M ODEL IS W RONG ?! S. Eguchi, ISM & GUAS. What is MODEL? No Model is True ! Feature of interests can reflect on Model Patterns of interests can incorporate.

Slides:

Advertisements

Similar presentations

Bayesian network classification using spline-approximated KDE Y. Gurwicz, B. Lerner Journal of Pattern Recognition.

Advertisements

Use of Estimating Equations and Quadratic Inference Functions in Complex Surveys Leigh Ann Harrod and Virginia Lesser Department of Statistics Oregon State.

ECE 8443 – Pattern Recognition LECTURE 05: MAXIMUM LIKELIHOOD ESTIMATION Objectives: Discrete Features Maximum Likelihood Resources: D.H.S: Chapter 3 (Part.

Probability and Statistics Basic concepts II (from a physicist point of view) Benoit CLEMENT – Université J. Fourier / LPSC

CS Statistical Machine learning Lecture 13 Yuan (Alan) Qi Purdue CS Oct

Uncertainty and confidence intervals Statistical estimation methods, Finse Friday , 12.45–14.05 Andreas Lindén.

An Overview of Machine Learning

Chap 8: Estimation of parameters & Fitting of Probability Distributions Section 6.1: INTRODUCTION Unknown parameter(s) values must be estimated before.

Model assessment and cross-validation - overview

Likelihood ratio tests

Survival analysis 1 The greatest blessing in life is in giving and not taking.

Raymond J. Carroll Texas A&M University Nonparametric Regression and Clustered/Longitudinal Data.

Part 2b Parameter Estimation CSE717, FALL 2008 CUBS, Univ at Buffalo.

Learning From Data Chichang Jou Tamkang University.

Presenting: Assaf Tzabari

Parametric Inference.

Machine Learning CMPT 726 Simon Fraser University

2. Point and interval estimation Introduction Properties of estimators Finite sample size Asymptotic properties Construction methods Method of moments.

Visual Recognition Tutorial

7. Nonparametric inference  Quantile function Q  Inference on F  Confidence bands for F  Goodness- of- fit tests 1.

The Paradigm of Econometrics Based on Greene’s Note 1.

Part 1: Introduction 1-1/22 Econometrics I Professor William Greene Stern School of Business Department of Economics.

METU Informatics Institute Min 720 Pattern Classification with Bio-Medical Applications PART 2: Statistical Pattern Classification: Optimal Classification.

Binary Variables (1) Coin flipping: heads=1, tails=0 Bernoulli Distribution.

ECE 8443 – Pattern Recognition LECTURE 06: MAXIMUM LIKELIHOOD AND BAYESIAN ESTIMATION Objectives: Bias in ML Estimates Bayesian Estimation Example Resources:

Information geometry of Statistical inference with selective sample S. Eguchi, ISM & GUAS This talk is a part of co-work with J. Copas, University of Warwick.

Introduction and Motivation Approaches for DE: Known model → parametric approach: p(x;θ) (Gaussian, Laplace,…) Unknown model → nonparametric approach Assumes.

Model Inference and Averaging

Fast Max–Margin Matrix Factorization with Data Augmentation Minjie Xu, Jun Zhu & Bo Zhang Tsinghua University.

A statistical model Μ is a set of distributions (or regression functions), e.g., all uni-modal, smooth distributions. Μ is called a parametric model if.

1 Information Geometry on Classification Logistic, AdaBoost, Area under ROC curve Shinto Eguchi – – ISM seminor on 17/1/2001 This talk is based on one.

2. Bayes Decision Theory Prof. A.L. Yuille Stat 231. Fall 2004.

CS 782 – Machine Learning Lecture 4 Linear Models for Classification  Probabilistic generative models  Probabilistic discriminative models.

Empirical Research Methods in Computer Science Lecture 7 November 30, 2005 Noah Smith.

CS Statistical Machine learning Lecture 10 Yuan (Alan) Qi Purdue CS Sept

By Sharath Kumar Aitha. Instructor: Dr. Dongchul Kim.

1 Information Geometry of Self-organizing maximum likelihood Shinto Eguchi ISM, GUAS This talk is based on joint research with Dr Yutaka Kano, Osaka Univ.

An Asymptotic Analysis of Generative, Discriminative, and Pseudolikelihood Estimators by Percy Liang and Michael Jordan (ICML 2008 ) Presented by Lihan.

Lecture 4: Statistics Review II Date: 9/5/02  Hypothesis tests: power  Estimation: likelihood, moment estimation, least square  Statistical properties.

Chapter 7 Point Estimation of Parameters. Learning Objectives Explain the general concepts of estimating Explain important properties of point estimators.

