This course focuses on using deep learning of dynamical systems for gaining mechanistic insight and prediction in the field of psychiatry. The learning outcomes include understanding dynamical systems theory, inferring dynamical systems from empirical data using deep generative recurrent neural networks, and applying these tools to analyze neural and behavioral phenomena in psychiatry. The course teaches skills such as constructing generative models, forecasting disease trajectories, and simulating therapeutic interventions. The teaching method involves presentations on example applications using fMRI and EMA data. The intended audience for this course includes researchers, practitioners, and students interested in computational psychiatry, neuroscience, and deep learning techniques for analyzing complex systems.
Deep Learning of Dynamical Systems for Mechanistic Insight and Prediction in Psychiatry
Institute for Pure & Applied Mathematics (IPAM) via YouTube
Overview
Syllabus
Intro
What is a dynamical system?
Attractor states in state space
Working memory tasks & persistent activity
Memory patterns as attractor states
Limit cycles ...
Limit cycles in motor behavior
Action/ thought sequences as "heteroclinic channels"
Altered dynamics in psychiatric states
Dynamical systems as a central layer of convergence
Recurrent Neural Network → time series
Making RNN deep in time
Piecewise-Linear (PL) RNN
Line-attractor regularization
Performance on ML benchmarks
Line-attractors and solving long-range tasks
Sequential MNIST benchmark
Generative PLRNN for dynamical systems
Reconstructing dynamical systems
Statistical inference for small data: Expectation.Maximization
Expectation-Maximization Algorithm
Statistical inference for big data: Sequential VAE & SGVB
Simple ahead prediction errors may be meaningless
Reconstructing DS benchmarks
Reconstructing DS: Lorenz system
Enforcing line attractor directions helps to capture multiple time scales
Inferring PLRNN from fMRI data
Does PLANN really capture measured dynamics?
Example 1. Unstable neuronal representations in schizophrenia
Example 2: Inference of dynamical systems from mobile data
Prediction of medical intervention effects
Take home's
Taught by
Institute for Pure & Applied Mathematics (IPAM)
