Introduction

NTCIR Math Density Estimator is a Python 3 command-line utility that computes and plots density, and probability estimates from judged datasets in the NTCIR-11 Math-2, and NTCIR-12 MathIR format. Most importantly, the package estimates the probability P(relevant | position), where position is a position of a paragraph in a document.

Usage

Installing:

$ pip install ntcir-math-density

Displaying the usage:

$ ntcir-math-density --help
usage: ntcir-math-density [-h] [--datasets DATASETS [DATASETS ...]]
                          [--judgements JUDGEMENTS [JUDGEMENTS ...]]
                          [--plots PLOTS [PLOTS ...]] [--positions POSITIONS]
                          [--estimates ESTIMATES] [--num-workers NUM_WORKERS]

Use NTCIR-10 Math, NTCIR-11 Math-2, and NTCIR-12 MathIR datasets to compute
density, and probability estimates.

optional arguments:
-h, --help            show this help message and exit
--datasets DATASETS [DATASETS ...]
                        Paths to the directories containing the datasets. Each
                        path must be prefixed with a unique single-letter
                        label (e.g. "A=/some/path"). Note that all the
                        datasets must be in the NTCIR-11 Math-2, and NTCIR-12
                        MathIR format, even the NTCIR-10 Math dataset.
--judgements JUDGEMENTS [JUDGEMENTS ...]
                        Paths to the files containing relevance judgements.
                        Each path must be prefixed with single-letter labels
                        corresponding to the judged datasets (e.g.
                        "A:/some/path/judgement.dat"). Note that all the
                        judgements must be in the NTCIR-11 Math-2, and
                        NTCIR-12 MathIR format, even the NTCIR-10 Math dataset
                        judgements.
--plots PLOTS [PLOTS ...]
                        The path to the files, where the probability
                        estimates will plotted. When no datasets are
                        specified, the estimates file will be loaded.
--positions POSITIONS
                        The path to the file, where the estimated positions of
                        all paragraph identifiers from all datasets will be
                        stored. Defaults to positions.pkl.gz.
--estimates ESTIMATES
                        The path to the file, where the density, and
                        probability estimates will be stored. When no
                        datasets are specified, this file will be loaded to
                        provide the estimates for plotting. Defaults to
                        estimates.pkl.gz.
--num-workers NUM_WORKERS
                        The number of processes that will be used for
                        processing the NTCIR-10 Math dataset, and for
                        computing the density, and probability estimates.
                        Defaults to 1.

Extracting density, and probability estimates, and plotting the estimates using 64 worker processes:

$ ntcir-math-density --num-workers 64 \
>     --datasets A=ntcir-10-converted B=ntcir-11-12 \
>     --judgements A:NTCIR_10_Math-qrels_fs-converted.dat A:NTCIR_10_Math-qrels_ft-converted.dat \
>                  B:NTCIR11_Math-qrels.dat B:NTCIR12_Math-qrels_agg.dat \
>                  B:NTCIR12_Math_simto-qrels_agg.dat \
>     --estimates estimates.pkl.gz --positions positions.pkl.gz \
>     --plots plot.pdf plot.svg
Retrieving judged paragraph identifiers, and scores from NTCIR_10_Math-qrels_fs-converted.dat
100%|█████████████████████████████████████████████████████| 2129/2129 [00:00<00:00, 334959.05it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR_10_Math-qrels_ft-converted.dat
100%|█████████████████████████████████████████████████████| 1425/1425 [00:00<00:00, 353201.94it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR11_Math-qrels.dat
100%|█████████████████████████████████████████████████████| 2500/2500 [00:00<00:00, 343345.12it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR12_Math-qrels_agg.dat
100%|█████████████████████████████████████████████████████| 4251/4251 [00:00<00:00, 342252.50it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR12_Math_simto-qrels_agg.dat
100%|█████████████████████████████████████████████████████| 654/654 [00:00<00:00, 314428.57it/s]
Retrieving all paragraph identifiers, and positions from ntcir-10-converted
get_all_identifiers(ntcir-10-converted): 5405167it [04:30, 19946.57it/s]
get_all_positions(ntcir-10-converted): 100%|█████████| 5405167/5405167 [08:44<00:00, 10306.72it/s]
Retrieving all paragraph identifiers, and positions from ntcir-11-12
get_all_identifiers(ntcir-11-12): 8301578it [08:08, 16985.19it/s]
get_all_positions(ntcir-11-12): 100%|█████████████████| 8301578/8301578 [44:30<00:00, 3108.88it/s]
1043 / 3146 / 5405167 relevant / judged / total identifiers in dataset ntcir-10-converted
1742 / 7059 / 8301578 relevant / judged / total identifiers in dataset ntcir-11-12
Pickling positions.pkl.gz
Fitting density, and probability estimators
Fitting prior p(position) density estimator
Fitting conditional p(position | relevant) density estimator
Computing density, and probability estimates
p(position): 100%|████████████████████████████████████████████████| 64/64 [01:19<00:00,  1.24s/it]
p(position | relevant): 100%|█████████████████████████████████████| 64/64 [01:19<00:00,  1.24s/it]
Pickling estimates.pkl.gz
Plotting plot.svg
Plotting plot.pdf

