Dynamical Systems (in Neuro) Reading List

Scope:

This reading list is mostly centered around the practical application of linear dynamical systems models to predict neural data.

I’ve marked papers I find to be especially useful with [++] or [+]

see the collapsible version of this list here: [collapsible outline]

Table of Contents:

• Shortlist
• Overviews
• Model types
  • (P)LDS
  • HMM
• State estimations
• System identification
• Software tools
• Control
• Stimulus optimization
• Misc.

Shortlist - " I only have time to read 5 papers"

[++] "A new look at state-space models for neural data" (2010) Paninski et al.

[++] "Empirical models of spiking in neural populations " (2011) Macke et al.

[++] "Selective modulation of cortical state during spatial attention" (2016) Engel et al.

• [Supplement] contains excellent methods details, including comparison of HMM to GPFA, and measuring performance as a function of number of discrete states

[++] "Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering" (2004) Eden et al.

[+] "Multiscale modeling and decoding algorithms for spike-field activity" Hsieh … Shanechi

ldsCtrlEst: dynamical system estimation & control library - Stanley Rozell labs:[docs] [code]

• primarily focused on implementing dynamical systems within systems neuroscience experiments

High Level - Overviews, Reviews, Tutorials

[++] "A new look at state-space models for neural data" (2010) Paninski et al.

"State-Space Models for the Analysis of Neural Spike Train and Behavioral Data" (2016) Chen & Brown

• see also: SSPPF - a kalman filter for point-process / spiking

  • [++] "Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering" (2004) Eden et al.

  • "Estimating a state-space model from point process observations" (2003) Smith, Brown

[+] "State-Space Models" (2013) scholarpedia page by Chen & Brown

• discusses model variants, fitting, applications

• has lots of great references

[+] Neuromatch Tutorial: Dynamical Systems in Neuro.

• video lectures + slides
• accompanying python tutorial
• See also a Brain Inspired podcast episode with some of the experts from that course

Tutorial: Statistical models for neural data - Jonathan Pillow [part 1] [part 2] [slides] [code]

"STATS320: Machine Learning Methods for Neural Data Analysis" course by Scott Linderman

• includes code labs:

  • A simple spike sorting algorithm

  • Kilosort: Spike sorting by Deconvolution 

  • CNMF: Calcium deconvolution via constrained NMF

  • DeepLabCut: Markerless pose tracking with CNNs

  • DeepRetina: Deep encoding models of retinal spike trains

  • Kalman Smoothers: Decoding movement from neural data

  • MoSeq: Autoregressive HMMs for animal movements 

  • SLDS: Switching LDS model of neural data

"Math Tools for Neuroscience" - Ella Batty

• video lectures & code tutorials

• great visual explanations

• see especially: Intro to dynamical systems

"Introduction to Dynamical Systems" lecture by Stephen Boyd

additional tutorials on dynamical systems (unvetted)

• Tutorial on Dynamical Systems by Dean, Leach, Shatkay @ Brown University

• Dynamical Systems Tutorial by Gregor Schöner

State-space, dynamical systems model types commonly used in neuro

Note: Most of these approaches fall under the umbrella of “state space models” (SSM)

• (see high-level section)

• This list was assisted / inspired by tables I saw at COSYNE, I believe from Adam Calhoun and Memming Park

• See [[Dimensionality reduction in neural data analysis]] by Patrick Minaeult for a broad and well-motivated discussion of techniques for dimensionality reduction (including dynamical systems) including a recap of taxonomies of models assembled by Cunninham, Park, and Hurwitz et al.

Gaussian Process Factor Analysis (GPFA)

• primarily used for dimensionality reduction

• [++] "Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity" (2009) Yu et al.

• "Temporal alignment and latent Gaussian process factor inference in population spike trains" Duncker & Sahani

• “Tutorial: GPFA (Gaussian Process Factor Analysis)”

Hidden Markov Models (HMM)

• [++] "Hidden Markov Models for the Stimulus-Response Relationships of Multistate Neural Systems" Escola et al.

  • extensive, tutorial style paper

• [++] "Selective modulation of cortical state during spatial attention" (2016) Engel et al.

