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Seminar on Probability and Statistics
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
| Organizer(s) | Nakahiro Yoshida, Teppei Ogihara, Yuta Koike |
|---|
Seminar information archive
2015/01/16
14:00-15:30 Room #052 (Graduate School of Math. Sci. Bldg.)
Ajay Jasra (National University of Singapore)
A stable particle filter in high-dimensions
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html
Ajay Jasra (National University of Singapore)
A stable particle filter in high-dimensions
[ Abstract ]
We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.
This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).
[ Reference URL ]We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.
This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html
2014/11/26
16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)
KATAYAMA, Shota (Tokyo Institute of Technology)
Sparse and robust linear regression: Iterative algorithm and its statistical convergence
KATAYAMA, Shota (Tokyo Institute of Technology)
Sparse and robust linear regression: Iterative algorithm and its statistical convergence
2014/11/11
16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)
Terada, Yoshikazu (CiNet / Center for Information and Neural Networks)
Local Ordinal Embedding
Terada, Yoshikazu (CiNet / Center for Information and Neural Networks)
Local Ordinal Embedding
2014/11/04
16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)
YANAGIHARA, Hirokazu (Graduate School of Science, Hiroshima University)
Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption
YANAGIHARA, Hirokazu (Graduate School of Science, Hiroshima University)
Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption
2014/05/20
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Maximum likelihood type estimation of diffusion processes with non synchronous observations contaminated by market microstructure noise (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Maximum likelihood type estimation of diffusion processes with non synchronous observations contaminated by market microstructure noise (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/02.html
2014/05/13
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Selma Chaker (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html
Selma Chaker (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
[ Abstract ]
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
[ Reference URL ]Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/01.html
2014/04/08
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Alexandre Brouste (Universite du Maine, France)
Parametric estimation in fractional Ornstein-Uhlenbeck process (ENGLISH)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/00.html
Alexandre Brouste (Universite du Maine, France)
Parametric estimation in fractional Ornstein-Uhlenbeck process (ENGLISH)
[ Abstract ]
Several statistical models that imply the fractional Ornstein-Uhlenbeck (fOU) process will be presented: direct observations of the process or partial observations in an additive independent noise, continuous observations or discrete observations. In this different settings, we exhibit large sample (or high-frequency) asymptotic properties of the estimators (maximum likelihood estimator, quadratic variation based estimator, moment estimator, …) for all parameters of interest of the fOU. We also illustrate our results with the R package yuima.
[ Reference URL ]Several statistical models that imply the fractional Ornstein-Uhlenbeck (fOU) process will be presented: direct observations of the process or partial observations in an additive independent noise, continuous observations or discrete observations. In this different settings, we exhibit large sample (or high-frequency) asymptotic properties of the estimators (maximum likelihood estimator, quadratic variation based estimator, moment estimator, …) for all parameters of interest of the fOU. We also illustrate our results with the R package yuima.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/00.html
2013/12/04
13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)
HINO, Hideitsu (University of Tsukuba)
A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html
HINO, Hideitsu (University of Tsukuba)
A quantile-based likelihood estimator for information theoretic clustering (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html
2013/11/27
13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)
TAKEUCHI, Atsushi (Osaka City University)
Density of solutions to stochastic functional differential equations (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/08.html
TAKEUCHI, Atsushi (Osaka City University)
Density of solutions to stochastic functional differential equations (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/08.html
2013/11/20
13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)
NOMURA, Ryosuke (Graduate school of Mathematical Sciences, Univ. of Tokyo)
TD法における価値関数への収束アルゴリズム (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/07.html
NOMURA, Ryosuke (Graduate school of Mathematical Sciences, Univ. of Tokyo)
TD法における価値関数への収束アルゴリズム (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/07.html
2013/11/11
14:50-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)
NINOMIYA, Yoshiyuki (Kyusyu University)
LASSO に対する AIC タイプの情報量規準 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html
NINOMIYA, Yoshiyuki (Kyusyu University)
LASSO に対する AIC タイプの情報量規準 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html
2013/10/25
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
MURATA, Noboru (Waseda University)
Sparse coding and structured dictionary learning (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/05.html
MURATA, Noboru (Waseda University)
Sparse coding and structured dictionary learning (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/05.html
2013/10/23
13:00-15:30 Room #006 (Graduate School of Math. Sci. Bldg.)
