Day 1/Jan 13

Here the time is given as IST (UTC+5:30)/ TST (UTC +8)/ JST (UTC+9).

Opening (09:57/12:27/13:27)

Hiroe Tsubaki, Director of ISM

Session 1. Inference (10:00-10:20/12:30-12:50/13:30-13:50)

Hiroe Tsubaki, ISM

The Least Informative Quasi-Likelihood under Restricted Moment Structures

The natural exponential family with a dispersion parameter is the least informative distribution of its expectation parameter given the variance function and its likelihood can be used as quasi-likelihood of the generalized linear models even if it is not the true likelihood with the same variance function. In this talk I will review the role of least informative likelihoods in the application of statistical models and expand quasi-likelihood given certain functional restrictions of the 3rd and 4th order moment structures.

Session 2. Regression (10:20-11:00/12:50-13:30/13:50-14:30)

Partha Sarathi Mukherjee, ISI

Image restoration using local pixel clustering and jump regression

In this talk, we will discuss various methods of image denoising and image deblurring techniques based on local pixel clustering and jump regression.

Daisuke Murakami, ISM

Transformation-based approach for large non-Gaussian spatial regression modeling

As with the advancement of geographical information systems, non-Gaussian spatial data is getting larger and more diverse. Given such a background, we develop a computationally efficient regression model for large non-Gaussian spatial data. We rely on a transformation-based approach for flexibly modeling a wide variety of non-Gaussian data without explicit assuming of data distribution. Besides, its computational efficiency is enhanced by employing a preconditioning. Monte Carlo experiments show the estimation accuracy and computational efficiency for modeling non-Gaussian data including fat-tailed and/or skewed distributions. The developed model is applied to a spatial analysis focusing on the influence of people flow on the coronavirus disease 2019 in Japan.

Session 3. Tail dependence (11:20-12:00/13:50-14:30/14:50-15:30)

Takaaki Koike, ISM

Tail concordance measures: A fair assessment of tail dependence

Quantifying tail dependence is an important issue in various fields such as finance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it fails to capture non-exchangeable tail dependence since the TDC evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the MTCM and the ATCM can capture non-exchangeable tail dependence. Moreover, they often admit analytical forms, and satisfy axiomatic properties naturally required to quantify tail dependence. Estimators of the two measures are also constructed. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.

This is joint work with Shogo Kato (ISM) and Marius Hofert (University of Waterloo).

Parthanil Roy, ISI

How to tell a tale of two tails?

This talk is going to focus on a model named “branching random walk”. Roughly speaking, the dynamics of this model goes as follows. It starts from one particle at the origin. This particle branches into a random number of particles according to a progeny distribution. Each new particle makes an independent displacement on the real line following a displacement distribution. These particles form the first generation. Each first generation particle behave in a similar fashion independently of each other and give rise to the second generation. This process goes on. More precisely, the displacements are iid following the displacement distribution and are independent of the branching mechanism. In this talk, we will discuss how the tails of progeny and displacement distributions determine the long run configuration of the particles.

It is based on a joint work with Souvik Ray, Rajat Subhra Hazra and Philippe Soulier.

Poster Session 1. (12:00-12:20/14:30-14:50/15:30-15:50)

Bilol Banerjee, ISI

Test of Independence for Hilbertian Random Variables

We propose a test of independence among several random functions, which are elements of separable Hilbert spaces. We provide a general recipe for constructing a measure of dependence among multiple random functions. This measure is non-negative and it takes the value zero only when the functions are independent. We focus on one such measure based on the d-variable Hilbert-Schmidt Independence Criterion. We propose an estimator of this measure and discuss some of its desirable properties. This estimator involves a kernel function with an associated bandwidth. We use this estimator to construct a test for independence and prove the large sample consistency of the resulting test. We also consider a multi-scale version of this test, where we look at the results for several choices of the bandwidth and aggregate them judiciously. The large sample consistency of this multiscale version is also established under appropriate regularity conditions. Extensive simulation studies involving $L_2[0,1]$-valued random functions are carried out to compare the performance of the proposed test with some existing tests.