  • [Supplement] contains excellent methods details, including comparison of HMM to GPFA, and measuring performance as a function of number of discrete states

• "Lecture 12: EM and Hidden Markov Models" - Linderman

  • from Machine Learning Methods for Neural Data Analysis

  • also covers Gaussian (obsv.) HMM

• HMM + guassian observation (GaussianHMM)

  • matlab [code] +[notes] (covers HMM, gHMM, GMM-HMM) - by Qiuqiang Kong

  • HMM + mixture of gaussian observations (GMM-HMM)

    • "HMM & gaussian mixture models" lecture notes by Shimodaira & Renals

linear dynamical systems (LDS)

• Gaussian observations (GLDS)

• Poisson observations (PLDS)

  • [++] "Empiricalmodelsof spiking in neural populations" (2011) Macke et al.

  • fitting toolbox:

    • pop_spike_dyn:This repository contains different methods for linear dynamical system models with Poisson observations.

      • example script: PLDSExample.m

• generalized count (GC LDS) and nonlinear function (fLDS)

  • “High-dimensional neural spike train analysis with generalized count linear dynamical systems” (2015) Gao et al.

  • "Linear dynamical neural population models through nonlinear embeddings" (2016) Gao et al.

• Switched dynamical systems (SLDS) - switches between multiple LDS models to capture distinct regimes of dynamical behavior

  • [+] "Dynamical segmentation of single trials from population neural data" Petreska et al.

  • Recurrent SLDS (rSLDS)

    • “The recurrent SLDS introduces an additional dependency between the discrete and continuous latent states, allowing the discrete state probability to depend upon the previous continuous state” - Linderman

    • [++] "Recurrent switching linear dynamical systems" Linderman et al.

    • "Recurrent Switching Linear Dynamical Systems for Neural and Behavioral Analysis" talk by Linderman

nonlinear / nonparametric / variational approaches (vLGP, LFADS)

• variational latent gaussian process (vLGP)

  • "Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains " (2017) Zhao & Park [code]

  • “Variational Online Learning of Neural Dynamics” Zhao & Park [paper][code]

• Variational Inference for Nonlinear Dynamics (VIND)

  • "Blackboxvariational inference for state space models" (2015) Archer et al.

  • "A Novel Variational Family for Hidden Nonlinear Markov Models" (2018) Hernandez et al.

• Latent Factor Analysis via Dynamical Systems (LFADS)

  • [++] "LFADS - Latent Factor Analysis via Dynamical Systems" Sussillo et al. [code & documentation]

  • LFADS tutorial from the "Computation through Dynamics" group

    • "Inferring single-trial neural population dynamics using sequential auto-encoders" Pandarinath et al.

• See also: Recurrent Neural Networks (RNN)

  • "Recurrent Neural Networks" Lecture slides & references by Adam Willats

(Latent-state) estimation in neuro

see also: SSPPF - a kalman filter for point-process / spiking

• [++] "Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering" (2004) Eden et al.

• "Estimating a state-space model from point process observations" (2003) Smith, Brown

estimation from spikes + local field potentials (LFP)

• [+] "Multiscale modeling and decoding algorithms for spike-field activity" Hsieh … Shanechi

System identification - fitting LDS models:

overviews:

• “System Identification” Lennary Ljung - canonical text on system ID, author is the architect of MATLAB’s sys ID toolbox

  • "Nonlinear System Identification: A User-Oriented Roadmap" Schoukens & Ljung

  • "Perspectives on System Identification" Ljung

• Overview by S.Brunton - "Data-Driven Control: Linear System Identification"

• Lecture notes by K.Pelckmans "System Identification"

• "Subspace Identification for Linear Systems" (1996) Van Overschee & De Moor

• "System Identification Methods" by Brian Douglas, a practical, control-focused overview in easy-to-understand terms

  • see also "Modeling Physical Systems, An Overview"

• "System Identification - Data-Driven Modelling of Dynamic Systems" - Paul Van den Hof

  • extensive, discusses the challenges of identificaiton in closed-loop

  • course page: [link]

    • includes lectures & exercises

  • lecture notes: [link]

application in neuro:

• "Estimating state and parameters in state space models of spike trains" Macke, Buesing, Sahani

  • chapter in “Advanced State-Space Methods for Neural and Clinical Data”

  • Subspace-ID for GLDS

  • Subspace-ID for PLDS

• "Spectral learning of linear dynamics from generalised-linear observations with application to neural population data" Buesing, Macke, Sahani

  • see also:

• "Extracting low-dimensional dynamics from multiple large-scale neural population recordings by learning to predict correlations" Nonnenmacher et al.

• "Blackboxvariational inference for state space models" (2015) Archer et al.

