arXiv subjects

Kenji Yamanishi

Publications and source records attributed to Kenji Yamanishi.

33 records · Page 2Linked to original sources

arXiv2020

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. We examine the following information criteria for the dimensionality selection problem: the Akaike Information Criterion, Bayesian Information Criterion, 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.

cs.LG↗

arXiv2020

A Novel Global Spatial Attention Mechanism in Convolutional Neural Network for Medical Image Classification

Spatial attention has been introduced to convolutional neural networks (CNNs) for improving both their performance and interpretability in visual tasks including image classification. The essence of the spatial attention is to learn a weight map which represents the relative importance of activations within the same layer or channel. All existing attention mechanisms are local attentions in the sense that weight maps are image-specific. However, in the medical field, there are cases that all the images should share the same weight map because the set of images record the same kind of symptom related to the same object and thereby share the same structural content. In this paper, we thus propose a novel global spatial attention mechanism in CNNs mainly for medical image classification. The global weight map is instantiated by a decision boundary between important pixels and unimportant pixels. And we propose to realize the decision boundary by a binary classifier in which the intensities of all images at a pixel are the features of the pixel. The binary classification is integrated into an image classification CNN and is to be optimized together with the CNN. Experiments on two medical image datasets and one facial expression dataset showed that with the proposed attention, not only the performance of four powerful CNNs which are GoogleNet, VGG, ResNet, and DenseNet can be improved, but also meaningful attended regions can be obtained, which is beneficial for understanding the content of images of a domain.

eess.IV↗

arXiv2020

Mixture Complexity and Its Application to Gradual Clustering Change Detection

In model-based clustering using finite mixture models, it is a significant challenge to determine the number of clusters (cluster size). It used to be equal to 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 propose to continuously measure the cluster size in a mixture model by a new concept called mixture complexity (MC). It is formally defined from the viewpoint of information theory and can be seen as a natural extension of the cluster size considering overlap and weight bias. Subsequently, we apply MC to the issue of gradual clustering change detection. Conventionally, clustering changes has been considered to be abrupt, induced by the changes in the mixture size or cluster size. Meanwhile, we consider the clustering changes to be gradual in terms of MC; it has the benefits of finding the changes earlier and discerning the significant and insignificant changes. We further demonstrate that the MC can be decomposed according to the hierarchical structures of the mixture models; it helps us to analyze the detail of substructures.

cs.LG↗

arXiv2020

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

Inter-event times of various human behavior 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. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e., constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected as opposed to more complex mixtures in various data sets and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behavior.

physics.soc-ph↗

arXiv2019

Descriptive Dimensionality and Its Characterization of MDL-based Learning and Change Detection

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for the parametric class, and can further be extended to real-valued dimensionality when a number of models are mixed. The paper then derives the rate of convergence of the MDL (Minimum Description Length) learning algorithm which outputs a normalized maximum likelihood (NML) distribution with model of the shortest NML codelength. The paper proves that the rate is governed by Ddim. The paper also derives error probabilities of the MDL-based test for multiple model change detection. It proves that they are also governed by Ddim. Through the analysis, we demonstrate that Ddim is an intrinsic quantity which characterizes the performance of the MDL-based learning and change detection.

cs.LG↗

arXiv2018

Upper Bound on Normalized Maximum Likelihood Codes for Gaussian Mixture Models

This paper shows that the normalized maximum likelihood~(NML) code-length calculated in [1] is an upper bound on the NML code-length strictly calculated for the Gaussian Mixture Model. When we use this upper bound on the NML code-length, we must change the scale of the data sequence to satisfy the restricted domain. However, we also show that the algorithm for model selection is essentially universal, regardless of the scale conversion of the data in Gaussian Mixture Models, and that, consequently, the experimental results in [1] can be used as they are. In addition to this, we correct the NML code-length in [1] for generalized logistic distributions.

cs.IT↗

arXiv2018

Adaptive Minimax Regret against Smooth Logarithmic Losses over High-Dimensional $\ell_1$-Balls via Envelope Complexity

