Examples

Here we provide examples from each of our papers [1], [2], and [3]. These examples can also be accessed with Jupiter notebook from our GitHub repository .

Moving beyond generalization to accurate interpretation of flexible models

The first example generates synthetic data from a double-well potential and uses this data to fit the model potential. It reproduces Figure 3 in the main text [1]. The second example demonstrates our feature consistency method for model selection in the case of stationary dynamics. It reproduces Figure 5 in the main text [1].

• Example 1
  • Step 1: Generate synthetic data
  • Step 2: Perform model optimization
  • Step 3: Visualize the results
• Example 2
  • Step 1: Load data and calculate Feature complexities (FC)
  • Step 2: Define the hyperparameters for feature consistency analysis
  • Step 3: Perform feature consistency analysis
  • Step 4: Visualise the results

Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

The first example generates synthetic data from the ramping dynamics, and optimizes the model potential on this data. Also the importance of various non-stationary components for accurate model inference is demonstrated. It reproduces Figures 2,3 in the main text [#Genkin2020preprint]_. The second example generates two synthetic datasets from ramping and stepping dynamics, and uses this data to infer the model potentials. It also infers the model potential, the initial distribution of the latent states, and the noise magnitude from data generated from the ramping dynamics. It reproduces Figure 4 in the main text [#Genkin2020preprint]_. The third example demonstrates feature consistency analysis for model selection for the case of non-stationary data. It reproduces Figure 5a-c in the main text [#Genkin2020preprint]_.

• Example 1
  • Step 1: Generate synthetic data
  • Step 2: Optimize model potential using the generated data
  • Step 3: Testing the contributions of non-stationary components
• Example 2
  • Step 1: Generate synthetic data from the ramping and stepping dynamics.
  • Step 2: Optimize the model potentials using the generated data
  • Step 3: Optimize the model potential, the initial latent state distribution, and D from data
• Example 3
  • Step 1: Load data and calculate Feature complexities (FC)
  • Step 2: Calculate JSD for each level of Feature complexity
  • Step 3. Visualize the results.

The dynamics and geometry of choice in premotor cortex

The first example fits single-neuron model from PMd data and selects an optimal model using feature consistency analysis, see Figure 3 in [3]. The second example fits population model from PMd data and selects an optimal model using feature consistency analysis, see Figure 4 in [3].

• Example 1
  • Step 1: Load the data and plot PSTH aligned to stimulus onset and sorted by chosen side and stimulus difficulty.
  • Step 2: Extract the data, split into two datasamples, and convert it into ISI format which can be used for model optimization.
  • Step 3. Set up optimization parameters and run optimization
  • Step 4. Perform feature complexity analysis.
  • Step 5: Visualize the optimization results
• Example 2
  • Step 1: Check PSTHs. Load the data and plot PSTH aligned to stimulus onset and sorted by chosen side and stimulus difficulty.
  • Step 2. Extract the data, split into two datasamples, and convert it into ISI format which can be used for model optimization.
  • Step 3: Perform optimization.
  • Step 4. Feature consistency analysis
  • Step 5. Visualize ther results.

References

[1] (1,2,3)

Genkin, M., Engel, T.A. Moving beyond generalization to accurate interpretation of flexible models. Nat Mach Intell 2, 674–683 (2020).

[2]

Genkin, M., Hughes, O. and Engel, T.A. Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories. Nat Commun 12, 5986 (2021).

[3] (1,2,3)

Genkin M, Shenoy KV, Chandrasekaran C, Engel TA. The dynamics and geometry of choice in premotor cortex. bioRxiv [Preprint] (2023) .