Introduction

1. Key Question: How do sensory inputs change the neural activity in neural circuits and influence behavioral choice?

1. Challenges:

   

• High-dimensional time series data
• Heterogeneous dataset
• Summarization + prediction + explanation

Part1 rSLDS

1. Previous studies: neural activity → structured trajectory in low dimension → different part of trajectory means different subset neurons work → corresponding to different behaviors

   

2. Hypothesis: High-dimensional neural data can be summarized as a sequence of behaviorally meaningful states and belong to different parts of low-dimensional state space/trajectory

3. Further Questions:

   

4. Probabilistic model of neural data

   

• the neural activity is oscillating: this is because the neural activity has time constants
  • where do the time constants come from?
  • there is a sampling frequency in which
  • the time constants of these dynamics linear functions

1. Graphical representation of the probabilistic model

   

2. Dependencies

   

3. rSLDS

   

4. Recurrent dependencies carve up continuous space

   

5. How to capture individual variability?

   

   

Part2 Approximate Bayesian inference in rSLDS