Multinomial Sampling Research Articles

Frequentist Prediction Sets for Species Abundance using Indirect Information

Abstract Citizen science databases that consist of volunteer-led sampling efforts of species communities are relied on as essential sources of data in ecology. Summarising such data across counties with frequentist-valid prediction sets for each county provides an interpretable comparison across counties of varying size or composition. As citizen science data often feature unequal sampling efforts across a spatial domain, prediction sets constructed with indirect methods that share information across counties may be used to improve precision. In this article, we present a nonparametric framework to obtain precise prediction sets for a multinomial random sample based on indirect information that maintain frequentist coverage guarantees for each county. We detail a simple algorithm to obtain prediction sets for each county using indirect information where the computation time does not depend on the sample size and scales nicely with the number of species considered. The indirect information may be estimated by a proposed empirical Bayes procedure based on information from auxiliary data. Our approach makes inference for under-sampled counties more precise, while maintaining area-specific frequentist validity for each county. Our method is used to provide a useful description of avian species abundance in North Carolina, USA based on citizen science data from the eBird database.

The real-time dynamic liquid level calculation method of the sucker rod well based on multi-view features fusion

In the production of the sucker rod well, the dynamic liquid level is important for the production efficiency and safety in the lifting process. It is influenced by multi-source data which need to be combined for the dynamic liquid level real-time calculation. In this paper, the multi-source data are regarded as the different views including the load of the sucker rod and liquid in the wellbore, the image of the dynamometer card and production dynamics parameters. These views can be fused by the multi-branch neural network with special fusion layer. With this method, the features of different views can be extracted by considering the difference of the modality and physical meaning between them. Then, the extraction results which are selected by multinomial sampling can be the input of the fusion layer. During the fusion process, the availability under different views determines whether the views are fused in the fusion layer or not. In this way, not only the correlation between the views can be considered, but also the missing data can be processed automatically. The results have shown that the load and production features fusion (the method proposed in this paper) performs best with the lowest mean absolute error (MAE) 39.63 m, followed by the features concatenation with MAE 42.47 m. They both performed better than only a single view and the lower MAE of the features fusion indicates that its generalization ability is stronger. In contrast, the image feature as a single view contributes little to the accuracy improvement after fused with other views with the highest MAE. When there is data missing in some view, compared with the features concatenation, the multi-view features fusion will not result in the unavailability of a large number of samples. When the missing rate is 10%, 30%, 50% and 80%, the method proposed in this paper can reduce MAE by 5.8, 7, 9.3 and 20.3 m respectively. In general, the multi-view features fusion method proposed in this paper can improve the accuracy obviously and process the missing data effectively, which helps provide technical support for real-time monitoring of the dynamic liquid level in oil fields.

MS-GDA: Improving Heterogeneous Recipe Representation via Multinomial Sampling Graph Data Augmentation

We study the problem of classifying different cooking styles, based on the recipe. The difficulty is that the same food ingredients, seasoning, and the very similar instructions result in different flavors, with different cooking styles. Existing methods have limitations: they mainly focus on homogeneous data (e.g., instruction or image), ignoring heterogeneous data (e.g., flavor compound or ingredient), which certainly hurts the classification performance. This is because collecting enough available heterogeneous data of a recipe is a non-trivial task. In this paper, we present a new heterogeneous data augmentation method to improve classification performance. Specifically, we first construct a heterogeneous recipe graph network to represent heterogeneous data, which includes four main-stream types of heterogeneous data: ingredient, flavor compound, image, and instruction. Then, we draw a sequence of augmented graphs for Semi-Supervised learning through multinomial sampling. The probability distribution of sampling depends on the Cosine distance between the nodes of graph. In this way, we name our approach as Multinomial Sampling Graph Data Augmentation (MS-GDA). Extensive experiments demonstrate that MS-GDA significantly outperforms SOTA baselines on cuisine classification and region prediction with the recipe benchmark dataset. Code is available at https://github.com/LiangzheChen/MS-GDA .

