---
license: mit
---


## General Description

MultiSetTransformerData is a large dataset designed to train and validate neural Symbolic Regression models.  It was designed to solve the Multi-Set Symbolic Skeleton Prediction (MSSP) problems, described in the paper **"Univariate Skeleton Prediction in Multivariate Systems Using Transformers"**. However, it can be used for training generic SR models as well.

This dataset consists of artificially generated **univariate symbolic skeletons**, from which mathematical expressions are sampled, which are then used to sample data sets. 
In this repository, a dataset **Q1** is presented:

* **Q1**: Consists of mathematical expressions that use up to 5 unary and binary operators (e.g., \\(1 + 1 / (\sin(2x) + 3)\\) uses five operators). It allows up to one nested operator (e.g., \\(\sin( \exp(x))\\) is allowed but \\(\sin( \exp(x^2))\\) is not).

## Dataset Structure

In the **Q1** folder, you will find a training set alongside its corresponding validation set.
Then, each folder consists of a collection of HDF5 files, as shown below:

```
├── Q1 
│   ├── training
│   │   ├── 0.h5
│   │   ├── 1.h5
│   │   ├── ...
│   ├── validation
│   │   ├── 0.h5
│   │   ├── 1.h5
│   │   ├── ...
```

Each HDF5 file contains 5000 **blocks** and has the following structure:

```
{  "block_1": {
        "X": "Support vector, shape (10000, 10)",
        "Y": "Response vector, shape (10000, 10)",
        "tokenized": "Symbolic skeleton expression tokenized using vocabulary, list",
        "exprs": "Symbolic skeleton expression, str",
        "sampled_exprs": "Ten mathematical expressions sampled from a common skeleton"
    },
    "block_2": {
        "X": "Support, shape (10000, 10)",
        "Y": "Response, shape (10000, 10)",
        "tokenized": "Symbolic skeleton expression tokenized using vocabulary, list",
        "exprs": "Symbolic skeleton expression, str",
        "sampled_exprs": "Ten mathematical expressions sampled from a common skeleton"
    },
    ...
}
```

More specifically, each block corresponds to one univariate symbolic skeleton (i.e., a function without defined constant values); for example, `c + c/(c*sin(c*x_1) + c)`. 
From this skeleton, 10 random functions are sampled; for example: 

* `-2.284 + 0.48/(-sin(0.787*x_1) - 1.136)`
* `4.462 - 2.545/(3.157*sin(0.422*x_1) - 1.826)`, ...

Then, for the \\(i\\)-th function (where \\(i \in [0, 1, ..., 9]\\)), we sample a **support vector** `X[:, i]` of 10000 elements whose values are drawn from a uniform distribution \\(\mathcal{U}(-10, 10)\\).
The support vector `X[:, i]` is evaluated on the \\(i\\)-th function to obtain the response vector `Y[:, i]`.
In other words, a block contains input-output data generated from 10 **different functions that share the same symbolic skeleton**.
For instance, the following figure shows 10 sets of data generated from the symbolic skeleton `c + c/(c*sin(c*x_1) + c)`:

<p align="center">
  <img src="images/data_example.jpg" alt="alt text" width="600">
</p>

## Loading Data

Once the data is downloaded, it can be loaded using Python as follows:

```
imort os
import glob
import h5py

def open_h5(path):
    block = []
    with h5py.File(path, "r") as hf:
        # Iterate through the groups in the HDF5 file (group names are integers)
        for group_name in hf:
            group = hf[group_name]
            X = group["X"][:]
            Y = group["Y"][:]
            # Load 'tokenized' as a list of integers
            tokenized = list(group["tokenized"])
            # Load 'exprs' as a string
            exprs = group["exprs"][()].tobytes().decode("utf-8")
            # Load 'sampled_exprs' as a list of sympy expressions
            sampled_exprs = [expr_str for expr_str in group["sampled_exprs"][:].astype(str)]
            block.append([X, Y, tokenized, exprs, sampled_exprs])
    return block

train_path = 'data/Q1/training'
train_files = glob.glob(os.path.join(self.sampledData_train_path, '*.h5'))
for tfile in train_files:
    # Read block
    block = open_h5(tfile)
    # Do stuff with your data
```

## Vocabulary and Expression Generation

The table below provides the vocabulary used to construct the expressions of this dataset.

<p align="center">
  <img src="images/vocabulary.jpg" alt="alt text" width="500">
</p>

We use a method that builds the expression tree recursively in a preorder fashion, which allows us to enforce certain conditions and constraints effectively.
That is, we forbid certain combinations of operators and set a maximum limit on the nesting depth of unary operators within each other.
For example, we avoid embedding the operator \\(\text{log}\\) within the operator \\(\text{exp}\\), or vice versa, since such composition could lead to direct simplification (e.g., \\(\text{log}\left( \text{exp} (x) \right) = x\\).
We can also avoid combinations of operators that would generate extremely large values (e.g., \\(\text{exp}\left( \text{exp} (x) \right)\\) and \\(\text{sinh} \left( \text{sinh} (x) \right)\\)). 
The table below shows the forbidden operators we considered for some specific parent operators.

<p align="center">
  <img src="images/forbidden_ops.jpg" alt="alt text" width="500">
</p>


## Citation

Use this Bibtex to cite this repository

```
@INPROCEEDINGS{MultiSetSR,
author="Morales, Giorgio
and Sheppard, John W.",
editor="Bifet, Albert
and Daniu{\v{s}}is, Povilas
and Davis, Jesse
and Krilavi{\v{c}}ius, Tomas
and Kull, Meelis
and Ntoutsi, Eirini
and Puolam{\"a}ki, Kai
and {\v{Z}}liobait{\.{e}}, Indr{\.{e}}",
title="Univariate Skeleton Prediction in Multivariate Systems Using Transformers",
booktitle="Machine Learning and Knowledge Discovery in Databases. Research Track and Demo Track",
year="2024",
publisher="Springer Nature Switzerland",
address="Cham",
pages="107--125",
isbn="978-3-031-70371-3"
}
```