Mark Podolskij (Universität Heidelberg)
Limit theorems for ambit processes (ENGLISH)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/04.html
Mark Podolskij (Universität Heidelberg)
Limit theorems for ambit processes (ENGLISH)
[ Abstract ]
We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.
本講演は数物フロンティア・リーディング大学院のレクチャーとして行います.
[ Reference URL ]We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.
本講演は数物フロンティア・リーディング大学院のレクチャーとして行います.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/04.html
2013/10/16
13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)
NAKATANI, Tomoaki (Hokkaido University)
統計解析環境Rにおける多変量GARCHモデルの推定とパッケージ化 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/03.html
NAKATANI, Tomoaki (Hokkaido University)
統計解析環境Rにおける多変量GARCHモデルの推定とパッケージ化 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/03.html
2013/07/04
14:50-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)
SUZUKI, Taiji (Tokyo Institute of Technology)
低ランク行列推定におけるベイズ推定法の性質 (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/02.html
SUZUKI, Taiji (Tokyo Institute of Technology)
低ランク行列推定におけるベイズ推定法の性質 (JAPANESE)
[ Abstract ]
真のパラメータが低ランク行列の構造を持つような低ランク行列推定問題を考える. 低ランク行列推定問題の例としては,低ランク行列の一部が見えている時にその残りを 推定する行列補完の問題などがある.応用としてはユーザへの推薦システムなどがある. これまでの理論解析は主にスパース正則化を用いた経験誤差最小化を対象としてきたが, 本発表ではベイズ法を考え,その統計的性質を調べる.ベイズ法においては, 正則化付き経験誤差最小化による方法とは異なるやや緩い仮定のもと, ほぼ最適な収束レートが導けることを示す.また,テンソル型データ (多次元アレイデータ)へも同様の議論が拡張可能であることも述べる.
[ Reference URL ]真のパラメータが低ランク行列の構造を持つような低ランク行列推定問題を考える. 低ランク行列推定問題の例としては,低ランク行列の一部が見えている時にその残りを 推定する行列補完の問題などがある.応用としてはユーザへの推薦システムなどがある. これまでの理論解析は主にスパース正則化を用いた経験誤差最小化を対象としてきたが, 本発表ではベイズ法を考え,その統計的性質を調べる.ベイズ法においては, 正則化付き経験誤差最小化による方法とは異なるやや緩い仮定のもと, ほぼ最適な収束レートが導けることを示す.また,テンソル型データ (多次元アレイデータ)へも同様の議論が拡張可能であることも述べる.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/02.html
2013/06/18
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
MASUDA, Hiroki (Institute of Mathematics for Industry, Kyushu University)
Locally stable distribution approximation of high-frequency data (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/01.html
MASUDA, Hiroki (Institute of Mathematics for Industry, Kyushu University)
Locally stable distribution approximation of high-frequency data (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/01.html
2013/05/17
13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)
SEI, Tomonari (Department of Mathematics, Keio University)
Computing the normalizing constant of the Bingham family by the holonomic gradient method (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/00.html
SEI, Tomonari (Department of Mathematics, Keio University)
Computing the normalizing constant of the Bingham family by the holonomic gradient method (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/00.html
2013/03/07
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
MAESONO, Yoshihiko (Kyushu University)
Smoothing of sign test and approximation of its p-value (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/16.html
MAESONO, Yoshihiko (Kyushu University)
Smoothing of sign test and approximation of its p-value (JAPANESE)
[ Abstract ]
In this talk we discuss theoretical properties of smoothed sign test, which based on a kernel estimator of the underlying distribution function of data. We show the smoothed sign test is equivalent to the usual sign test in the sense of Pitman efficiency, and its main term of the variance does not depend on the distribution of the population, under the null hypothesis. Though smoothed sign test is not distribution-free, we can obtain Edgeworth expansion which does not depend on the distribution. This is a joint work with Ms. Mengxin Lu of Kyushu University.
