latent models of stepping and ramping an update on the
play

Latent models of stepping and ramping: an update on (the debate - PowerPoint PPT Presentation

Sep 09, 2022 •391 likes •884 views

Latent models of stepping and ramping: an update on (the debate over) single-trial dynamics in LIP Jonathan Pillow Princeton Neuroscience Institute, Princeton University Comp. Neurosci. Workshop: Computation, Cognition and the Brain

  1. Latent models of stepping and ramping: 
 an update on (the debate over) 
 single-trial dynamics in LIP Jonathan Pillow Princeton Neuroscience Institute, Princeton University Comp. Neurosci. Workshop: Computation, Cognition and the Brain Rutgers University May 30, 2018

  2. “random dots” decision-making task fixed duration or RT fixate targets motion saccade RF

  3. “random dots” decision-making task fixed duration or RT fixate targets motion saccade RF Q : what are the latent dynamics of spike trains in LIP during sensory evidence accumulation?

  4. What do we mean by latent dynamics? “direct” sensory 
 encoding model sensory s stimulus spike spike r response response e.g., “LN” cascade: nonlinearity stimulus filter

  5. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  6. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  7. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  8. <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> What do we mean by latent dynamics? latent dynamical model sensory ... ... s t-1 s t s t+1 stimulus latent 
 dynamics noisy x t-1 x t x t+1 ... trajectory ... r t-1 r t r t+1 ... spike spike response response observations dynamics probability of data: dx 1 dx 2 · · · dx T

  9. Classic account: drift-diffusion model (DDM) • neuron integrates motion “evidence” Accumulated evidence [logLR] time [Gold & Shadlen 2007]

  10. Classic account: drift-diffusion model (DDM) • neuron integrates motion “evidence” LIP response ... IN [spikes/sec] Roitman & Shadlen, 2002 Gold & Shadlen, 2002 = Huk & Shadlen, 2005 Yang & Shadlen, 2007 Accumulated Churchland & Shadlen, 2008 evidence OUT ... [logLR] time [sec]

  11. normative modeling approach: what LIP neurons ought to do, based on a theory of “optimal” decision-making examples : • log-probability (Shadlen & Newsome 1996) • expected utility (Platt & Glimcher 1999) • posterior probability (Beck et al 2008) • change in the RL value function (Seo, Barraclough, & Lee 2009) descriptive modeling approach: • find most accurate statistical description of spike responses • agnostic about function (“l et the data speak for themselves”) example : • variance of conditional expectation (varCE) - (Churchland et al 2011)

  12. classical analysis of LIP responses motion on IN motion sp/s OUT motion sp/s [Shadlen & Newsome, 2001]

  13. but what are the dynamics on single trials? motion on IN motion spike train • averaging obscures sp/s single-trial dynamics noisy “ramping” our goal: 
 infer latent dynamics from spike trains discrete stepping

  14. Chapter 1: Formalizing the models [Latimer et al 2015]

  15. ramping (“diffusion-to-bound”) model noise variance bound height slope initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: spiking:

  16. ramping (“diffusion-to-bound”) model noise variance bound height initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: spiking:

  17. ramping (“diffusion-to-bound”) model noise variance bound height initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: , , 8 model parameters: spiking:

  18. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times latent

  19. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times latent

  20. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times 14 parameters: latent

  21. Fitting: difficult for both models coherence parameters likelihood: 60 bound spike rate (Hz) requires summing over all 30 possible latent paths specified by model • Bayesian inference: use MCMC to compute this integral [Latimer et al 2015]

  22. Which model is better? Q: how to compare models with different numbers of parameters? naively, more parameters ⟹ more flexibility to fit the data • but with too many parameters, we will overfit (fit noise in data)!

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

1 Latent variable models In the next section we will discuss latent variable models for

1 Latent variable models In the next section we will discuss latent variable models for

Statistical Modeling and Analysis of Neural Data (NEU 560) Princeton University, Spring 2018 Jonathan Pillow Lecture 16 notes: Latent variable models and EM Tues, 4.10 1 Latent variable models In the next section we will discuss latent

271 views • 4 slides
Latent Variable Models CS3750 Xiaoting Li 1 Out utli line Latent Variable Models

Latent Variable Models CS3750 Xiaoting Li 1 Out utli line Latent Variable Models

2/4/2020 Latent Variable Models CS3750 Xiaoting Li 1 Out utli line Latent Variable Models Expectation Maximization Algorithm (EM) Factor Analysis Probabilistic Principal Component Analysis Model Formulation Maximum

654 views • 18 slides
Part III: Latent Tree Models Le Song ICML 2012 Tutorial on Spectral Algorithms for Latent

Part III: Latent Tree Models Le Song ICML 2012 Tutorial on Spectral Algorithms for Latent

Spectral Algorithms for Latent Variable Models Part III: Latent Tree Models Le Song ICML 2012 Tutorial on Spectral Algorithms for Latent Variable Models, Edinburgh, UK Joint work with Mariya Ishteva, Ankur Parikh, Eric Xing, Byron Boots , Geoff

