determinantal point process models and statistical
play

Determinantal point process models and statistical inference Fr ed - PowerPoint PPT Presentation

Apr 24, 2023 •430 likes •1.31k views

Introduction Definition Stationary models Approximation Inference Conclusion Determinantal point process models and statistical inference Fr ed eric Lavancier , Laboratoire de Math ematiques Jean Leray, Nantes (France) Joint work

  1. Introduction Definition Stationary models Approximation Inference Conclusion Determinantal point process models and statistical inference Fr´ ed´ eric Lavancier , Laboratoire de Math´ ematiques Jean Leray, Nantes (France) Joint work with Jesper Møller (Aalborg University, Danemark) and Ege Rubak (Aalborg University, Danemark). Some recent results with Christophe Biscio (Nantes).

  2. Introduction Definition Stationary models Approximation Inference Conclusion 1 Introduction 2 Definition, existence and basic properties 3 Parametric stationary models 4 Approximation and modelling of the eigen expansion 5 Inference 6 Examples of real data 7 Conclusion and references

  3. Introduction Definition Stationary models Approximation Inference Conclusion Examples of point pattern datasets ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● (a) Spanish towns (b) Kidney cells of (c) Japanese pines two types (hamster)

  4. Introduction Definition Stationary models Approximation Inference Conclusion First look at DPPs Determinantal point processes (DPPs): a class of repulsive (or regular, or inhibitive) point processes. Some examples : ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● DPP with Poisson DPP stronger repulsion

  5. Introduction Definition Stationary models Approximation Inference Conclusion First look at DPPs Determinantal point processes (DPPs): a class of repulsive (or regular, or inhibitive) point processes. Some examples : ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● DPP with Poisson DPP stronger repulsion Statistical motivation : Do DPPs constitute a tractable and flexible class of models for repulsive point processes?

  6. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs Gibbs point processes : The usual class when modelling repulsiveness (e.g. Strauss model, Area interaction model).

  7. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs Gibbs point processes : The usual class when modelling repulsiveness (e.g. Strauss model, Area interaction model). In general: � moments are not expressible in closed form; � likelihoods involve intractable normalizing constants; � elaborate McMC methods are needed for simulations and approximate likelihood inference; � for infinite Gibbs point processes defined on R d , ‘things’ become rather complicated (existence and uniqueness)

  8. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties:

  9. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties: (a) simple conditions for existence;

  10. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties: (a) simple conditions for existence; (b) all orders of moments are known;

  11. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties: (a) simple conditions for existence; (b) all orders of moments are known; (c) the density of the DPP restricted to any compact set S ⊂ R d is expressible on closed form;

  12. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties: (a) simple conditions for existence; (b) all orders of moments are known; (c) the density of the DPP restricted to any compact set S ⊂ R d is expressible on closed form; (d) the DPP on any compact set can easily be simulated;

  13. Introduction Definition Stationary models Approximation Inference Conclusion Gibbs point processes vs DPPs DPPs possess a number of appealing properties: (a) simple conditions for existence; (b) all orders of moments are known; (c) the density of the DPP restricted to any compact set S ⊂ R d is expressible on closed form; (d) the DPP on any compact set can easily be simulated; (e) parametric models are available, and inference can be done by MLEs or using the moments.

  14. Introduction Definition Stationary models Approximation Inference Conclusion Background

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Determinantal point process models and statistical inference Fr ed eric Lavancier ,

Determinantal point process models and statistical inference Fr ed eric Lavancier ,

Introduction Definition Parametric models Approximation Inference Conclusion Determinantal point process models and statistical inference Fr ed eric Lavancier , Laboratoire de Math ematiques Jean Leray, Nantes (France) Joint work

791 views • 57 slides
Statistical aspects of determinantal point processes Fr ed eric Lavancier , Laboratoire de

Statistical aspects of determinantal point processes Fr ed eric Lavancier , Laboratoire de

Introduction Definition Simulation Parametric models Inference Statistical aspects of determinantal point processes Fr ed eric Lavancier , Laboratoire de Math ematiques Jean Leray, Nantes (France) Joint work with Jesper Mller

1.07k views • 91 slides
Statistical aspects of determinantal point processes eric Lavancier , Fr ed Laboratoire de

Statistical aspects of determinantal point processes eric Lavancier , Fr ed Laboratoire de

Introduction Definition Simulation Parametric models Inference Statistical aspects of determinantal point processes eric Lavancier , Fr ed Laboratoire de Math ematiques Jean Leray, Nantes (France) Joint work with Jesper Mller

1k views • 57 slides
Statistical aspects of determinantal point processes Jesper Mller , Department of Mathematical

Statistical aspects of determinantal point processes Jesper Mller , Department of Mathematical