SONGS CONTINUATION GENERATION TECHNOLOGY BASED ON TEST GENERATION STRATEGIES, TEXTMINING AND LANGUAGE MODEL T5

Context. Pre-trained large language models are currently the driving force behind the development of not only NLP, but also deep learning systems in general. Model transformers are able to solve virtually all problems that currently exist, provided that certain requirements and training practices are met. In turn, words, sentences and texts are the basic and most important way of communication between intellectually developed beings. Of course, speech and texts are used to convey certain emotions, events, etc. One of the main ways of using language to describe experienced emotions is songs with lyrics. However, often due to the need to preserve rhyme and rhyming, the dimensions of verse lines, song structure, etc., artists have to use repetition of lines in the lyrics. In addition, the process of writing texts can be long.
 Objective of the study is to develop information technology for generating the continuation of song texts based on the T5 machine learning model with (SA, specific author) and without (NSA, non-specific author) consideration of the author's style.
 Method. Choosing a decoding strategy is important for the generation process. However, instead of favoring a particular strategy, the system will support multiple strategies. In particular, the following 8 strategies: Contrastive search, Top-p sampling, Top-k sampling, Multinomial sampling, Beam search, Diverse beam search, Greedy search, and Beam-search multinomial sampling.
 Results. A machine learning model was developed to generate the continuation of song lyrics using large language models, in particular the T5 model, to accelerate, complement and increase the flexibility of the songwriting process.
 Conclusions. The created model shows excellent results of generating the continuation of song texts on test data. Analysis of the raw data showed that the NSA model has less degrading results, while the SA model needs to balance the amount of text for each author. Several text metrics such as BLEU, RougeL and RougeN are calculated to quantitatively compare the results of the models and generation strategies. The value of the BLEU metric is the most variable, and its value varies significantly depending on the strategy. At the same time, Rouge metrics have less variability, a smaller range of values. For comparison, 8 different decoding methods for text generation, supported by the transformers library, were used. From all the results of the text comparison, it is clear that the metrically best method of song text generation is beam search and its variations, in particular beam sampling. Contrastive search usually outperformed the conventional greedy approach. The top-p and top-k methods are not clearly superior to each other, and in different situations gave different results.

On the sub-Gaussianity of the missing mass

We sharpen the best-known sub-Gaussian concentration of the missing mass to the variance factor c/n for some 0<c<1/2 in terms of the alphabet size under multinomial sampling. A simple lower bound for c is also demonstrated.

Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law.

We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and Fisher) are normal, describe well a variety of simulated data. In addition, we obtain test statistics for comparing (possibly different types of) entropies from two samples without requiring the same number of categories. Finally, we apply these tests to social survey data and verify that the results are consistent but more general than those obtained with a χ2 test.

Conditional inference of Poisson models and information geometry: an ancillary review

The Poisson distribution is a fundamental tool in categorical data analysis. This paper reviews conditional inference for the independent Poisson model. It is noted that the conditioning variable is not an ancillary statistic in the exact sense except in the case of the product multinomial sampling scheme, whereas two versions of the ancillary property hold in general. The ancillary properties justify the use of conditional inference, as first proposed by R. A. Fisher and subsequently discussed by many researchers. The mixed coordinate system developed in information geometry is emphasized as effective for the description of facts.

Investigating Constructed‐Response Scoring Over Time: The Effects of Study Design on Trend Rescore Statistics

When constructed‐response items are administered for a second time, it is necessary to evaluate whether the current Time B administration's raters have drifted from the scoring of the original administration at Time A. To study this, Time A papers are sampled and rescored by Time B scorers. Commonly the scores are compared using the proportion of exact agreement across times and/or t‐statistics comparing Time A means to Time B means. It is common to treat these rescores with procedures that assume a multinomial sampling model, which is incorrect. The correct, product‐multinomial model reflects the stratification of Time A scores. Using direct computation, the research report demonstrates that both proportion of exact agreement and the t‐statistic can deviate substantially from expected behavior, providing misleading results. Reweighting the rescore table gives each statistic the correct expected value but does not guarantee that the usual sampling distributions hold. It is also noted that the results apply to a wider class of situations in which a set of papers is scored by one group of raters or scoring engine and then a sample is selected to be evaluated by a different group of raters or scoring engine.

Perplexity-Based Molecule Ranking and Bias Estimation of Chemical Language Models.

Chemical language models (CLMs) can be employed to design molecules with desired properties. CLMs generate new chemical structures in the form of textual representations, such as the simplified molecular input line entry system (SMILES) strings. However, the quality of these de novo generated molecules is difficult to assess a priori. In this study, we apply the perplexity metric to determine the degree to which the molecules generated by a CLM match the desired design objectives. This model-intrinsic score allows identifying and ranking the most promising molecular designs based on the probabilities learned by the CLM. Using perplexity to compare “greedy” (beam search) with “explorative” (multinomial sampling) methods for SMILES generation, certain advantages of multinomial sampling become apparent. Additionally, perplexity scoring is performed to identify undesired model biases introduced during model training and allows the development of a new ranking system to remove those undesired biases.

