Waseda Cherry Blossom Workshop
on Topological Data Science

Date: March 19-23, 2021
Venue: Nishi-Waseda Campus, Waseda University
Building 63 - 1 Meeting Room

Organizer: Masanobu TANIGUCHI(Research Institute for Science & Engineering, Waseda University)

Supported by:
JSPS KAKENHI Kiban (S) Grand-in-Aid No. 18H05290 (M. Taniguchi)

Waseda Cherry Blossom Workshop
on Topological Data Science
Date: March 19-23, 2021
Venue: Nishi-Waseda Campus, Waseda University
Building 63 - 1 Meeting Room(Access map: https://www.waseda.jp/fsci/en/access/)

Organizer: Masanobu TANIGUCHI(Research Institute for Science & Engineering, Waseda University)

This workshop is supported by:
JSPS KAKENHI Kiban (S) Grand-in-Aid No. 18H05290(M. Taniguchi)!

Program
March 1909:50-10:00: Masanobu Taniguchi (Waseda Univ.)
Opening
Session I (10:00-12:00) chaired by Victor De Oliveira
10:00-11:00: Yan Liu (Waseda Univ.)
Statistical and Topological Inference of the Granger Causality
11:00-12:00: Takayuki Shiohama (Tokyo Univ. of Science)
Topological data analysis based classification and anomaly
detection in time series
12:00-13:30: Lunch Time
Session II (13:30-17:00) chaired by Yan Liu
13:30-14:30: Yuichi Ike (Waseda Univ.)
Convergence result of stochastic subgradient descent for
persistence-based functions

Zoom

14:30-15:00: Coffee Break
15:00-16:00: Momoko Hayamizu (Waseda Univ.)
A structure theorem for tree-based phylogenetic networks: fromtheory to algorithms
16:10-17:00: Frederic Chazal (INRIA, France)
An Introduction to Topological Data Analysis, Part I

Zoom

March 20
Session III (10:00-12:00) chaired by Takayuki Shiohama
10:00-12:00: Yusu Wang (UC San Diego)
Zoom
Topological Data Analysis: How it can help in modern data analysis
Lunch & Cherry Blossom Festival

March 22
Session IV (9:00-11:50) chaired by Fumiya Akashi
9:00-9:50: Victor De Oliveira (Univ. of Texas)
An Introduction to Geostatistcs, Part I

Zoom

10:00-10:50: Victor De Oliveira (Univ. of Texas)
An Introduction to Geostatistcs, Part II

Zoom

11:00-11:50: Victor De Oliveira (Univ. of Texas)
Gaussian Copula Models for Geostatistical Count Data

Zoom

11:50-13:30: Lunch Time
Session V (13:30-15:30) chaired by Xiaofei Xu
13:30-14:30: Yuichi Goto (Waseda Univ.)
Tests for a structural break and conditional variance of count timeseries14:30-15:30: Fumiya Akashi (Univ. of Tokyo)
Zoom
Robust regression methods in heavy-tailed processes and sphericalpredictors
15:30-16:00: Tea Time

Session VI (16:00-17:50) chaired by Masanobu Taniguchi
16:00-16:50: Frederic Chazal (INRIA, France)
An Introduction to Topological Data Analysis, Part II

Zoom

17:00-17:50: Frederic Chazal (INRIA, France)
Zoom
Linearization of persistence and the density of expected persistence
diagrams

March 23
Session VII (10:00-12:00) chaired by Yuichi Goto
10:00-11:00: Xuze Zhang (Univ. of Maryland)
Zoom
Estimation of residential radon concentration in Pennsylvania
counties by data fusion
11:00-12:00: Xiaofei Xu (Waseda Univ.)
Adaptive log-linear zero-inflated generalized Poisson autoregressivemodel with applications to crime counts
12:00-13:30: Lunch Time
Session VIII (13:30-14:30) chaired by Masanobu Taniguchi
13:30-14:30: Tadashi Uratani (Hosei Univ.)
Pandemic, Insurance and Extreme Value Theory

Abstracts
March 19 (10:00–12:00)