Introduction Definition Simulation Parametric models Inference Statistical aspects of determinantal point processes Jesper Mller , Department of Mathematical Sciences, Aalborg University. Joint work with Fr ed eric Lavancier,

1.09k views • 79 slides
Determinantal point processes statistical modeling and inference November 27, 2014 Jesper

Determinantal point processes statistical modeling and inference November 27, 2014 Jesper

Determinantal point processes statistical modeling and inference November 27, 2014 Jesper Mller jm@math.aau.dk Department of Mathematical Sciences Aalborg University Denmark Joint work Determinantal point processes on R d : Jesper Mller

1.3k views • 114 slides
Gibbs Sampling from -Determinantal Point Processes Alireza Rezaei University of Washington

Gibbs Sampling from -Determinantal Point Processes Alireza Rezaei University of Washington

Gibbs Sampling from -Determinantal Point Processes Alireza Rezaei University of Washington Based on joint work with Shayan Oveis Gharan Point Process: A distribution on subsets of = {1,2, , } . Determinantal Point Process:

285 views • 12 slides
GDPP Learning Diverse Generations using Determinantal Point Process Mohamed Elfeki , Camille

GDPP Learning Diverse Generations using Determinantal Point Process Mohamed Elfeki , Camille

GDPP Learning Diverse Generations using Determinantal Point Process Mohamed Elfeki , Camille Couprie, Morgane Rivire and Mohamed Elhoseiny * https://github.com/M-Elfeki/GDPP Whats wrong with Generative models? Whats wrong with

576 views • 28 slides
Rates of f Estimation for Dis iscrete Determinantal Point Processes V.-E. Brunel, A. Moitra, P.

Rates of f Estimation for Dis iscrete Determinantal Point Processes V.-E. Brunel, A. Moitra, P.

Rates of f Estimation for Dis iscrete Determinantal Point Processes V.-E. Brunel, A. Moitra, P. Rigollet, J. Urschel COLT 2017, Amsterdam Discrete DPPs Random variables on the hypercube , , represented as subsets of [] .

228 views • 12 slides
Spherical Designs and Determinantal Point Processes Masatake HIRAO ( ) (Aichi

Spherical Designs and Determinantal Point Processes Masatake HIRAO ( ) (Aichi

Spherical Designs and Determinantal Point Processes Masatake HIRAO ( ) (Aichi Prefectural University, Japan) 2015 April 22 Workshop on Spherical Design and Numerical Analysis@SJTU 1.

657 views • 29 slides
Learning Determinantal Processes wit ith Moments and Cycles J. Urschel, V.-E. Brunel, A. Moitra,

Learning Determinantal Processes wit ith Moments and Cycles J. Urschel, V.-E. Brunel, A. Moitra,

Learning Determinantal Processes wit ith Moments and Cycles J. Urschel, V.-E. Brunel, A. Moitra, P. Rigollet ICML 2017, Sydney Determinantal Point Processes (D (DPPs) DPP: Random subset of [] For all ,

281 views • 13 slides
Limit theorems for determinantal point processes Tomoyuki Shirai 1 2 Kyushu University May. 8,

Limit theorems for determinantal point processes Tomoyuki Shirai 1 2 Kyushu University May. 8,

Limit theorems for determinantal point processes Tomoyuki Shirai 1 2 Kyushu University May. 8, 2019 1 Joint work with Makoto Katori (Chuo University) 2 A Probability Conference Random Matrices and Related Topics @KIAS, Seoul, Korea, May

540 views • 37 slides
Determinantal point processes and spaces of holomorphic functions Yanqi Qiu AMSS, Chinese

Determinantal point processes and spaces of holomorphic functions Yanqi Qiu AMSS, Chinese

Determinantal point processes and spaces of holomorphic functions Yanqi Qiu AMSS, Chinese Academy of Sciences; CNRS 2019 Apr 09 Part I. Lyons-Peres completeness conjecture joint with Alexander Bufetov and Alexander Shamov Sets related to

948 views • 43 slides
STA 214: Probability & Statistical Models STA 214: Analysis of Statistical Models

STA 214: Probability & Statistical Models STA 214: Analysis of Statistical Models

STA 214: Probability & Statistical Models STA 214: Analysis of Statistical Models Probability/Statistical Models: Theory prob/math stats Simulation samples of y ( | ) p y Statistical analysis: Computation: Likelihood

250 views • 11 slides
Introduction to Statistical Process Control Statistical Process Control (SPC) uses seven major

Introduction to Statistical Process Control Statistical Process Control (SPC) uses seven major

ST 435/535 Statistical Methods for Quality and Productivity Improvement / Statistical Process Control Introduction to Statistical Process Control Statistical Process Control (SPC) uses seven major tools: Histogram or stem-and-leaf plot; 1

465 views • 14 slides
Basics of Point-Referenced Data Models Basic tool is a spatial process , { Y ( s ) , s D } ,