548 views • 40 slides
Examples and Implementations [Bayesian approach to Latent Class Models: Definition, Simulation,

Examples and Implementations [Bayesian approach to Latent Class Models: Definition, Simulation,

BIOSTAT 830 GRAPHICAL MODELS Problem Set 4 Case Study: Latent Class Models Note: 1. Due 11:59PM, December 21, 2016. 2. Electronic submission to your instructors email. 3. You are VERY MUCH encouraged to form teams to discuss proofs and

545 views • 3 slides
Learning Overcomplete Latent Variable Models through Tensor Methods Anima Anandkumar UC Irvine

Learning Overcomplete Latent Variable Models through Tensor Methods Anima Anandkumar UC Irvine

Learning Overcomplete Latent Variable Models through Tensor Methods Anima Anandkumar UC Irvine Joint work with Majid Janzamin Rong Ge UC Irvine Microsoft Research Latent Variable Probabilistic Models Latent (hidden) variable h R k ,

769 views • 47 slides
C unobserved construct (e.g. Disordered v. Non- Disordered) Latent classes are mutually

C unobserved construct (e.g. Disordered v. Non- Disordered) Latent classes are mutually

University of Ulster at Magee, Friday 15 th June 2012 Latent Transition Analysis Overview of latent class and Dr Oliver Perra latent transition models Institute of Child Care Research Queens University Belfast email : o.perra@qub.ac.uk

812 views • 38 slides
Chapter 4: Advanced IR Models 4.1 Probabilistic IR 4.2 Statistical Language Models (LMs) 4.3

Chapter 4: Advanced IR Models 4.1 Probabilistic IR 4.2 Statistical Language Models (LMs) 4.3

Chapter 4: Advanced IR Models 4.1 Probabilistic IR 4.2 Statistical Language Models (LMs) 4.3 Latent-Concept Models 4.3.1 Foundations from Linear Algebra 4.3.2 Latent Semantic Indexing (LSI) 4.3.3 Probabilistic Aspect Model (pLSI) 4-1 IRDM

330 views • 32 slides
Learning Latent Variable Models through Tensor Methods Anima Anandkumar U.C. Irvine Challenges

Learning Latent Variable Models through Tensor Methods Anima Anandkumar U.C. Irvine Challenges

Learning Latent Variable Models through Tensor Methods Anima Anandkumar U.C. Irvine Challenges in Unsupervised Learning Learn a latent variable model without labeled examples. E.g. topic models, hidden Markov models, Gaussian mixtures,

763 views • 61 slides
Outline Latent Variable Generative Models Cooperative Vector Quantizer Model Model

Outline Latent Variable Generative Models Cooperative Vector Quantizer Model Model

2/4/2020 CS 3750 Advanced Machine Learning Latent Variable Generative Models II Ahmad Diab AHD23@cs.pitt.edu Feb 4, 2020 Based on slides of Professor Milos Hauskrecht Outline Latent Variable Generative Models Cooperative Vector

435 views • 20 slides
Models for Replicated Discrimination Tests: A Synthesis of Latent Class Mixture Models and

Models for Replicated Discrimination Tests: A Synthesis of Latent Class Mixture Models and

Models for Replicated Discrimination Tests Models for Replicated Discrimination Tests: A Synthesis of Latent Class Mixture Models and Generalized Linear Mixed Models Rune Haubo Bojesen Christensen &amp; Per Bruun Brockhoff DTU Informatics

868 views • 21 slides
Case Study: Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested

Case Study: Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested

Case Study: Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations BIOSTAT830: Graphical Models December 08, 2016 Introduction - INLA Inference for latent Gaussian Markov random field

605 views • 35 slides
Latent Class Models: The Latent Class Logit Model Accouting for unobserved heterogeneity:

Latent Class Models: The Latent Class Logit Model Accouting for unobserved heterogeneity:

Latent Class Models: The Latent Class Logit Model Accouting for unobserved heterogeneity: Accouting for unobserved heterogeneity: Random Parameters Parametric assumption: must specify the functional form of the mixing distribution (for

190 views • 8 slides
Models for Retrieval Models for Retrieval 1. HMM/N-gram-based 2. Latent Semantic Indexing (LSI)

Models for Retrieval Models for Retrieval 1. HMM/N-gram-based 2. Latent Semantic Indexing (LSI)

Models for Retrieval Models for Retrieval 1. HMM/N-gram-based 2. Latent Semantic Indexing (LSI) 3. Probabilistic Latent Semantic Analysis (PLSA) Berlin Chen 2003 References: 1. Berlin Chen et al., An HMM/N-gram-based Linguistic Processing

723 views • 47 slides
ramping impacts and proposed resolution September 2019 Aggregate ramping issues with gate-

ramping impacts and proposed resolution September 2019 Aggregate ramping issues with gate-

RC_2017_02: Aggregate ramping impacts and proposed resolution September 2019 Aggregate ramping issues with gate- closure The WEM Rules ensure that generation equals the demand forecast at the last second of the Trading Interval Balance

