Eulerianial / premise-selection-deepmath-style

premise-selection-deepmath-style

Machine Learning experiments for premise selection for Mizar-originating data. We are planning to beat neural nets from the Deepmath paper with help of modern and popular ML algorithms like xgboost, ExtraTrees, et al. Probably some sophisticated techniques of data preprocessing and densification will help.

Data preparation

Original data comes from two places:

• https://github.com/JUrban/deepmath (big dataset)
• https://github.com/JUrban/MPTP2078 (similar but smaller dataset)

More precisely,

• from first dataset (deepmath) we take:
  • these files witch contain names of theorems along with balanced set of useful and unuseful premises for proving them
  • this file providing description of every theorem (premise) by features
• from second dataset (MPTP2078) we take, analogously:
  • these files with useful/unuseful premises
  • this file with features.

In order to train ML models on the data we preprocessed it to the following shape:

1. Every theorem (premise) was associated with a binary vector representing features possesed by it.
2. For every pair (theorem, premise) for which we have have information from the data about relevance of the premise for proving the theorem was labelled according to this information by 0 or 1, and linked to concatenation of two binary vectors associated to this pair.
3. In case of deepmath dataset we have 522528 such pairs and 451706 different features, thus resulting (very sparse) matrix has size 522528 x 903412.
4. The matrix is saved in Compressed Sparse Row format (and its size is 202M; in dense representation it took > 20G).

Preprocessed data are in ./data/MPTP2078 and ./data/deepmath:

• CSR matrix with features: ./data/features_csr.pkl
• labels: .data/labels.pkl and .data/labels.csv

You can reproduce data preprocessing by running

python3 prepare_data.py trivdata features data_output 4

in the main directory where:

• trivdata is path to directory containing these or these files
• features is path to this (unpacked) or this
• data_output is directory for preprocessed data
• number 4 at the end indicates number of cores you want to use to preprocess data.