This is based on a joint work with Anil K. Ghosh

Kazuharu Harada, ISM

Outlier-resistant and doubly robust estimator for average treatment effect

Estimators of causal quantities sometimes suffer from outliers. On the estimation of the average treatment effect (ATE), the doubly-robust (DR) estimator is well-known to be robust to model misspecification. However, the DR estimator is vulnerable to outliers. The median-based DR estimators are outlier-resistant alternatives to the estimator of the ATE, but their outlier resistance is limited when the ratio of outliers is not small. Also, the median-based estimators are less efficient than the average-based estimators. In this work, we propose a novel DR-type estimator of the ATE. This estimator is highly resistant to outliers besides model misspecification since it combines the DR estimator and the outlier-resistant M-estimator. In development, we first consider a relatively straight form, which is just a special case of the DR M-estimator. The DR M-estimator typically holds double robustness, however, we find double robustness is violated under contamination. Then, we further investigate the estimating equation, and then we construct a bias-corrected version. The bias-corrected estimator holds double robustness even under heavy contamination. The key of the correction is the ratio of outliers. The bias-corrected estimator also holds consistency approximately and asymptotic normality even under contamination. In numerical experiments, our estimator effectively reduces the bias of outliers and is more efficient than the median-based DR estimators.

This is joint work with Hironori Fujisawa (ISM).

Hao-Yun Huang, ISSAS

Multi-Resolution Spatial Methods on the Sphere

In this talk, we consider spatial prediction on the sphere in the presence of measurement errors, where data may be irregularly located. We first develop a special class of basis functions in the thin-plate-spline (TPS) function space on the sphere. These basis functions are ordered according to their degrees of smoothness from large-scale features to small-scale details, leading to an orthogonal transformation of the data with a multi-resolution representation. Theoretically, we show that by keeping a small number of basis functions relative to the sample size, the resulting least squares estimate is not only computationally more efficient than but it also achieves the same convergence rate as the full penalized TPS method. In addition, we develop a multi-resolution mixed0effects spatial model on the sphere, which further captures finer-scale variation by including a Gaussian spatial process. Since large-scale features are captured by basis functions, the small-scale spatial process tends to have a short spatial dependence range, and hence the krging equation involves only a sparse covariance matrix inversion, which facilitate computation. A simulation experiment is performed and an application to global sea-surface-temperature data observed from a satellite is given to demonstrate the effectiveness of the proposed method.

This is joint work with Hsin-Cheng Huang (ISI) and Ching-Kang Ing (Institute of Statistics, National Tsing Hua University).

Megumi Iwayama, ISM, The Graduate University for Advanced Studies, Japan

High-dimensional multi-output regression in materials informatics

In recent years, various techniques of statistical machine learning have been rapidly introduced to materials science. In general, a trained statistical model describes the output variable, such as thermodynamic, electronic, mechanical, and energetic properties, as a function of a descriptor vector that encodes the structure of a given material such as a molecule, chemical composition, and crystal system. The model is used to evaluate the properties of millions or billions of candidate materials, including virtually designed materials, and to identify promising candidates with innovative properties from a vast search space. On the other hand, in the data analysis in materials research, the output variable is sometimes given in a non-numerical form. For example, in the task of predicting the light absorption spectrum of a conjugated polymer, the output variable is the spectral function defined on a frequency domain. Also, in the task of predicting the microstructure of a polymer nanocomposite, the output variable is an image obtained from electron microscopy imaging. Herein we present two unified frameworks for such multidimensional output regression that can cover various applications in materials research. The first approach is based on the generative adversarial learning. We also consider another framework based on statistical modeling inspired by the idea of functional data analysis for multidimensional or functional-type outputs. This model is an extension of kernel regression to functional or multidimensional data and has a simplified mathematical structure. We demonstrate the present method through several case studies.

This is joint work with Prof. Ryo Yoshida (ISM) and Dr. Stephen Wu (ISM).

Session 4. Clustering and networks (13:00-14:00/15:30-16:30/16:30-17:30)

Arijit Chakrabarty, ISI

Clustering of rare events

This talk is on understanding how the rare events of deviation of sample mean from population mean cluster. Consider data coming from a stationary process whose marginal distribution has all exponential moments finite. Conditional on the event that the average of the first n observations exceeds the population mean by a prefixed threshold, we study the asymptotic distribution of the length of time for which this deviation persists, as n goes to infinity. It turns out that the answer depends on the memory of the stationary process. In the short memory regime, the asymptotic conditional distrubtion of the persistence time is a law on the set of natural numbers, whereas in the long memory regime, the persistence time goes almost surely to infinity. In the latter regime, the asymptotic conditional law under an appropriate scaling is studied.

This is a joint work with Gennady Samorodnitsky.

Frederick Kin Hing Phoa, ISSAS

A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.

This is a joint work with Dr. Hohyun Jung.

Rahul Roy, ISI

Drainage networks and the Brownian web

We discuss various models of drainage networks and show that their asymptotic limit under diffusive scaling is the Brownian web.

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