Extracting density, and probability estimates using 64 worker processes:

$ ntcir-math-density --num-workers 64 \
>     --datasets A=ntcir-10-converted B=ntcir-11-12 \
>     --judgements A:NTCIR_10_Math-qrels_fs-converted.dat A:NTCIR_10_Math-qrels_ft-converted.dat \
>                  B:NTCIR11_Math-qrels.dat B:NTCIR12_Math-qrels_agg.dat \
>                  B:NTCIR12_Math_simto-qrels_agg.dat \
>     --estimates estimates.pkl.gz --positions positions.pkl.gz
Retrieving judged paragraph identifiers, and scores from NTCIR_10_Math-qrels_fs-converted.dat
100%|█████████████████████████████████████████████████████| 2129/2129 [00:00<00:00, 334959.05it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR_10_Math-qrels_ft-converted.dat
100%|█████████████████████████████████████████████████████| 1425/1425 [00:00<00:00, 353201.94it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR11_Math-qrels.dat
100%|█████████████████████████████████████████████████████| 2500/2500 [00:00<00:00, 343345.12it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR12_Math-qrels_agg.dat
100%|█████████████████████████████████████████████████████| 4251/4251 [00:00<00:00, 342252.50it/s]
Retrieving judged paragraph identifiers, and scores from NTCIR12_Math_simto-qrels_agg.dat
100%|█████████████████████████████████████████████████████| 654/654 [00:00<00:00, 314428.57it/s]
Retrieving all paragraph identifiers, and positions from ntcir-10-converted
get_all_identifiers(ntcir-10-converted): 5405167it [04:30, 19946.57it/s]
get_all_positions(ntcir-10-converted): 100%|█████████| 5405167/5405167 [08:44<00:00, 10306.72it/s]
Retrieving all paragraph identifiers, and positions from ntcir-11-12
get_all_identifiers(ntcir-11-12): 8301578it [08:08, 16985.19it/s]
get_all_positions(ntcir-11-12): 100%|█████████████████| 8301578/8301578 [44:30<00:00, 3108.88it/s]
1043 / 3146 / 5405167 relevant / judged / total identifiers in dataset ntcir-10-converted
1742 / 7059 / 8301578 relevant / judged / total identifiers in dataset ntcir-11-12
Pickling positions.pkl.gz
Fitting density, and probability estimators
Fitting prior p(position) density estimator
Fitting conditional p(position | relevant) density estimator
Computing density, and probability estimates
p(position): 100%|████████████████████████████████████████████████| 64/64 [01:19<00:00,  1.24s/it]
p(position | relevant): 100%|█████████████████████████████████████| 64/64 [01:19<00:00,  1.24s/it]
Pickling estimates.pkl.gz

Plotting the estimates using 64 worker processes:

$ ntcir-math-density --num-workers 64 \
>     --estimates estimates.pkl.gz --plots plot.pdf plot.svg
Unpickling estimates.pkl.gz
Plotting plot.svg
Plotting plot.pdf