1 Standard error Estimated standard error,s,. 2 Example 1 While measuring the thermal conductivity of Armco iron, using a temperature of 100F and a power.

사업팀 구성 Nonparametric and Semiparametric Function Estimation 비모수적, 준모수적 함수추정 연구팀 ( 서울대학교 통계학과 ) Nonparametric Stochastic.

1 観察研究のための統計推測 - general misspecification model approach - S. Eguchi, ISM & GUAS This talk is a part of co-work with J. Copas, University of Warwick ISM.

Boosted Particle Filter: Multitarget Detection and Tracking Fayin Li.

Chapter 20 Classification and Estimation Classification – Feature selection Good feature have four characteristics: –Discrimination. Features.

29 August 2013 Venkat Naïve Bayesian on CDF Pair Scores.

Histograms h=0.1 h=0.5 h=3. Theoretically The simplest form of histogram B j = [(j-1),j)h.

1 Chapter 8: Model Inference and Averaging Presented by Hui Fang.

Statistical Data Analysis 2011/2012 M. de Gunst Lecture 4.

DENCLUE 2.0: Fast Clustering based on Kernel Density Estimation Alexander Hinneburg Martin-Luther-University Halle-Wittenberg, Germany Hans-Henning Gabriel.

1 Double the confidence region S. Eguchi, ISM & GUAS This talk is a part of co-work with J. Copas, University of Warwick.

Week 21 Order Statistics The order statistics of a set of random variables X 1, X 2,…, X n are the same random variables arranged in increasing order.

Hypothesis Testing Steps for the Rejection Region Method State H 1 and State H 0 State the Test Statistic and its sampling distribution (normal or t) Determine.

LECTURE 05: CLASSIFICATION PT. 1 February 8, 2016 SDS 293 Machine Learning.

Week 21 Statistical Model A statistical model for some data is a set of distributions, one of which corresponds to the true unknown distribution that produced.

Chapter 4. The Normality Assumption: CLassical Normal Linear Regression Model (CNLRM)

1 C.A.L. Bailer-Jones. Machine Learning. Data exploration and dimensionality reduction Machine learning, pattern recognition and statistical data modelling.

Stat 223 Introduction to the Theory of Statistics

Visual Recognition Tutorial

Model Inference and Averaging

Multiple Imputation Using Stata

CONCEPTS OF HYPOTHESIS TESTING

Some Nonparametric Methods

Summarizing Data by Statistics

Pattern Recognition and Machine Learning

Chengyaun yin School of Mathematics SHUFE

Generally Discriminant Analysis

LECTURE 07: BAYESIAN ESTIMATION

Learning From Observed Data

Statistical Model A statistical model for some data is a set of distributions, one of which corresponds to the true unknown distribution that produced.

Presentation transcript:

M ODEL IS W RONG ?! S. Eguchi, ISM & GUAS

What is MODEL? No Model is True ! Feature of interests can reflect on Model Patterns of interests can incorporate into Model Observations can only be made to finite precision ● ● ● Cf. J K Lindsay “ Parametric Statistical Inference ”

Asymptotics on correct model Large sample asymptotics Asymptotic consistency, normality Asymptotic efficiency (Higher-order asymptotics) Non-parametric asymptotics

Outline ● Near-Model Bridge para and non-parametrics Non-efficiency under Near model ● ●

Near model parametric non-parametric near-parametric

Tubular Neighborhood M g

Density estimation Estimate g(y) Kernel estimate

Local Likelihood The main body Localization versions (Eguchi, Copas, 1998)

Local likelihood density estimate Maximum Local Likelihood Estimator The density estimator normalizing const )

h y

Global vs Local likelihood Global (h =  ) Local (h = 3.65) opt

Regression function Estimate  (x) = E(Y|x) GLM Cf.Eguchi,Kim,Park (2002)

Bridge of nonpara / parametric

Discriminant Analysis Input vectorlabel Logistic model Almost logistic model

A class of loss functions For a given data Estimate the score

Logistic loss

Error rate Medical screening where

Empirical loss For a training data score

Estimating function IRLS where Logistic

Asymptotic efficiency Cramer-Rao type （ logistic loss) ．

Risk under correct model Under the correct model Expected D-loss Let

Risk under near model where Let

λ-family Target risk λ-family score

λ (Proof ) opt (Eguchi, Copas, 2002)

Some analysis False positive rate 0.435% 0.423% λ

Conclusions ● Near-Model Bridge para and non-parametrics Non-efficiency under Near model ● ● α-neighborhood

Future project??