Dates: 19th (Wed) — 20th (Thu) February, 2020
Location: Room D222, The Institute of Statistical Mathematics, Tokyo
Registration: No registration required (except for dinner)
Computational statistics is a rapidly developing research field due to the increasing high demand in analysing large and complex data in many areas of science. Motivated by the recent innovations in efficient computational techniques for statistical inference and a variety of computationally challenging applications, this workshop aims to facilitate discussions amongst researchers working on different aspects of statistical computations, and promotes new ideas in both methodological and applied directions.
Some of the speakers are unable to attend the workshop due to travel restrictions resulted from the coronavirus disease outbreak.
|Day 1 (19 Feb)||Day 2 (20 Feb)|
|9:30 – 10:30|
|10:30 – 11:00|
|11:00 – 12:00||Richard Gerlach|
|12:00 – 13:30||Lunch|
|13:30 – 14:30||Heishiro Kanagawa||Pavel Shevchenko|
|14:30 – 15:00||Afternoon tea||Afternoon tea|
|15:00 – 16:00||Shin-Itiro Goto||Takeru Matsuda|
|16:00 – 17:00||Wenkai Xu||Daisuke Murakami|
|19:00 – late||Dinner & Discussion|
Heishiro Kanagawa (University College London, UK)
Title: A Kernel Stein Test for Comparing Latent Variable Models
Abstract: I will present a nonparametric, kernel-based test to assess the relative goodness of fit of latent variable models with intractable unnormalized densities. The test generalises the kernel Stein discrepancy (KSD) tests of (Liu et al., 2016, Chwialkowski et al., 2016, Yang et al., 2018, Jitkrittum et al., 2018) which required exact access to unnormalized densities. It relies on the simple idea of using an approximate observed-variable marginal in place of the exact, intractable one. As our main theoretical contribution, we prove that the new test, with a properly corrected threshold, has a well-controlled type-I error. In the case of models with low-dimensional latent structure and high-dimensional observations, our test significantly outperforms the relative maximum mean discrepancy test (Bounliphone et al., 2015), which cannot exploit the latent structure.
Shin-Itiro Goto (Institute of Statistical Mathematics, Japan)
Title: Information and Contact Geometries for Expectation Variables Exactly Derived From a Class of Master Equations
Abstract: Information geometry is a discipline that studies differential geometric aspects of statistics, and has contributed to progress in mathematics and engineering applications including Monte-Carlo simulation techniques. Monte-Carlo techniques are formulated based on the theory of Markov chains, where Markov chains are modeled as master equations that have been studied in statistical mechanics and thermodynamics. Contact geometry is known as an odd-dimensional counterpart of symplectic geometry, and has been applied to build differential geometric statistical mechanics and thermodynamics. Although such applications exist in the literature, many pure mathematical findings in contact geometry have not yet been applied. Since some mathematical ideas, including Legendre transform and conjugate variables, are commonly used in thermodynamics, contact geometry, and information geometry, an amalgamation of these geometries is expected to be fruitful in the studies of thermodynamics and Monte-Carlo techniques. Thus, how theorems found in these differential geometries can be used should be explored in the application areas above. In this talk we propose a class of continuous-time master equations, and show how information-contact geometric tools can be used. Here this class is simple enough to exactly derive a dynamical system for expectation variables from the master equations, and allows to discuss a relaxation process in a differential geometric manner.
Wenkai Xu (University College London, UK)
Title: A Stein Goodness-of-fit Test for Directional Distributions
Abstract: In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose non-parametric goodness-of-fit testing procedures for general directional distributions based on kernel Stein discrepancy. Our method is based on Stein’s operator on spheres, which is derived by using Stokes’ theorem. Notably, the proposed method is applicable to distributions with an intractable normalization constant, which commonly appear in directional statistics. Experimental results demonstrate that the proposed methods control type-I error well and have larger power than existing tests, including the test based on the maximum mean discrepancy.
Richard Gerlach (University of Sydney, Australia)
Title: A Semi-parametric Realized Joint Value-at-Risk and Expected Shortfall Regression Framework
Abstract: A new realized joint Value-at-Risk (VaR) and expected shortfall (ES) regression framework is proposed, through incorporating a measurement equation into the original joint VaR and ES regression model of Taylor (2017). The measurement equation models the contemporaneous dependence between the realized measure (e.g. Realized Variance and Realized Range) and the latent conditional quantile. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood estimator through simulation study. In a forecasting study, the proposed models are applied to 7 market indices and 7 individual assets, compared to a range of parametric, non-parametric and semi-parametric models, including GARCH, Realized-GARCH, conditional autoregressive Expectile and Taylor (2017) joint VaR and ES quantile regression models, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed models, especially when incorporating the sub-sampled Realized Variance and the sub-sampled Realized Range in the model.
Pavel Shevchenko (Macquarie University, Australia)
Title: Bias-corrected Least Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems
Abstract: The Least-Squares Monte Carlo (LSMC) method has gained popularity in recent years due to its ability to handle multi-dimensional stochastic control problems, including problems with state variables affected by control. However, when applied to the stochastic control problems in the multi-period expected utility models, the regression fit tends to contain errors which accumulate over time and typically blow up the numerical solution. In this study we propose to transform the value function of the problems to improve the regression fit, and then using either the smearing estimate or smearing estimate with controlled heteroskedasticity to avoid the re-transformation bias in the estimates of the conditional expectations calculated in the LSMC algorithm. We also present and utilise recent improvements in the LSMC algorithms such as control randomisation with policy iteration to avoid accumulation of regression errors over time. Presented numerical examples demonstrate that transformation method leads to an accurate solution. In addition, in the forward simulation stage of the control randomisation algorithm, we propose a re-sampling of the state and control variables in their full domain at each time t and then simulating corresponding state variable at t+1, to improve the exploration of the state space that also appears to be critical to obtain a stable and accurate solution for the expected utility models.
Takeru Matsuda (University of Tokyo, Japan)
Title: Information Criteria for Non-Normalized Models
Abstract: Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general non-normalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are derived as approximately unbiased estimators of discrepancy measures for non-normalized models. Experimental results demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner. Extension to a finite mixture of non-normalized models is also discussed.
Daisuke Murakami (Institute of Statistical Mathematics, Japan)
Title: A Scalable Spatial Additive Modeling for Large Dataset
Abstract: Regression problem for large samples is now commonplace, and fast and memory-efficient egression models accommodating group effects, non-linear effects, and other effects are increasingly important. This study develops a spatial additive regression approach for large samples. Therein, we developed an algorithm estimating spatial and non-spatial effects whose computational complexity and memory consumption are independent of the sample size after pre-conditioning. The performance of the developed approach is examined through Monte Carlo simulation experiments and empirical application.
Popular lunch spots around ISM:
The Institute of Statistical Mathematics (ISM) is in Tachikawa (立川), situated in the western portion of Tokyo Metropolis. Tokyo has two international airports: Narita (成田) and Haneda (羽田). Airport limousine bus services to Tachikawa are available at both airports:
Tickets can be purchased at the Bus Ticket Counter in the arrival hall. On the bus, each approaching stop will be announced in English. Once you arrive at the Tachikawa Station or the Palace Hotel (if you are from Narita) you may take a short taxi ride to the ISM (統計数理研究所) by showing the driver the following address:
This workshop is supported by the Risk Analysis Research Center, Institute of Statistical Mathematics.