Prediction and risk stratification from hospital discharge records based on Hierarchical sLDA

Background The greatly accelerated development of information technology has conveniently provided adoption for risk stratification, which means more beneficial for both patients and clinicians. Risk stratification offers accurate individualized prevention and therapeutic decision making etc. Hospital discharge records (HDRs) routinely include accurate conclusions of diagnoses of the patients. For this reason, in this paper, we propose an improved model for risk stratification in a supervised fashion by exploring HDRs about coronary heart disease (CHD). Methods We introduced an improved four-layer supervised latent Dirichlet allocation (sLDA) approach called Hierarchical sLDA model, which categorized patient features in HDRs as patient feature-value pairs in one-hot way according to clinical guidelines for lab test of CHD. To address the data missing and imbalance problem, RFs and SMOTE methods are used respectively. After TF-IDF processing of datasets, variational Bayes expectation-maximization method and generalized linear model were used to recognize the latent clinical state of a patient, i.e., risk stratification, as well as to predict CHD. Accuracy, macro-F1, training and testing time performance were used to evaluate the performance of our model. Results According to the characteristics of our datasets, i.e., patient feature-value pairs, we construct a supervised topic model by adding one more Dirichlet distribution hyperparameter to sLDA. Compared with established supervised algorithm Multi-class sLDA model, we demonstrate that our proposed approach enhances training time by 59.74% and testing time by 25.58% but almost no loss of average prediction accuracy on our datasets. Conclusions A model for risk stratification and prediction of CHD based on sLDA model was proposed. Experimental results show that Hierarchical sLDA model we proposed is competitive in time performance and accuracy. Hierarchical processing of patient features can significantly improve the disadvantages of low efficiency and time-consuming Gibbs sampling of sLDA model.

The short texts classification based on neural network topic model

Aiming at the low effectiveness of short texts feature extraction, this paper proposes a short texts classification model based on the improved Wasserstein-Latent Dirichlet Allocation (W-LDA), which is a neural network topic model based on the Wasserstein Auto-Encoder (WAE) framework. The improvements of W-LDA are as follows: Firstly, the Bag of Words (BOW) input in the W-LDA is preprocessed by Term Frequency–Inverse Document Frequency (TF-IDF); Subsequently, the prior distribution of potential topics in W-LDA is replaced from the Dirichlet distribution to the Gaussian mixture distribution, which is based on the Variational Bayesian inference; And then the sparsemax function layer is introduced after the hidden layer inferred by the encoder network to generate a sparse document-topic distribution with better topic relevance, the improved W-LDA is named the Sparse Wasserstein-Variational Bayesian Gaussian mixture model (SW-VBGMM); Finally, the document-topic distribution generated by SW-VBGMM is input to BiGRU (Bidirectional Gating Recurrent Unit) for the deep feature extraction and the short texts classification. Experiments on three Chinese short texts datasets and one English dataset represent that our model is better than some common topic models and neural network models in the four evaluation indexes (accuracy, precision, recall, F1 value) of text classification.

Techniques to Deal with Off-Diagonal Elements in Confusion Matrices

Confusion matrices are numerical structures that deal with the distribution of errors between different classes or categories in a classification process. From a quality perspective, it is of interest to know if the confusion between the true class A and the class labelled as B is not the same as the confusion between the true class B and the class labelled as A. Otherwise, a problem with the classifier, or of identifiability between classes, may exist. In this paper two statistical methods are considered to deal with this issue. Both of them focus on the study of the off-diagonal cells in confusion matrices. First, McNemar-type tests to test the marginal homogeneity are considered, which must be followed from a one versus all study for every pair of categories. Second, a Bayesian proposal based on the Dirichlet distribution is introduced. This allows us to assess the probabilities of misclassification in a confusion matrix. Three applications, including a set of omic data, have been carried out by using the software R.

On Johnson’s “Sufficientness” Postulates for Feature-Sampling Models

In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e., species-sampling models. In this paper, we review “sufficientness” postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

Compositional Data Modeling through Dirichlet Innovations

The Dirichlet distribution is a well-known candidate in modeling compositional data sets. However, in the presence of outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary. In this paper, the Kummer–Dirichlet distribution and the gamma distribution are coupled, using the beta-generating technique. This development results in the proposal of the Kummer–Dirichlet gamma distribution, which presents greater flexibility in modeling compositional data sets. Some general properties, such as the probability density functions and the moments are presented for this new candidate. The method of maximum likelihood is applied in the estimation of the parameters. The usefulness of this model is demonstrated through the application of synthetic and real data sets, where outliers are present.

FSTruct: An Fst-based tool for measuring ancestry variation in inference of population structure

In model-based inference of population structure from individual-level genetic data, individuals are assigned membership coefficients in a series of statistical clusters generated by clustering algorithms. Distinct patterns of variability in membership coefficients can be produced for different groups of individuals, for example, representing different predefined populations, sampling sites, or time periods. Such variability can be difficult to capture in a single numerical value; membership coefficient vectors are multivariate and potentially incommensurable across groups, as the number of clusters over which individuals are distributed can vary among groups of interest. Further, two groups might share few clusters in common, so that membership coefficient vectors are concentrated on different clusters. We introduce a method for measuring the variability of membership coefficients of individuals in a predefined group, making use of an analogy between variability across individuals in membership coefficient vectors and variation across populations in allele frequency vectors. We show that in a model in which membership coefficient vectors in a population follow a Dirichlet distribution, the measure increases linearly with a parameter describing the variance of a specified component of the membership vector. We apply the approach, which makes use of a normalized Fst statistic, to data on inferred population structure in three example scenarios. We also introduce a bootstrap test for equivalence of two or more groups in their level of membership coefficient variability. Our methods are implemented in the R package FSTruct.

Gibbs partitions, Riemann–Liouville fractional operators, Mittag–Leffler functions, and fragmentations derived from stable subordinators

Pitman (2003), and subsequently Gnedin and Pitman (2006), showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing feature. The most notable case are random partitions derived from the two-parameter Poisson–Dirichlet distribution, $\textrm{PD}(\alpha,\theta)$, whose corresponding $\alpha$-diversity/local time have generalized Mittag–Leffler distributions, denoted by $\textrm{ML}(\alpha,\theta)$. Our aim in this work is to provide indications on the utility of the wider class of Gibbs partitions as it relates to a study of Riemann–Liouville fractional integrals and size-biased sampling, and in decompositions of special functions, and its potential use in the understanding of various constructions of more exotic processes. We provide characterizations of general laws associated with nested families of $\textrm{PD}(\alpha,\theta)$ mass partitions that are constructed from fragmentation operations described in Dong et al. (2014). These operations are known to be related in distribution to various constructions of discrete random trees/graphs in [n], and their scaling limits. A centerpiece of our work is results related to Mittag–Leffler functions, which play a key role in fractional calculus and are otherwise Laplace transforms of the $\textrm{ML}(\alpha,\theta)$ variables. Notably, this leads to an interpretation within the context of $\textrm{PD}(\alpha,\theta)$ laws conditioned on Poisson point process counts over intervals of scaled lengths of the $\alpha$-diversity.