WeiYa's Work Yard

A dog, who fell into the ocean of statistics, tries to write down his ideas and notes to save himself.

The General Decision Problem

May 06, 2019

This note is based on Chapter 1 of Lehmann EL, Romano JP. Testing statistical hypotheses. Springer Science & Business Media; 2006 Mar 30.

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Self-normalized Limit Theory and Stein's Method

May 01, 2019

This note consists of the lecture material of STAT 6060 taught by Prof. Shao, four homework (indexed by “Homework”) and several personal comments (indexed by “Note”).

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Identifiability and Estimability

April 20, 2019

Materials from STAT 5030.

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Least Squares for SIMs

April 15, 2019

In the last lecture of STAT 5030, Prof. Lin shared one of the results in the paper, Neykov, M., Liu, J. S., & Cai, T. (2016). L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs. Journal of Machine Learning Research, 17(87), 1–37., or say the start point for the paper—the following Lemma. Because it seems that the condition and the conclusion is completely same with Sliced Inverse Regression, except for a direct interpretation—the least square regression.

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Statistical Inference for Lasso

April 15, 2019

This note is based on the Chapter 6 of Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical Learning with Sparsity. 362..

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Multiple Tracking with Rao-Blackwellized marginal particle filtering

April 10, 2019

This note is for Smal, I., Meijering, E., Draegestein, K., Galjart, N., Grigoriev, I., Akhmanova, A., … Niessen, W. (2008). Multiple object tracking in molecular bioimaging by Rao-Blackwellized marginal particle filtering. Medical Image Analysis, 12(6), 764–777.

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Normalizing Constant

April 10, 2019

Larry discussed the normalizing constant paradox in his blog.

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Methods for Cell Tracking

April 09, 2019

This post is for the survey paper, Meijering, E., Dzyubachyk, O., & Smal, I. (2012). Chapter nine - Methods for Cell and Particle Tracking. In P. M. conn (Ed.), Methods in Enzymology (pp. 183–200).

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Tracking Multiple Interacting Targets via MCMC-MRF

April 09, 2019

This note is for Khan, Z., Balch, T., & Dellaert, F. (2004). An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets. In T. Pajdla & J. Matas (Eds.), Computer Vision - ECCV 2004 (pp. 279–290). Springer Berlin Heidelberg.

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Subgradient

April 08, 2019

This post is mainly based on Hastie et al. (2015), and incorporated with some materials from Watson (1992).

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Wierd Things in Mixture Models

April 04, 2019

This note is based on Larry’s post, Mixture Models: The Twilight Zone of Statistics.

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Coupled Minimum-Cost Flow Cell Tracking

April 02, 2019

This note is for Padfield, D., Rittscher, J., & Roysam, B. (2011). Coupled minimum-cost flow cell tracking for high-throughput quantitative analysis. Medical Image Analysis, 15(4), 650–668..

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Soft Imputation in Matrix Completion

April 01, 2019

This post is based on Chapter 7 of Statistical Learning with Sparsity: The Lasso and Generalizations, and I wrote R program to reproduce the simulations to get a better understanding.

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Frequentist Accuracy of Bayesian Estimates

March 31, 2019

This note is for Efron’s slide: Frequentist Accuracy of Bayesian Estimates, which is recommended by Larry’s post: Shaking the Bayesian Machine.

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FARM-Test

March 29, 2019

This note is for Fan, J., Ke, Y., Sun, Q., & Zhou, W.-X. (2017). FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control. ArXiv:1711.05386 [Stat]..

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Multiple Object Tracking

March 26, 2019

This note is for Luo, W., Xing, J., Milan, A., Zhang, X., Liu, W., Zhao, X., & Kim, T.-K. (2014). Multiple Object Tracking: A Literature Review. ArXiv:1409.7618 [Cs].

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Theoretical Results of Lasso

March 26, 2019

Prof. Jon A. WELLNER introduced the application of a new multiplier inequality on lasso in the distinguish lecture, which reminds me that it is necessary to read more theoretical results of lasso, and so this is the post, which is based on Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical Learning with Sparsity. 362.

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Joint Summarized by Marginal or Conditional?

March 25, 2019

I happened to read Yixuan’s blog about a question related to the course Statistical Inference, whether two marginal distributions can determine the joint distribution. The question is adopted from Exercise 4.47 of Casella and Berger (2002).

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Convergence rates of least squares

March 25, 2019

This note is for Han, Q., & Wellner, J. A. (2017). Convergence rates of least squares regression estimators with heavy-tailed errors.

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Generalized Gradient Descent

March 20, 2019

I read the topic in kiytay’s blog: Proximal operators and generalized gradient descent, and then read its reference, Hastie et al. (2015), and write some program to get a better understanding.

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High Dimensional Covariance Matrix Estimation

March 19, 2019

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Functional Data Analysis by Matrix Completion

March 15, 2019

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Functional Data Analysis

March 14, 2019

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Distributed inference for quantile regression processes

March 13, 2019

This note is for Volgushev, S., Chao, S.-K., & Cheng, G. (2019). Distributed inference for quantile regression processes. The Annals of Statistics, 47(3), 1634–1662.

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The Correlated Topic Model

March 12, 2019

This note is for Blei, D. M., & Lafferty, J. D. (2007). A correlated topic model of Science. The Annals of Applied Statistics, 1(1), 17–35.

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Tweedie's Formula and Selection Bias

March 11, 2019

Prof. Inchi HU will give a talk on Large Scale Inference for Chi-squared Data tomorrow, which proposes the Tweedie’s formula in the Bayesian hierarchical model for chi-squared data, and he mentioned a thought-provoking paper, Efron, B. (2011). Tweedie’s Formula and Selection Bias. Journal of the American Statistical Association, 106(496), 1602–1614., which is the focus of this note.

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Bernstein Bounds

March 08, 2019

I noticed that the papers of matrix/tensor completion always talk about the Bernstein inequality, then I picked the Bernstein Bounds discussed in Wainwright (2019).

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Evaluate Variational Inference

March 07, 2019

A brief summary of the post, Eid ma clack shaw zupoven del ba.

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Tensor Completion

March 07, 2019

Prof. YUAN Ming will give a distinguish lecture on Low Rank Tensor Methods in High Dimensional Data Analysis. To get familiar with his work on tensor, I read his paper, Yuan, M., & Zhang, C.-H. (2016). On Tensor Completion via Nuclear Norm Minimization. Foundations of Computational Mathematics, 16(4), 1031–1068., which is the topic of this post.

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Illustrate Path Sampling by Stan Programming

March 06, 2019 0 Comments

This post reviewed the topic of path sampling in the lecture slides of STAT 5020, and noted a general path sampling described by Gelman and Meng (1998), then used a toy example to illustrate it with Stan programming language.

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