Yan Liu
Title: Statistical and Topological Inference of the Granger Causality

Abstract: Granger causality has been employed to investigate
causality relations between components of stationary multiple timeseries. Here, we generalize this concept by developing statisticalinference for local Granger causality for multivariate locally stationary
processes. Thus, our proposed local Granger causality approach
captures time-evolving causality relationships in nonstationary
processes. The proposed local Granger causality is well represented
in the frequency domain and estimated based on the parametric timevarying spectral density matrix using the local Whittle likelihood.
Under regularity conditions, we demonstrate that the estimatorsconverge weakly to a Gaussian process. Additionally, the test statistic
for the local Granger causality is shown to be asymptotically
distributed as a quadratic form of a multivariate normal distribution.
The finite sample performance is confirmed with several simulation
studies for multivariate time-varying VAR models. For practicaldemonstration, the proposed local Granger causality method
uncovered

new functional connectivity

relationships

betweenchannels in brain signals. Moreover, the method was able to identify

structural changes of Granger causality in financial data. (Joint workwith Masanobu Taniguchi and Hernando Ombao)

Takayuki Shiohama
Title: Topological data analysis based classification and anomaly detection
in time series

Abstract: Time series often contain outliers and level shifts or
structural changes. These unexpected events are of the utmost
importance in anomaly detection. The presence of such unusual
events can easily mislead conventional time series analysis and yielderroneous conclusions. Anomaly detection methods for time series
have been studied for decades and demonstrated to be useful inmany applications. There exist many notable methods in machinelearning, which include clustering analysis, isolation forests, andclassifiers using artificial neural networks. Most of these techniques
often are most effective when there are many additional features. In
this study, we use topological data analysis (TDA) in order to provide
more accurate classifier that can also detect unusual events in timeseries.

March 19 (13:30–17:00)

Yuichi Ike
Title:

Convergence

resultofstochastic

subgradientdescent

for

persistence-based functions

Abstract: Optimization of functions and losses with topological flavor
is an active and growing field of research in Topological Data Analysis,
with plenty of applications to Machine Learning. In practice, one justapplies stochastic subgradient descent to such a topological function,
but the corresponding gradient and associated algorithm do not comewith theoretical guarantees. In this talk, we will talk about aconvergence result of stochastic subgradient descent for such afunction, relying on the theory of o-minimal structures. This result
includes all the constructions and applications for topologicaloptimization in the literature. We show some experiments such as
dimension reduction and filter selection to showcase the versatility of
our approach. (Joint work with Mathieu Carrière, Frédéric Chazal,
Marc Glisse, Hariprasad Kannan, and Yuhei Umeda)

Momoko Hayamizu
Title: A structure theorem for tree-based phylogenetic networks:
from theory to algorithms

Abstract: While phylogenetic networks are useful to visualise nontreelike data or complex evolutionary histories, there are many

computationally hard problems regarding them. Therefore, it isimportant to define nice subclasses of phylogenetic networks that aremathematically tractable and biologically meaningful. In view of this,the concept of "tree-based" phylogenetic networks, which was
originally introduced by Francis and Steel in 2015, has attracted great
attention and given rise to various interesting research problems in
combinatorial phylogenetics. In this talk, I provide the necessary
background and explain how to solve those different problems in a
unified manner. The talk is mainly based on arXiv:1811.05849[math.CO]. I also mention more recent advancement that is joint workwith Kazuhisa Makino (arXiv:1904.12432 [math.CO]).

Frederic Chazal
Title: An introduction to Topological Data Analysis
Part I: persistent homology theory

Abstract: Topological Data Analysis (TDA) is a recent and fast growing
field providing a set of new topological and geometric tools to infer
relevant features of possibly complex data. Among these tools,
persistent homology plays a central role. It provides a mathematicallywell-founded basis to design efficient and robust methods to estimate,analyze and exploit the topological and geometric structure of data.
This first talk will be dedicated to a brief introduction to persistenthomology and its usage in TDA. We will introduce persistenthomology for functions and point cloud data and study its stability
properties. The talk does not require any specific background intopology, the basic notions needed to introduce the persistenthomology will be recalled or introduced during the talks.

March 20 (10:00–12:00)

Yusu Wang
Title: Topological Data Analysis: How it can help in modern data analysis

Abstract: In recent years, a new field for data, called Topological data
analysis, has attracted much attention from researchers from diverse
background, including computer science, applied mathematics andstatistics. Leveraging various fundamental developments both intheoretical and algorithmic fronts in the past two decades, topological
data analysis has been growing rapidly, and already applied in many
applied domains, such as computational neuroscience, materialscience and bioinformatics.
In this time, I want to give some examples on where topological ideas
could help with analyzing complex modern data. I will specificallyfocus on the following three aspects: (1) Topolgoical methods could
provide flexibile yet generic framework for feature summarization /characterization. (2) Topological methods could help model, infer, andexplore the hidden space behind data. (3) How to combine topologicalideas with machine learning pipelines. I will use recent work from myresearch group to illustrate these points. Through the course, we will

touch upon multiple topological objects, including persistenthomology, discrete Morse theory, and contour trees.