Multinomial Logit Model of Bayesian Age-Period-Cohort Analysis:Factor Decomposition of Political Issues Using Repeated Cross-Sectional Survey

The purpose of this study is to discussthe implementation and importanceabout the multinomial logit model of Bayesian Age-Period-Cohort analysis. Since the design matrix of three factorsdoes not become full rankdue to the identification problem derived fromlinear dependency between age, period and cohort, few studies have useda complex model. In contrast, this paper presents the practical multinomial logit model withefficient sampling by reparameterizationabout the constraints of assuming a random walk for each effect. Furthermore, we compared the estimates ofthe logit model andthe multidimensional modelabout political issuesthat should be considered from multiple perspectives. Using repeated cross-sectional survey in Japanfrom 1973 to 2013, the multinomial logit model was shown to be effectivebecause it was able to obtain a trendthat were not captured in the logit model.

Maximum‐likelihood estimation of the geometric niche preemption model

AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May's equation. This article proposes a maximum‐likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum‐likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum‐likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

Bayesian shrinkage approaches to unbalanced problems of estimation and prediction on the basis of negative multinomial samples

In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and, in particular, consider unbalanced settings. First, the problem of estimating multiple negative multinomial parameter vectors under the standardized squared error loss is treated and a new empirical Bayes estimator which dominates the uniformly minimum variance unbiased (UMVU) estimator under suitable conditions is derived. Next, we consider estimation of the joint predictive density of several multinomial tables under the Kullback–Leibler divergence and obtain a sufficient condition under which the Bayesian predictive density with respect to a hierarchical shrinkage prior dominates the Bayesian predictive density with respect to the Jeffreys prior. Finally, our proposed Bayesian estimator and predictive density give risk improvements in simulations and our methods are applied to real data resulting from the inverse sampling method.

Individual level lifestyle changes during the COVID-19 pandemic – A Finnish population-based study

BackgroundThe COVID-19 pandemic containment measures may affect lifestyle. We aimed to examine the changes in key lifestyle factors based on the data from same individuals before (2017) and during (2020) the COVID-19 pandemic.MethodsThe study is based on the FinHealth 2017 Study representing the Finnish adult population, and its follow-up questionnaire conducted in autumn 2020. A total of 4814 individuals aged 25 and older at baseline answered the same questions on lifestyle in both years. Regular leisure-time physical activity (LPA), daily use of vegetables and/or fruits, experience of adequate sleep, daily use of nicotine products and high-risk use of alcohol, were dichotomized (yes/no) for the analysis. Weighted prevalence (no/favorable/unfavorable change) for three age groups (25-49, 50-69, 70+ years) was analyzed using multinomial logistic regression, sampling design and non-response acknowledged.ResultsIn general, the prevalence of total changes observed varied 6 − 27% between lifestyle factors. The changes were both unfavorable and favorable for health. About 14% (95% CI 11,17) and 12% (95% CI 9,16) of older women and men, respectively, had LPA in 2017 but not in 2020. Corresponding prevalence for favorable change in LPA were smaller, 6% (95% CI 4,8) in older women and 7% (95% CI 4,9) in men. In older women, the results concerning daily use of vegetables and fruits were parallel. In contrast, in older women the changes observed in the experience of adequate sleep were mainly favorable. In all age groups, high-risk use of alcohol slightly decreased especially in men but the changes in use of nicotine products were minor.ConclusionsThe results highlight unfavorable changes in LPA and vegetable consumption especially in older women during the COVID-19 pandemic. Part of the unfavorable changes may be explained by aging, but the pandemic containment measures may have accelerated them indicating the need for health promotion actions among the elderly.Key messages The lifestyle changes observed during COVID-19 pandemic were complex, varying by sex and age groups and being both favorable and unfavorable for health.Special attention should be given to promotion of physical activity in the elderly during and after the pandemic.

Multinomial Sampling of Latent Variables for Hierarchical Change-Point Detection

Bayesian change-point detection, with latent variable models, allows to perform segmentation of high-dimensional time-series with heterogeneous statistical nature. We assume that change-points lie on a lower-dimensional manifold where we aim to infer a discrete representation via subsets of latent variables. For this particular model, full inference is computationally unfeasible and pseudo-observations based on point-estimates of latent variables are used instead. However, if their estimation is not certain enough, change-point detection gets affected. To circumvent this problem, we propose a multinomial sampling methodology that improves the detection rate and reduces the delay while keeping complexity stable and inference analytically tractable. Our experiments show results that outperform the baseline method and we also provide an example oriented to a human behavioral study.

Fixed-width confidence interval for treatment difference in multinomial sampling

This article deals with fixed-width confidence intervals for the difference between two treatments with ordered categorical data. Related asymptotics are obtained. Procedures are evaluated by simulations, followed by a data illustration.