We develop a new theoretical framework, the \emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional $\ell_1$-balls within a factor of two. The prior is newly derived for achieving the minimax regret and called the \emph{spike-and-tails~(ST) prior} as it looks like. The resulting regret bound is so simple that it is completely determined with the smoothness of the loss function and the radius of the balls except with logarithmic factors, and it has a generalized form of existing regret/risk bounds. In the preliminary experiment, we confirm that the ST prior outperforms the conventional minimax-regret prior under non-high-dimensional asymptotics.

stat.ML↗

arXiv2018

Stable Geodesic Update on Hyperbolic Space and its Application to Poincare Embeddings

A hyperbolic space has been shown to be more capable of modeling complex networks than a Euclidean space. This paper proposes an explicit update rule along geodesics in a hyperbolic space. The convergence of our algorithm is theoretically guaranteed, and the convergence rate is better than the conventional Euclidean gradient descent algorithm. Moreover, our algorithm avoids the "bias" problem of existing methods using the Riemannian gradient. Experimental results demonstrate the good performance of our algorithm in the \Poincare embeddings of knowledge base data.

stat.ML↗

arXiv2018

High-dimensional Penalty Selection via Minimum Description Length Principle

We tackle the problem of penalty selection of regularization on the basis of the minimum description length (MDL) principle. In particular, we consider that the design space of the penalty function is high-dimensional. In this situation, the luckiness-normalized-maximum-likelihood(LNML)-minimization approach is favorable, because LNML quantifies the goodness of regularized models with any forms of penalty functions in view of the minimum description length principle, and guides us to a good penalty function through the high-dimensional space. However, the minimization of LNML entails two major challenges: 1) the computation of the normalizing factor of LNML and 2) its minimization in high-dimensional spaces. In this paper, we present a novel regularization selection method (MDL-RS), in which a tight upper bound of LNML (uLNML) is minimized with local convergence guarantee. Our main contribution is the derivation of uLNML, which is a uniform-gap upper bound of LNML in an analytic expression. This solves the above challenges in an approximate manner because it allows us to accurately approximate LNML and then efficiently minimize it. The experimental results show that MDL-RS improves the generalization performance of regularized estimates specifically when the model has redundant parameters.

stat.ML↗

arXiv2018

Exact Calculation of Normalized Maximum Likelihood Code Length Using Fourier Analysis

The normalized maximum likelihood code length has been widely used in model selection, and its favorable properties, such as its consistency and the upper bound of its statistical risk, have been demonstrated. This paper proposes a novel methodology for calculating the normalized maximum likelihood code length on the basis of Fourier analysis. Our methodology provides an efficient non-asymptotic calculation formula for exponential family models and an asymptotic calculation formula for general parametric models with a weaker assumption compared to that in previous work.

math.ST↗

arXiv2017

Grafting for Combinatorial Boolean Model using Frequent Itemset Mining

This paper introduces the combinatorial Boolean model (CBM), which is defined as the class of linear combinations of conjunctions of Boolean attributes. This paper addresses the issue of learning CBM from labeled data. CBM is of high knowledge interpretability but naïve learning of it requires exponentially large computation time with respect to data dimension and sample size. To overcome this computational difficulty, we propose an algorithm GRAB (GRAfting for Boolean datasets), which efficiently learns CBM within the $L_1$-regularized loss minimization framework. The key idea of GRAB is to reduce the loss minimization problem to the weighted frequent itemset mining, in which frequent patterns are efficiently computable. We employ benchmark datasets to empirically demonstrate that GRAB is effective in terms of computational efficiency, prediction accuracy and knowledge discovery.

stat.ML↗

arXiv2016

Predicting Glaucoma Visual Field Loss by Hierarchically Aggregating Clustering-based Predictors