[ Reference URL ]In this talk we discuss theoretical properties of smoothed sign test, which based on a kernel estimator of the underlying distribution function of data. We show the smoothed sign test is equivalent to the usual sign test in the sense of Pitman efficiency, and its main term of the variance does not depend on the distribution of the population, under the null hypothesis. Though smoothed sign test is not distribution-free, we can obtain Edgeworth expansion which does not depend on the distribution. This is a joint work with Ms. Mengxin Lu of Kyushu University.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/16.html
2013/03/05
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
TANAKA, Fuyuhiko (University of Tokyo)
ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/15.html
TANAKA, Fuyuhiko (University of Tokyo)
ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/15.html
2013/02/07
11:00-12:10 Room #006 (Graduate School of Math. Sci. Bldg.)
Stefano M. Iacus (Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)
On L^p model selection for discretely observed diffusion processes (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html
Stefano M. Iacus (Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)
On L^p model selection for discretely observed diffusion processes (JAPANESE)
[ Abstract ]
The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ Reference URL ]The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html
2013/01/28
13:00-14:10 Room #006 (Graduate School of Math. Sci. Bldg.)
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
[ Abstract ]
A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ Reference URL ]A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
2012/12/07
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
TANAKA, Kentaro (Tokyo Institute of Technology)
Conditional Independence and Linear Algebra (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/12.html
TANAKA, Kentaro (Tokyo Institute of Technology)
Conditional Independence and Linear Algebra (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/12.html
2012/11/30
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
YATA, Kazuyoshi (Institute of Mathematics, University of Tsukuba)
Effective PCA for high-dimensional, non-Gaussian data under power spiked model (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/11.html
YATA, Kazuyoshi (Institute of Mathematics, University of Tsukuba)
Effective PCA for high-dimensional, non-Gaussian data under power spiked model (JAPANESE)
[ Abstract ]
In this talk, we introduce a general spiked model called the power spiked model in high-dimensional settings. We first consider asymptotic properties of the conventional estimator of eigenvalues under the power spiked model. We give several conditions on the dimension $p$, the sample size $n$ and the high-dimensional noise structure in order to hold several consistency properties of the estimator. We show that the estimator is affected by the noise structure, directly, so that the estimator becomes inconsistent for such cases. In order to overcome such difficulties in a high-dimensional situation, we develop new PCAs called the noise-reduction methodology and the cross-data-matrix methodology under the power spiked model. This is a joint work with Prof. Aoshima (University of Tsukuba).
[ Reference URL ]In this talk, we introduce a general spiked model called the power spiked model in high-dimensional settings. We first consider asymptotic properties of the conventional estimator of eigenvalues under the power spiked model. We give several conditions on the dimension $p$, the sample size $n$ and the high-dimensional noise structure in order to hold several consistency properties of the estimator. We show that the estimator is affected by the noise structure, directly, so that the estimator becomes inconsistent for such cases. In order to overcome such difficulties in a high-dimensional situation, we develop new PCAs called the noise-reduction methodology and the cross-data-matrix methodology under the power spiked model. This is a joint work with Prof. Aoshima (University of Tsukuba).
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/11.html
2012/11/09
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
HIROSE, Kei (Graduate School of Engineering Science, Osaka University)
Tuning parameter selection in sparse regression modeling (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
HIROSE, Kei (Graduate School of Engineering Science, Osaka University)
Tuning parameter selection in sparse regression modeling (JAPANESE)
[ Abstract ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ Reference URL ]In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
2012/10/26
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
HIROSE, Kei (Graduate School of Engineering Science, Osaka University)
Tuning parameter selection in sparse regression modeling (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
HIROSE, Kei (Graduate School of Engineering Science, Osaka University)
Tuning parameter selection in sparse regression modeling (JAPANESE)
[ Abstract ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ Reference URL ]In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