March 20 (9:00–11:50)

Victor De Oliveira
Title: An Introduction to Geostatistics, Part I

Abstract: In this talk I introduce some of the types of data and scientificproblems for which geostatistics is used, the basic probabilistic tools
needed to model geostatistical data, and the classical statisticalmethods of analysis. First, I describe the semivariogram function, thebasic tool used in geostatistics to model the spatial association
displayed by the quantity of interest, and then I describe the classicalmethods used for its estimation. These involve a two—step approachthat is distribution-free as is based on moments and least squares.
The pros and cons of these classical methods are discussed. Second,
I describe several variants of the so--called ‘kriging’ prediction
method, which are nothing other than applications of best linear
unbiased prediction. I will review some of the properties of thesepredictors and their mean squared prediction errors, as well as theability (or lack of) of the latter to properly account for the prediction
uncertainty. The pros and cons of kriging predictors are discussed.
The models and methods will be illustrated with several real data sets.

Victor De Oliveira
Title: An Introduction to Geostatistics, Part II

Abstract: In this talk I introduce models for geostatistical data basedon Gaussian random fields. First, I describe the frequentist methodsof maximum likelihood and restricted maximum likelihood to estimate
the model parameters, as well as some of the properties of these. I
also describe the optimal predictors and their relation to kriging
predictors. The two main asymptotic frameworks for this type of data
are reviewed, called increasing and fixed domain frameworks, andthe dissimilar large-- sample properties of maximum likelihood
estimators under these two frameworks are discussed. Second,
Bayesian methods for estimation and prediction are described as well
as some basic Markov chain Monte Carlo algorithms currently used
to make inference about these models. The issue of how to select`good priors' for these model is also briefly discussed. Finally, twoclasses of non--Gaussian models are introduced to describe
continuous data with skewed distributions and geostatistical countdata that use Gaussian random fields as building blocks: transformed
Gaussian random fields and Poisson hierarchical models. The
models and methods will be illustrated with several real data sets.

Victor De Oliveira
Title: Gaussian Copula Models for Geostatistical Count Data

Abstract: In this talk I describe a class of random field models forgeostatistical count data based on Gaussian copulas. Unlike
hierarchical Poisson models often used to describe this type of data,
Gaussian copula models allow a more direct modeling of the marginal
distributions and association structure of the count data. I describe indetail the correlation structure of these random fields when the familyof marginal distributions is either negative binomial or zero--inflated
Poisson; these represent two types of overdispersion often
encountered in geostatistical count data. I also contrast thecorrelation structure of one of these Gaussian copula models with thatof a hierarchical Poisson model having the same family of marginal
distributions. I also describe the computation of maximum likelihood
estimators which are a computationally challenging task. Finally, adata analysis of Lansing Woods tree counts is used to illustrate themethods.

March 22 (13:30–17:50)

Yuichi Goto
Title: Tests for a structural break and conditional variance of count timeseriesAbstract: Count time series have been attracted attention and widely
studied. We deal with count time series whose conditional expectation
has dependence structure. This model is motivated by generalizedlinear models. In this talk, we discuss two hypothesis testing problems
for count time series. The first is a test for a structural break. We
propose Wald type, score type, residual type of CUSUM test statistics,
and show the asymptotic null distributions. This result enables us toconstruct distribution-free and asymptotic size alpha tests. Moreover,
the tests based on a modified Wald statistic and a score type statistic
are consistent. The second is a test for the conditional variance. We
elucidate the asymptotic null distribution of a proposed test statistic
and show the consistency of the proposed test. Moreover, the local
alternative power is also clarified. This test can be applied to various
testing problems such as a goodness of fit test, a specification test ofintensity function, and a test for equidispersion. The simulation study
illustrates the finite sample performance of the above methods. The
number of patients with Escherichia coli in a state of Germany is also
analyzed. (The test for a conditional variance of count time series isbased on the joint work with K. Fujimori)Fumiya Akashi
Title: Robust regression methods in heavy-tailed processes and sphericalpredictors