557 views • 10 slides
Piecewise Bounds for Estimating Bernoulli- Logistic Latent Gaussian Models Mohammad Emtiyaz Khan

Piecewise Bounds for Estimating Bernoulli- Logistic Latent Gaussian Models Mohammad Emtiyaz Khan

Piecewise Bounds for Estimating Bernoulli- Logistic Latent Gaussian Models Mohammad Emtiyaz Khan Joint work with Benjamin Marlin, and Kevin Murphy University of British Columbia June 29, 2011 Piecewise Bounds for Binary Latent Gaussian Models

694 views • 34 slides
Pengtao Xie Joint work with Yuntian Deng and Eric Xing Carnegie Mellon University 1 Latent

Pengtao Xie Joint work with Yuntian Deng and Eric Xing Carnegie Mellon University 1 Latent

Mutual Angular Regularization of Latent Variable Models: Theory, Algorithm and Applications Pengtao Xie Joint work with Yuntian Deng and Eric Xing Carnegie Mellon University 1 Latent Variable Models (LVMs) Machine Learning Latent Variable

1.04k views • 47 slides
Attention, Binding, and Consciousness 1. Perceptual binding, dynamic binding 2. Neural

Attention, Binding, and Consciousness 1. Perceptual binding, dynamic binding 2. Neural

4/22/17 Attention, Binding, and Consciousness 1. Perceptual binding, dynamic binding 2. Neural Correlates of Consciousness: Binocular rivalry 3. Attention vs. consciousness 4. Binding revisited: Split-brain, split-consciousness 2 1

404 views • 21 slides
Learning and Optimization: Lower Bounds and Tight Connections Nati Srebro TTI-Chicago On The

Learning and Optimization: Lower Bounds and Tight Connections Nati Srebro TTI-Chicago On The

Learning and Optimization: Lower Bounds and Tight Connections Nati Srebro TTI-Chicago On The Universality of Online Mirror Descent S, Karthik Sridharan (UPenn), Ambuj Tewari (Michigan), NIPS11 Learning from an Optimization Viewpoint Karthik

682 views • 25 slides
Static analysis of numerical programs Sylvie Putot with Eric Goubault, Franck V edrine and

Static analysis of numerical programs Sylvie Putot with Eric Goubault, Franck V edrine and

Static analysis of numerical programs Sylvie Putot with Eric Goubault, Franck V edrine and Karim Tekkal (Digiteo) Laboratory for the Modelling and Analysis of Interacting Systems, CEA LIST RAIM09: 3es Rencontres Arithm etique de

204 views • 19 slides
Financial Help for Forest Landowners: Landowner Incentive Program Overview Presented by: Brett

Financial Help for Forest Landowners: Landowner Incentive Program Overview Presented by: Brett

KING CONSERVATION DISTRICT Financial Help for Forest Landowners: Landowner Incentive Program Overview Presented by: Brett Anderson, Forest Stewardship Planner Todays webinar outline: KCD as an organization The who KCD Forest

519 views • 24 slides
Robustness of the Young/Daly formula for stochastic iterative applications Yishu Du 1 , 2 Loris

Robustness of the Young/Daly formula for stochastic iterative applications Yishu Du 1 , 2 Loris

Robustness of the Young/Daly formula for stochastic iterative applications Yishu Du 1 , 2 Loris Marchal 2 Guillaume Pallez 3 Yves Robert 2 , 4 1 Tongji University, China 2 CNRS, ENS Lyon and Inria, France 3 Inria and University of Bordeaux, France

820 views • 34 slides
Supports and approximation properties in Lipschitz-free spaces Eva Perneck a Czech Technical

Supports and approximation properties in Lipschitz-free spaces Eva Perneck a Czech Technical

Lipschitz-free spaces Supports Approximation properties Supports and approximation properties in Lipschitz-free spaces Eva Perneck a Czech Technical University, Prague Workshop on Banach spaces and Banach lattices Madrid, September 2019

1.14k views • 83 slides
Concentration for Coulomb gases and Coulomb transport inequalities Myl` ene Ma da U.

Concentration for Coulomb gases and Coulomb transport inequalities Myl` ene Ma da U.

Concentration for Coulomb gases and Coulomb transport inequalities Myl` ene Ma da U. Lille, Laboratoire Paul Painlev e Joint work with Djalil Chafa and Adrien Hardy U. Paris-Dauphine and U. Lille ICERM, Providence - February

769 views • 58 slides
Protection of Arithmetic Circuits against Physical Attacks Arnaud Tisserand CNRS, Lab-STICC LIP

Protection of Arithmetic Circuits against Physical Attacks Arnaud Tisserand CNRS, Lab-STICC LIP

Protection of Arithmetic Circuits against Physical Attacks Arnaud Tisserand CNRS, Lab-STICC LIP Lyon, 2018.11.09 Summary Introduction Physical Attacks Arithmetic Circuits Protections Conclusion and References Arnaud

594 views • 46 slides

More recommend