Datasets:
license: cc-by-sa-4.0
language:
- en
FIM-Estimation
In a FIM-Estimation task, the input consists of the following components:
- 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.
- 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.
- 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.