• "Variational EM for SLDS (switching linear dynamical systems)" Lecture by Linderman

contstrained & regularized LDS identification

• [++] "Learning stable, regularised latent models of neural population dynamics" Buesing, Macke, Sahani

• "A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis" Liu and Hauskrecht

• "Identification of stable models in subspace identification by using regularization" Gestel et al.

• "Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework" Liu and Hauskrecht

Software tools for dynamical systems

useful functions in MATLAB

• ss() to build models

  • rss() to generate random models

• ssest() and ssregest() to fit models

  • modred() to reduce model order

    • see also balred(), Model Reducer app

• for fitting nonlinearities: cftool() and fit()

• eig, pzmap for inspecting eignevalues (and eigenvectors) of a system

Other software for dynamical system modeling (mostly Python)

• ldsCtrlEst: dynamical system estimation & control library - Stanley Rozell labs:[docs] [code]

  • primarily focused on implementing dynamical systems within systems neuroscience experiments

• hmm: generation & decoding of hidden markov models [docs] [code]

• pmtk3: probabilistic machine learning

  • usupported as of 2019, succeeded by PyProbML

• "SSM: Bayesian learning and inference for state space models" [ink]

• Additional

  • GLMSpikeTools: Fitting and simulation of Poisson generalized linear model for single and multi-neuron spike trains [link]

    • associated paper: "Spatio-temporal correlations and visual signalling in a complete neuronal population"

  • pop_spike_dyn:This repository contains different methods for linear dynamical system models with Poisson observations.

    • example script: PLDSExample.m

  • slinderman/recurrent-slds:

    • may be redundant with lindermanlab/ssm

  • SSIDforPLDS: Subspace Identification for Poisson Linear Dynamical system

  • poisson-gpfa: Gaussian process factor analysis with Poisson observations - Macke Lab

  • hmmlearn: set of algorithms for unsupervised learning and inference of Hidden Markov Models

    • see also seqlearn: sequence learning toolkit for python

  • autohmm: packages provides an implementation of Hidden Markov Models (HMMs) with tied states and autoregressive observations, written in Python

resources for understanding dynamical systems in control

UMich - Control tutorials for MATLAB and Simulink

•  these controls tutorials by UMich are excellent, and involve some discussion of state-space representation of dynamical systems

Feedback Systems: An Introduction for Scientists and Engineers - by Åström and Murray

• Python Control Systems Library a toolbox for analysis and design of feedback control systems as well as demos for several exercises from "Feedback Systems" mentioned above

Nonlinear control lectures - Slotine @ MIT

• good at bridging the intuitive and mathematical concepts

• topics include:

  • stability analysis (of nonlinear, time-varying systems)

  • robust & adaptive control

Chapter 3: Dynamics, of “Control System Design” by Karl Astrom is excellent.

• see also: "Chapter 2. System Modeling" from “Feedback Control” by Karl Astrom

"Linear Matrix Inequalities in System and Control Theory" by Stephen Boyd

• excellent for constrained controller design

experimental design / (model-based) stimulus optimization

"Automating the design of informative sequences of sensory stimuli" Lewi et al.

“Statistical models for neural encoding, decoding, and optimal stimulus design.” Paninski, Pillow, Lewi

Other reference lists:

Siplab Dynamics Zotero group (please email to request access):

• https://www.zotero.org/groups/2174905/siplab

Some slides on interpretation of neural systems as dynamical systems which compute are presented here:

• Dynamics In Neuro Lectures

High-level references for understanding dynamics in neuro

• "Neural circuits as computational dynamical systems" (2014) Sussillo

• “Latent Factors and Dynamics in Motor Cortex and Their Application to Brain–Machine Interfaces“ (2018) Pandarinath et al.

• "Neural field models for latent state inference: Application to large-scale neuronal recordings" (2019) Rule et al.

• “Computation through Neural Population Dynamics” (2020) Vyas et al.

Textbooks

• Neuronal Dynamics- Gerstner et al.

  • Has video lectures and python exercises

  • Covers a lot of math very clearly

• “Data Driven Science & Engineering Machine Learning, Dynamical Systems, and Control" Brunton & Kutz

• "Probabilistic Machine Learning" - a book series by Kevin Murphy

  • has an associated codebase of tools: https://github.com/probml/pyprobml/

    • prior toolbox:

• Nonlinear Dynamics and Chaos - Strogatz

• “Neuroscience” (2004) Purves et al