Add basic info and TODOs to README

README.md

@@ -1,3 +1,20 @@
+# 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`.
+
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 license: cc-by-sa-4.0
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