ebtech/autoode-dsl

autoode-dsl's Issues

Implement a loss function

Something very easy, like MSE on populations + L2 on all other parameters.

Blocked by #6

History refactor

The History class could be a thin wrapper around a 3D Tensor that is shaped (n_days, n_populations, n_regions). A State corresponds to an index in the i=1 dimension. This may be easier to work with.

Log parameters to logit params

This way we don't go out of bounds when taking derivatives.

helper to compute actual log probabilities

For model selection, it would be good to be able to compute actual full likelihoods of our model.

• SeiturdModel.log_prob currently doesn't return an actual likelihood: it uses mean instead of sum for all the different bits, so it's multiplied by a constant. Doesn't matter for training only on itself, but needs to scale the likelihood of "other bits."
• demographics.get_regularizer kind of corresponds to normal priors on the w and delta components, with w having a variance of whatever mu we multiply the whole thing by (up to a factor of 2), and delta having a variance of mu * lambda; would be good to be able to compute likelihoods under that, including the normalizers based on lambda and mu.
• The L1 time-smoothness bit we currently have: need to think about how to phrase this probabilistically.

Implement SEITURD in the Epidemic_models.ipynb

We need to implement the SEITURD model in Epidemic_models.ipynb on our way to generating data. This should be straightforward, since it can follow the same implementation as the other models. For now we can ballpark the rate parameters.

Literature to review

• the SUTRA paper: https://arxiv.org/abs/2101.09158. There are links to a few different data sources including serotracker (another link to serotracker) and worldometeres. These may be useful data sources as well for constructing additional datasets.
• kernel-modulated SIR

Generate synthetic SEITURD model curves

Blocked by #3.

Run the SEITURD model with randomized initial conditions with initial total populations corresponding to each state in our study. Save these curves in a dataframe that will be of shape (n_days, 7 * n_states) where the 7 is for the populations. This way, sub-selecting the T and D columns will yield a version of the dataframe that mimics our C19Dataset.

Find good initial guesses for our physical parameters

Things like decay rates. We don't have a good grasp of if they are O(1) or O(100). Look at the literature.

Dataset -> initial history tensor generator

We need a class that given our dataset of shape (n_days, 2, n_regions) where the 2 refers to tested and deceased populations, we spit out a proposed initial history for the training data that could have any number of m>2 populations in it. The constraint also is that for all days for region i, the populations must sum to N_i.

The API should look something like:

def raw_data_to_history(data: Tensor, N: Tensor, state: type) -> History:
    # `N` has the populations of each region
    # inspect `state` to figure out how many populations it has
    # draw from RNGs
    ...