Abstract: Statistical treatment for non-stationarity, heteroscedasticity
and heavy tails of the real data has attracted a lot of attention in these
decades. The analysis for the locally stationary (LS) processes has
been also developed under the finite variance assumptions. The
former half of this talk extends the framework to the LS processes

with possibly infinite variance error terms and construct the L1regression-based local linear estimator for the coefficients of themodel. In addition, the self-weighting method is also employed toreduce the leverage effect brought by the past values of theobservations. The proposed local-linear estimator is shown to haveasymptotic normality regardless of whether the innovation process
has finite variance or dependence structure. The latter half section ofthis talk considers a nonlinear regression model whose predictor is arandom vector on a hyper-sphere. To construct a robust estimator forthe nonlinear regression function, we consider a spherical kernel-type
objective function, and elucidate robust properties of the estimator.
Some simulation experiments illustrate desired finite sample
properties of the proposed methods. (Joint works with Junichi
Hirukawa, Konstantinos Fokianos and Holger Dette)

Frederic Chazal
Title: An introduction to Topological Data Analysis
Part II: statistical properties of persistent homology

Abstract: This second talk will be dedicated to the statistical study of
persistent homology. We will show how the stability properties of
persistence can be used to understand the behavior of persistence
diagrams in various (selected) statistical settings. We will also
illustrate how these statistical properties can be used to overcome
some computational and noise issues encountered in practical TDA
applications.

Frederic Chazal
Title: Linearization of persistence and the density of expected persistence
diagrams

Abstract: Persistence diagrams play a fundamental role in Topological
Data Analysis (TDA) where they are used as topological descriptorsof data represented as point cloud. They consist in discrete multisetsof points in the plane that can equivalently be seen as discretemeasures. When they are built on top of random data sets,
persistence diagrams become random measures. In this talk, we willshow that, in many cases, the expectation of these random discretemeasures has a density with respect to the Lebesgue measure in theplane. We will discuss its estimation and show that various classicalrepresentations of persistence diagrams (persistence images, Betti
curves,...) can be seen as kernel- based estimates of quantities
deduced from it. This is a joint work with Vincent Divol (ENS Paris /Inria DataShape team).

March 23 (10:00–12:00)

Xuze Zhang
Title: Estimation of residential radon concentration in Pennsylvania
counties by data fusion

Abstract: Radon is a tasteless, colorless, and odorless radioactive
gas that is considered as the leading cause of lung cancer among
nonsmoker. Residential exposure to radon has been a serious publichealth problem in Pennsylvania (PA) in the past several years sincerecord shows that a considerable proportion of PA houses have radon
concentration beyond safety level 4 pCi/L. Thus, estimation ofresidential radon concentration, especially estimation of exceedance
probability for a high threshold, becomes a prob- lem of interest. A
multisample density ratio model (DRM) with variable tilts is proposed
and applied to fused data from a reference county of interest and its
neighboring counties to obtain the estimated distribution of radon
concentration and confidence intervals that correspond to theestimates of exceedance probabilities of interest. (Joint work with
Saumyadipta Pyne and Benjamin Kedem)

Xiaofei Xu
Title: Adaptive log-linear zero-inflated generalized Poisson autoregressivemodel with applications to crime counts

Abstract: This research proposes a comprehensive ALG model(Adaptive Log-linear zero-inflated Generalized Poisson integervalued GARCH) to describe the dynamics of integer-valued timeseries of crime incidents with the features of autocorrelation,
heteroscedasticity, over-dispersion, and excessive number of zero
observations. The proposed ALG model captures time-varying
nonlinear dependence and simultaneously incorporates the impact ofmultiple exogenous variables in a unified modeling framework. We
use an adaptive approach to automatically detect subsamples of local
homogeneity at each time point of interest and estimate the timedependent parameters through an adaptive Bayesian Markov Chain
Monte Carlo (MCMC) sampling scheme. A simulation study shows
stable and accurate finite sample performances of the ALG model
under both homogeneous and heterogeneous scenarios. When
implemented with data on crime incidents in Byron, Australia, the ALG
model delivers a persuasive estimation of the stochastic intensity ofcriminals and provides insightful interpretations on both the dynamics
of intensity and the impacts of temperature and demographic factors
to different crime categories. (Joint work with Ying Chen, Cathy W. S.
Chen and Xiancheng Lin)

March 23 (13:30–14:30)

Tadashi Uratani
Title: Pandemic, Insurance and Extreme Value Theory

Abstract: The pandemic of COVID-19 is the most devastating shocks
experienced by the world in peacetime in mortality and economy.
“Excess deaths” is different in countries, more are Europe andAmerica while less are Asians, but it affects uniformly national
economy and government budget. Government spending for Covid19 has increased sharply deficit finance. We discuss on the financing

to extreme event risk management by Catastrophe Bond in Extreme
Value Theory.