free energy estimates are adjusted online by stochastic approximation. We propose two stochastic approximation schemes by Rao–Blackwellization of the scheme commonly used, and derive the optimal choice of a gain matrix, resulting in the minimum asymptotic variance for free energy estimation, in a simple and feasible form. Second, we develop an offline method, locally weighted histogram analysis, for estimating free energies and expectations, using all the simulated data from multiple distributions by either self-adjusted mixture sampling or other sampling algorithms. This method can be computationally much faster, with little sacrifice of statistical efficiency, than a global method currently used, especially when a large number of distributions are involved. We provide both theoretical results and numerical studies to demonstrate the advantages of the proposed methods.

Sparse Bayesian modelling of underreported count data

We consider Bayesian inference for regression models of count data subject to underreporting. For the data generating process of counts as well as the fallible reporting process a joint model is specified, where the outcomes in both processes are related to a set of potential covariates. Identification of the joint model is achieved by additional information provided through validation data and incorporation of variable selection. For posterior inference we propose a convenient Markov chain Monte Carlo (MCMC) sampling scheme which relies on data augmentation and auxiliary mixture sampling techniques for this two-part model. Performance of the method is illustrated for simulated data and applied to analyse real data, collected to estimate risk of cervical cancer death.

Identifying PCB Contaminated Transformers Through Active Learning

Exposure to polychlorinated biphenyals (PCBs) is hazardous to human health. The United Nations Environment Programme has decreed that nations, including Canada and USA, must eliminate PCB contaminated equipment such as transformers by 2025. To determine the PCB status of a transformer with absolute certainty, the oil mixture of the transformer must be sampled because transformers labeled as non-PCB could be cross-contaminated. Since sealed oil mixture sampling is costly, for the first time, we apply an iterative machine learning technique called active learning to classify PCB contaminated transformers while minimizing a cost metric that integrates the classification error cost and the sampling cost. We propose a dynamic sampling method to address two key issues in active learning: the sampling size per iteration and the stopping criterion of the sampling process. The proposed algorithm is evaluated using the real-world datasets from BC Hydro in Canada.

Evaluating Laboratory Compaction of Asphalt Mixtures Using the Shear Box Compactor

Abstract Laboratory produced test specimens are usually obtained with devices like Marshall compaction, gyratory compaction, or roller compaction. However, with these methods it is difficult to control the sample-to-sample variation of the final density of the test specimens, which can strongly influence the results of performance testing. It is very important to have a repeatable and efficient production method of test specimens available in the laboratory. The shear box compactor was recently developed to simulate field compaction with a constant compressive force and a cyclic shear force with constant maximum shear angle applied to the asphalt mixture. The shear box compactor produces asphalt blocks with a size of 450 mm in length, 150 mm in width, and 145–185 mm in height. Test specimens like beams or cylinders can be obtained from the block for laboratory performance testing. In this paper, the compaction results with the shear box compactor are reported for asphalt mixtures with different gradations and binder types. Asphalt specimens with different mixture compositions, shapes, sizes, and sampling positions were investigated by volumetric properties. Finite element modeling was introduced to obtain more understanding of the compacting process of the shear box compactor. The results indicate that the decreasing of voids content of asphalt mixtures during compaction process is dependent on the gradation than the binder type. The asphalt mixture specimens obtained from the same asphalt mixture block has a variation in voids content of less than 1 %. Test specimens obtained from the upper part of the asphalt block are more compacted than specimens from the lower part. And the specimens obtained close to the side of the block are less compacted due to lack of shear stress. As a result, the shear box compactor provides a reliable means of sample preparation, making it very suitable for producing specimens with constant volumetric properties.

GREG estimation and probabilistic editing

The purpose of editing is to correct erroneous entries in the dataset and assure the quality of data. It takes a lot of resources to correct all errors, so editing procedures where only a subset of errors to be corrected are sought after. Correcting only a subset of all errors will influence the final estimates, and tools evaluating the properties of the estimates like bias and variance need to be available. This paper introduces a probabilistic editing procedure where the responses are selected for editing through Poisson Mixture (PoMix) sampling and a bias adjusted GREG estimator is used for estimation. An expression for the variance of the bias adjusted GREG estimator is derived, and variance estimator is proposed. The effectiveness of the proposed editing procedure and the GREG estimator is illustrated using empirical data from Statistics Sweden.

Combining counts and incidence data: an efficient approach for estimating the log-normal species abundance distribution and diversity indices

Obtaining accurate estimates of diversity indices is difficult because the number of species encountered in a sample increases with sampling intensity. We introduce a novel method that requires that the presence of species in a sample to be assessed while the counts of the number of individuals per species are only required for just a small part of the sample. To account for species included as incidence data in the species abundance distribution, we modify the likelihood function of the classical Poisson log-normal distribution. Using simulated community assemblages, we contrast diversity estimates based on a community sample, a subsample randomly extracted from the community sample, and a mixture sample where incidence data are added to a subsample. We show that the mixture sampling approach provides more accurate estimates than the subsample and at little extra cost. Diversity indices estimated from a freshwater zooplankton community sampled using the mixture approach show the same pattern of results as the simulation study. Our method efficiently increases the accuracy of diversity estimates and comprehension of the left tail of the species abundance distribution. We show how to choose the scale of sample size needed for a compromise between information gained, accuracy of the estimates and cost expended when assessing biological diversity. The sample size estimates are obtained from key community characteristics, such as the expected number of species in the community, the expected number of individuals in a sample and the evenness of the community.