Basics of Point-Referenced Data Models Basic tool is a spatial process , { Y ( s ) , s D } ,

Basics of Point-Referenced Data Models Basic tool is a spatial process , { Y ( s ) , s D } , where D r Note that time series follows this approach with r = 1 ; we will usually have r = 2 or 3 We begin with essentials of point-level data

616 views • 38 slides
DETERMINANTAL POINT PROCESSES FOR NATURAL LANGUAGE PROCESSING Jennifer Gillenwater Joint work

DETERMINANTAL POINT PROCESSES FOR NATURAL LANGUAGE PROCESSING Jennifer Gillenwater Joint work

DETERMINANTAL POINT PROCESSES FOR NATURAL LANGUAGE PROCESSING Jennifer Gillenwater Joint work with Alex Kulesza and Ben Taskar OUTLINE OUTLINE Motivation & background on DPPs OUTLINE Motivation & background on DPPs Large-scale

1.73k views • 155 slides
Particle Monte Carlo methods in statistical learning and rare event simulation P. Del Moral

Particle Monte Carlo methods in statistical learning and rare event simulation P. Del Moral

Particle Monte Carlo methods in statistical learning and rare event simulation P. Del Moral (INRIA team ALEA) INRIA & Bordeaux Mathematical Institute & X CMAP MCQMC 2012, Sydney, February 13-th 2012 Some hyper-refs Feynman-Kac

1.38k views • 63 slides
An introduction to particle rare event simulation P. Del Moral INRIA Bordeaux- Sud Ouest &

An introduction to particle rare event simulation P. Del Moral INRIA Bordeaux- Sud Ouest &

An introduction to particle rare event simulation P. Del Moral INRIA Bordeaux- Sud Ouest & IMB & CMAP Computation of transition trajectories and rare events in non equilibrium systems , ENS Lyon, June 2012 Some hyper-refs

671 views • 54 slides
Specification of Landmarks and Forecasting Water Temperature Water Management in the River

Specification of Landmarks and Forecasting Water Temperature Water Management in the River

Specification of Landmarks and Forecasting Water Temperature Water Management in the River Wupper G oran Kauermann Thomas Mestekemper Center for Statistics University Bielefeld University Bielefeld 14. August 2008 The River Wupper

455 views • 32 slides
Discussion Dean Foster Amazon @ NYC Differential privacy means in statistics language: Fit the

Discussion Dean Foster Amazon @ NYC Differential privacy means in statistics language: Fit the

Discussion Dean Foster Amazon @ NYC Differential privacy means in statistics language: Fit the world not the data. Differential privacy means in statistics language: Fit the world not the data. You shouldnt be able to tell which data set

697 views • 45 slides
BAYESIAN SURFACE SMOOTHING UNDER ANISOTROPY Subhashish Chakravarty Advisor: Prof. George G.

BAYESIAN SURFACE SMOOTHING UNDER ANISOTROPY Subhashish Chakravarty Advisor: Prof. George G.

BAYESIAN SURFACE SMOOTHING UNDER ANISOTROPY Subhashish Chakravarty Advisor: Prof. George G. Woodworth Co-Advisor: Dr. Matthew A. Bognar April 24, 2007 Subhashish Chakravarty BAYESIAN SURFACE SMOOTHING UNDER ANISOTROPY Objective of the thesis

360 views • 32 slides
Practical Issues in Applications of Multivariate Extreme Values Jonathan Tawn with Caroline

Practical Issues in Applications of Multivariate Extreme Values Jonathan Tawn with Caroline

Practical Issues in Applications of Multivariate Extreme Values Jonathan Tawn with Caroline Keef and Mark Latham Lancaster, UK Two Applications Sea-surge data Modelling of surge process over space for joint flood risk assessment for

505 views • 38 slides
Fusing space-time data under measurement error for computer model output Veronica J. Berrocal (

Fusing space-time data under measurement error for computer model output Veronica J. Berrocal (

Fusing space-time data under measurement error for computer model output Veronica J. Berrocal ( vjb2@stat.duke.edu ) SAMSI joint work with Alan E. Gelfand and David M. Holland Veronica J. Berrocal Fusing space-time data under measurement error

577 views • 46 slides
Heavy rainfall modeling in high dimensions Philippe Naveau naveau@lsce.ipsl.fr Laboratoire des

Heavy rainfall modeling in high dimensions Philippe Naveau naveau@lsce.ipsl.fr Laboratoire des

Intro Metric PAM Spectral Conclusions Heavy rainfall modeling in high dimensions Philippe Naveau naveau@lsce.ipsl.fr Laboratoire des Sciences du Climat et lEnvironnement (LSCE) Gif-sur-Yvette, France joint work with A. Sabourin, E.

841 views • 54 slides

More recommend