# FIM-Estimation
In a FIM-Estimation task, the input consists of

1. A dataset of the form $\mathcal{D}_ {train} = \{(\mathbf{\lambda}_ i, x_ i)\}_ {i=1}^{\left|\mathcal{D}\right|}$, where $\vlambda_ i$ is a point in the parameter space and $x_ i$ is a sample.
2. The structure of the samples $x_ i$. For example, if $x_ i\in\{0,1\}^n$ is a bitstring representing a measurement of a quantum system on a lattice with $n$ sites, then the said structure is the lattice and the correspondence between the bitstring bits and the lattice sites.
3. Optionally, additional information about the statistical manifold. This could involve, e.g., the symmetries of the system used to generate the statistical manifold.

The task is to estimate Fisher Information Metric as a matrix-valued function of parameter $\mathbf{\lambda}$.

We (TODO:plan to) present datasets corresponding to 6 statistical manifolds: `XXZ300_Z`, `FIL24`, etc.
The data is stored as follows:
`data/xxz300_z` contains the data for `XXZ300_Z` datasets. Within that directory, there are subdirectories of the form `seed_??` each containing a dataset describing the same statistical manifold, but generated using a different seed (e.g. `seed_05`). We have `seed_05/d_train.parquet`, which is the dataset as described in #1 above. `seed_05/d_test.parquet` is a hold-out dataset which should not be used in estimation of $\mathbf{\lambda}$ (not even for hyperparameter tuning).
`data/xxz300_z/meta.json` (TODO) represents the metadata (including information listed in #2 and #3 above)
`data/xxz300_z/fim_ground_truth.json` (TODO) represents the ground truth FIM.

An algorithm attempting to solve the FIM-Estimation task `XXZ300_Z(seed=05)` shall take `data/xxz300_z/seed_05/d_train.parquet` and `data/xxz300_z/meta.json` as inputs and produce FIM estimates to be compared with `data/xxz300_z/fim_ground_truth.json`.

---
license: cc-by-sa-4.0
---