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. We implemented pattern-based regularisation on top of CNN to avoid overfitting. Using an external testing data set of 160 eyes of 131 patients with OAG, the prediction performance (absolute error (AE) and R² between predicted and actual TH values) was calculated for (1) mean TH in whole VF and (2) each TH of 68 points. For comparison, we trained support vector machine (SVM) and multiple linear regression (MLR). Results: AE of whole VF with CNN was 2.84±2.98 (mean±SD) dB, significantly smaller than those with SVM (5.65±5.12 dB) and MLR (6.96±5.38 dB) (all, p<0.001). Mean of point-wise mean AE with CNN was 5.47±3.05 dB, significantly smaller than those with SVM (7.96±4.63 dB) and MLR (11.71±4.15 dB) (all, p<0.001). R² with CNN was 0.74 for the mean TH of whole VF, and 0.44±0.24 for the overall 68 points. Conclusion: DL model showed considerably accurate prediction of HFA 10-2 VF from SD-OCT.

This paper addresses the issue of estimating from a given data sequence the number of mixture components for a Gaussian mixture model(GMM). Our approach is to compute the normalized maximum likelihood (NML) code length for the data sequence relative to a GMM, then to find the mixture size that attains the minimum of the NML on the basis of the minimum description length principle. For finite domains, Kontkanen and Myllymäki proposed a method for efficient computation of the NML code length for specific models, however, for general classes over infinite domains, it has remained open how we compute the NML code length efficiently. We first propose a general method for calculating the NML code length for a general exponential family. Then, we apply it to the efficient computation of the NML code length for a GMM. The key idea is to restrict the data domain in combination with the technique of employing a generating function for computing the normalization term for a GMM. We use artificial datasets to empirically demonstrate that our estimate of the mixture size converges to the true one significantly faster than other criteria.

We are concerned with the issue of detecting model changes in probability distributions. We specifically consider the strategies based on the minimum description length (MDL) principle. We theoretically analyze their basic performance from the two aspects: data compression and hypothesis testing. From the view of data compression, we derive a new bound on the minimax regret for model changes. Here, the mini-max regret is defined as the minimum of the worst-case code-length relative to the least normalized maximum likelihood code-length over all model changes. From the view of hypothesis testing, we reduce the model change detection into a simple hypothesis testing problem. We thereby derive upper bounds on error probabilities for the MDL-based model change test. The error probabilities are valid for finite sample size and are related to the information-theoretic complexity as well as the discrepancy measure of the hypotheses to be tested.

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. We examine the following information criteria for the dimensionality selection problem: the Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), and Sequential Normalized Maximum Likelihood (SNML) criterion. SNML is the total codelength required for the sequential encoding of a data sequence on the basis of the minimum description length. The proposed approach is applied to both the original SG model and the SG Negative Sampling model to clarify the idea of using information criteria. Additionally, as the original SNML suffers from computational disadvantages, we introduce novel heuristics for its efficient computation. Moreover, we empirically demonstrate that SNML outperforms both BIC and AIC. In comparison with other evaluation methods for word embedding, the dimensionality selected by SNML is significantly closer to the optimal dimensionality obtained by word analogy or word similarity tasks.