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Kentaro Tanaka

Publications and source records attributed to Kentaro Tanaka.

11 recordsLinked to original sources
arXiv2026

Space of prime congruences in tropical geometry

We investigate spaces of prime congruences on tropical algebras and study their geometry, inspired by classical scheme theory. Our main strategy is to use tropical algebras associated to ordered monoids, which play the role of the monomial structure of these algebras. Using the space of prime congruences as local models, we introduce a tropical toric scheme which contains the usual tropical toric variety as a subspace. We show how the separatedness and properness of these schemes are captured by scheme-theoretic points. As an application of our framework, we obtain a necessary and sufficient condition for a prime congruence to be finitely generated.

math.AG↗
arXiv2024

REST-HANDS: Rehabilitation with Egocentric Vision Using Smartglasses for Treatment of Hands after Surviving Stroke

Stroke represents the third cause of death and disability worldwide, and is recognised as a significant global health problem. A major challenge for stroke survivors is persistent hand dysfunction, which severely affects the ability to perform daily activities and the overall quality of life. In order to regain their functional hand ability, stroke survivors need rehabilitation therapy. However, traditional rehabilitation requires continuous medical support, creating dependency on an overburdened healthcare system. In this paper, we explore the use of egocentric recordings from commercially available smart glasses, specifically RayBan Stories, for remote hand rehabilitation. Our approach includes offline experiments to evaluate the potential of smart glasses for automatic exercise recognition, exercise form evaluation and repetition counting. We present REST-HANDS, the first dataset of egocentric hand exercise videos. Using state-of-the-art methods, we establish benchmarks with high accuracy rates for exercise recognition (98.55%), form evaluation (86.98%), and repetition counting (mean absolute error of 1.33). Our study demonstrates the feasibility of using egocentric video from smart glasses for remote rehabilitation, paving the way for further research.

cs.CV↗
arXiv2018

Neutrino mixing from finite modular groups

We study the lepton flavor models, whose flavor symmetries are finite subgroups of the modular group such as $S_3$ and $A_4$. In our models, couplings are also nontrivial representations of these groups and modular functions of the modulus. We study the possibilities that these models realize realistic values of neutrino masses and lepton mixing angles.

hep-ph↗
arXiv2018

The Group Lasso for Design of Experiments

We introduce an application of the group lasso to design of experiments. Note that we are NOT trying to explain experimental design for the group lasso. Conversely, we explain how we can use the idea of the group lasso in experimental design, showing that the problem of constructing an optimal design matrix can be transformed into a problem of the group lasso. In some numerical examples, we show that we can obtain the orthogonal arrays as the solutions of the group lasso problems.

stat.ML↗
arXiv2011

Cones of elementary imsets and supermodular functions: a review and some new results

In this paper we give a review of the method of imsets introduced by Studeny (2005) from a geometric point of view. Elementary imsets span a polyhedral cone and its dual cone is the cone of supermodular functions. We review basic facts on the structure of these cones. Then we derive some new results on the following topics: i) extreme rays of the cone of standardized supermodular functions, ii) faces of the cones, iii) small relations among elementary imsets, and iv) some computational results on Markov basis for the toric ideal defined by elementary imsets.

math.ST↗
arXiv2011

Application of Mathematical Optimization Procedures to Intervention Effects in Structural Equation Models

For a given statistical model, it often happens that it is necessary to intervene the model to reduce the variances of the output variables. In structural equation models, this can be done by changing the values of the path coefficients by intervention. First, we explain that the expectations and variance matrix can be decomposed into several parts in terms of the total effects. Then, we show that an algorithm to obtain intervention method which minimizes the weighted sum of the variances can be formulated as a convex quadratic programming. This formulation allows us to impose boundary conditions for the intervention, so that we can find the practical solutions. We also treat a problem to adjust the expectations on targets.

stat.ME↗
arXiv2011

Properties of semi-elementary imsets as sums of elementary imsets

We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.

math.ST↗
arXiv2008

Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when penalty is imposed on the ratios of the scale parameters

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a penalized likelihood, where the penalty is a function of the minimum of the ratios of the scale parameters and the sample size. It is shown that the penalized maximum likelihood estimator is strongly consistent. We also analyze the consistency of a penalized maximum likelihood estimator where the penalty is imposed on the scale parameters themselves.

math.ST↗
arXiv2007

Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small

In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum likelihood estimate exists. We prove that the maximum likelihood estimator (MLE) is strongly consistent, if the ratios of the scale parameters are restricted from below by $\exp(-n^{d}), 0 < d < 1 $, where $n$ is the sample size.

math.ST↗
arXiv2006

Strong consistency of MLE for finite mixtures of location-scale distributions when the scale parameters are exponentially small (full version)

In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study the strong consistency of maximum likelihood estimator, we consider the case that the scale parameters of the component distributions are restricted from below by $c_n$, where $c_n$ is a sequence of positive real numbers which tend to zero as the sample size $n$ increases. We prove that under mild regularity conditions maximum likelihood estimator is strongly consistent if the scale parameters are restricted from below by $c_{n} = \exp(-n^d)$, $0 < d < 1$.

math.ST↗