This study addresses the issue of predicting the glaucomatous visual field loss from patient disease datasets. Our goal is to accurately predict the progress of the disease in individual patients. As very few measurements are available for each patient, it is difficult to produce good predictors for individuals. A recently proposed clustering-based method enhances the power of prediction using patient data with similar spatiotemporal patterns. Each patient is categorized into a cluster of patients, and a predictive model is constructed using all of the data in the class. Predictions are highly dependent on the quality of clustering, but it is difficult to identify the best clustering method. Thus, we propose a method for aggregating cluster-based predictors to obtain better prediction accuracy than from a single cluster-based prediction. Further, the method shows very high performances by hierarchically aggregating experts generated from several cluster-based methods. We use real datasets to demonstrate that our method performs significantly better than conventional clustering-based and patient-wise regression methods, because the hierarchical aggregating strategy has a mechanism whereby good predictors in a small community can thrive.

stat.ML↗

arXiv2012

Normalized Maximum Likelihood Coding for Exponential Family with Its Applications to Optimal Clustering

We are concerned with the issue of how to calculate the normalized maximum likelihood (NML) code-length. There is a problem that the normalization term of the NML code-length may diverge when it is continuous and unbounded and a straightforward computation of it is highly expensive when the data domain is finite . In previous works it has been investigated how to calculate the NML code-length for specific types of distributions. We first propose a general method for computing the NML code-length for the exponential family. Then we specifically focus on Gaussian mixture model (GMM), and propose a new efficient method for computing the NML to them. We develop it by generalizing Rissanen's re-normalizing technique. Then we apply this method to the clustering issue, in which a clustering structure is modeled using a GMM, and the main task is to estimate the optimal number of clusters on the basis of the NML code-length. We demonstrate using artificial data sets the superiority of the NML-based clustering over other criteria such as AIC, BIC in terms of the data size required for high accuracy rate to be achieved.

cs.LG↗

arXiv2011

Discovering Emerging Topics in Social Streams via Link Anomaly Detection

Detection of emerging topics are now receiving renewed interest motivated by the rapid growth of social networks. Conventional term-frequency-based approaches may not be appropriate in this context, because the information exchanged are not only texts but also images, URLs, and videos. We focus on the social aspects of theses networks. That is, the links between users that are generated dynamically intentionally or unintentionally through replies, mentions, and retweets. We propose a probability model of the mentioning behaviour of a social network user, and propose to detect the emergence of a new topic from the anomaly measured through the model. We combine the proposed mention anomaly score with a recently proposed change-point detection technique based on the Sequentially Discounting Normalized Maximum Likelihood (SDNML), or with Kleinberg's burst model. Aggregating anomaly scores from hundreds of users, we show that we can detect emerging topics only based on the reply/mention relationships in social network posts. We demonstrate our technique in a number of real data sets we gathered from Twitter. The experiments show that the proposed mention-anomaly-based approaches can detect new topics at least as early as the conventional term-frequency-based approach, and sometimes much earlier when the keyword is ill-defined.

stat.ML↗

arXiv1997

Document Classification Using a Finite Mixture Model

We propose a new method of classifying documents into categories. The simple method of conducting hypothesis testing over word-based distributions in categories suffers from the data sparseness problem. In order to address this difficulty, Guthrie et.al. have developed a method using distributions based on hard clustering of words, i.e., in which a word is assigned to a single cluster and words in the same cluster are treated uniformly. This method might, however, degrade classification results, since the distributions it employs are not always precise enough for representing the differences between categories. We propose here the use of soft clustering of words, i.e., in which a word can be assigned to several different clusters and each cluster is characterized by a specific word probability distribution. We define for each document category a finite mixture model, which is a linear combination of the probability distributions of the clusters. We thereby treat the problem of classifying documents as that of conducting statistical hypothesis testing over finite mixture models. In order to accomplish this testing, we employ the EM algorithm which helps efficiently estimate parameters in a finite mixture model. Experimental results indicate that our method outperforms not only the method using distributions based on hard clustering, but also the method using word-based distributions and the method based on cosine-similarity.

cmp-lg↗