Mixture Complexity and Its Application to Gradual Clustering Change Detection.

We consider measuring the number of clusters (cluster size) in the finite mixture models for interpreting their structures. Many existing information criteria have been applied for this issue by regarding it as the same as the number of mixture components (mixture size); however, this may not be valid in the presence of overlaps or weight biases. In this study, we argue that the cluster size should be measured as a continuous value and propose a new criterion called mixture complexity (MC) to formulate it.

A Joint Multitask Learning Model for Cross-sectional and Longitudinal Predictions of Visual Field Using OCT.

Purpose: We constructed a multitask learning model (latent space linear regression and deep learning [LSLR-DL]) in which the 2 tasks of cross-sectional predictions (using OCT) of visual field (VF; central 10°) and longitudinal progression predictions of VF (30°) were performed jointly via sharing the deep learning (DL) component such that information from both tasks was used in an auxiliary manner (The Association for Computing Machinery's Special Interest Group on Knowledge Discovery and Data Mining [SIGKDD] 2021). The purpose of the current study was to investigate the prediction accuracy preparing an independent validation dataset.

Design: Cohort study.

Summarizing Finite Mixture Model with Overlapping Quantification.

Finite mixture models are widely used for modeling and clustering data. When they are used for clustering, they are often interpreted by regarding each component as one cluster. However, this assumption may be invalid when the components overlap.

Predicting 10-2 Visual Field From Optical Coherence Tomography in Glaucoma Using Deep Learning Corrected With 24-2/30-2 Visual Field.

Purpose: To investigate whether a correction based on a Humphrey field analyzer (HFA) 24-2/30-2 visual field (VF) can improve the prediction performance of a deep learning model to predict the HFA 10-2 VF test from macular optical coherence tomography (OCT) measurements.

Methods: This is a multicenter, cross-sectional study. The training dataset comprised 493 eyes of 285 subjects (407, open-angle glaucoma [OAG]; 86, normative) who underwent HFA 10-2 testing and macular OCT.

Word2vec Skip-Gram Dimensionality Selection via Sequential Normalized Maximum Likelihood.

In this paper, we propose a novel information criteria-based approach to select the dimensionality of the word2vec Skip-gram (SG). From the perspective of the probability theory, SG is considered as an implicit probability distribution estimation under the assumption that there exists a true contextual distribution among words. Therefore, we apply information criteria with the aim of selecting the best dimensionality so that the corresponding model can be as close as possible to the true distribution.

Improving Visual Field Trend Analysis with OCT and Deeply Regularized Latent-Space Linear Regression.

Purpose: To investigate whether OCT measurements can improve visual field (VF) trend analyses in glaucoma patients using the deeply regularized latent-space linear regression (DLLR) model.

Design: Retrospective cohort study.

Participants: Training and testing datasets included 7984 VF results from 998 eyes of 592 patients and 1184 VF results from 148 eyes of 84 patients with open-angle glaucoma, respectively.

Deep learning model to predict visual field in central 10° from optical coherence tomography measurement in glaucoma.

Background/aim: To train and validate the prediction performance of the deep learning (DL) model to predict visual field (VF) in central 10° from spectral domain optical coherence tomography (SD-OCT).

Methods: This multicentre, cross-sectional study included paired Humphrey field analyser (HFA) 10-2 VF and SD-OCT measurements from 591 eyes of 347 patients with open-angle glaucoma (OAG) or normal subjects for the training data set. We trained a convolutional neural network (CNN) for predicting VF threshold (TH) sensitivity values from the thickness of the three macular layers: retinal nerve fibre layer, ganglion cell layer+inner plexiform layer and outer segment+retinal pigment epithelium.

Long-tailed distributions of inter-event times as mixtures of exponential distributions.

Inter-event times of various human behaviour are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states, in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values.

Model Selection for Non-Negative Tensor Factorization with Minimum Description Length.

Non-negative tensor factorization (NTF) is a widely used multi-way analysis approach that factorizes a high-order non-negative data tensor into several non-negative factor matrices. In NTF, the non-negative rank has to be predetermined to specify the model and it greatly influences the factorized matrices. However, its value is conventionally determined by specialists' insights or trial and error.

Detection of Longitudinal Visual Field Progression in Glaucoma Using Machine Learning.

Purpose: Global indices of standard automated perimerty are insensitive to localized losses, while point-wise indices are sensitive but highly variable. Region-wise indices sit in between. This study introduces a machine learning-based index for glaucoma progression detection that outperforms global, region-wise, and point-wise indices.

A basket two-part model to analyze medical expenditure on interdependent multiple sectors.

This study proposes a novel statistical methodology to analyze expenditure on multiple medical sectors using consumer data. Conventionally, medical expenditure has been analyzed by two-part models, which separately consider purchase decision and amount of expenditure. We extend the traditional two-part models by adding the step of basket analysis for dimension reduction.

Predicting disease progression from short biomarker series using expert advice algorithm.

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history.