Chernoff-Type Concentration of Empirical Probabilities in Relative Entropy

We study the relative entropy of the empirical probability vector with respect to the true probability vector in multinomial sampling of k categories, which, when multiplied by sample size n, is also the log-likelihood ratio statistic. We generalize a recent result and show that the moment generating function of the statistic is bounded by a polynomial of degree n on the unit interval, uniformly over all true probability vectors. We characterize the family of polynomials indexed by (k,n) and obtain explicit formulae. Consequently, we develop Chernoff-type tail bounds, including a closed-form version from a large sample expansion of the bound minimizer. Our bound dominates the classic method-of-types bound and is competitive with the state of the art. We demonstrate with an application to estimating the proportion of unseen butterflies.

Robustness of Minimum Density Power Divergence Estimators and Wald-type test statistics in loglinear models with multinomial sampling

In this paper we propose a new family of estimators, Minimum Density Power Divergence Estimators (MDPDE), as a robust generalization of maximum likelihood estimators (MLE) for the loglinear model with multinomial sampling by using the Density Power Divergence (DPD) measure introduced by Basu et al. (1998). Based on these estimators, we further develop two types of confidence intervals (asymptotic and bootstrap ones), as well as a new robust family of Wald-type test statistics for testing a nested sequence of loglinear models. Furthermore, we study theoretically the robust properties of both the MDPDE as well as Wald-type tests through the classical influence function analysis. Finally, a simulation study provides further confirmation of the validity of the theoretical results established in the paper.

Power of Microbiome Beta-Diversity Analyses Based on Standard Reference Samples.

A simple method to analyze microbiome beta-diversity computes mean beta-diversity distances from a test sample to standard reference samples. We used reference stool and nasal samples from the Human Microbiome Project and regressed an outcome on mean distances (2 degrees-of-freedom (df) test) or additionally on squares and cross-product of mean distances (5-df test). We compared the power of 2-df and 5-df tests with the microbiome regression-based kernel association test (MiRKAT). In simulations, MiRKAT had moderately greater power than the 2-df test for discriminating skin versus saliva and skin versus nasal samples, but differences were negligible for skin versus stool and stool versus nasal samples. The 2-df test had slightly greater power than MiRKAT for Dirichlet multinomial samples. In associating body mass index with beta-diversity in stool samples from the American Gut Project, the 5-df test yielded smaller P values than MiRKAT for most taxonomic levels and beta-diversity measures. Unlike procedures like MiRKAT that are based on the beta-diversity matrix, mean distances to reference samples can be analyzed with standard statistical tools and shared or meta-analyzed without sharing primary DNA data. Our data indicate that standard reference tests have power comparable to MiRKAT's (and to permutational multivariate analysis of variance), but more simulations and applications are needed to confirm this.

Using sigLASSO to optimize cancer mutation signatures jointly with sampling likelihood

Multiple mutational processes drive carcinogenesis, leaving characteristic signatures in tumor genomes. Determining the active signatures from a full repertoire of potential ones helps elucidate mechanisms of cancer development. This involves optimally decomposing the counts of cancer mutations, tabulated according to their trinucleotide context, into a linear combination of known signatures. Here, we develop sigLASSO (a software tool at github.com/gersteinlab/siglasso) to carry out this optimization efficiently. sigLASSO has four key aspects: (1) It jointly optimizes the likelihood of sampling and signature fitting, by explicitly factoring multinomial sampling into the objective function. This is particularly important when mutation counts are low and sampling variance is high (e.g., in exome sequencing). (2) sigLASSO uses L1 regularization to parsimoniously assign signatures, leading to sparse and interpretable solutions. (3) It fine-tunes model complexity, informed by data scale and biological priors. (4) Consequently, sigLASSO can assess model uncertainty and abstain from making assignments in low-confidence contexts.

Application of a Negative Multinomial Model Gives Insight into Rarity-Area Relationships

The distribution of individuals of different species across different sampling units is typically non-random. This distributional non-independence can be interpreted and modelled as a correlated multivariate distribution. However, this correlation cannot be modelled using a totally independent and random distribution such as the Poisson distribution. In this study, we utilized the negative multinomial distribution to overcome the problem encountered by the commonly used Poisson distribution and used it to derive insight into the implications of field sampling for rare species’ distributions. Mathematically, we derived, from the negative multinomial distribution and sampling theory, contrasting relationships between sampling area, and the proportions of locally rare and regionally rare species in ecological assemblages presenting multi-species correlated distribution. With the suggested model, we explored the cross-scale relationships between the spatial extent, the population threshold for defining the rarity of species, and the multi-species correlated distribution pattern using data from two 50-ha tropical forest plots in Barro Colorado Island (Panama) and Heishiding Provincial Reserve (Guangdong Province, China). Notably, unseen species (species with zero abundance in the studied local sample) positively contributed to the distributional non-independence of species in a local sample. We empirically confirmed these findings using the plot data. These findings can help predict rare species–area relationships at various spatial scales, potentially informing biodiversity conservation and development of optimal field sampling strategies.