diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..47986d2 --- /dev/null +++ b/.gitignore @@ -0,0 +1,110 @@ +#### joe made this: http://goel.io/joe + +#####=== Python ===##### + +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ + +data/ diff --git a/README.md b/README.md index 9946200..c51ada4 100644 --- a/README.md +++ b/README.md @@ -20,10 +20,25 @@ This code depends on the following packages: - `preprocesed_weights.csv` contains estimated model parameters for the [HLR model](https://github.com/duolingo/halflife-regression), as described in section 8 of supplementary materials. - `observations_1k.csv` contains a set of 1K user-item pairs and associated number of total/correct attempts by every user for given items. This dataset has been curated from a larger dataset released by Duolingo, available [here](https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/N8XJME). - ## Execution +## Execution - The code can by executed as follows: +The code can by executed as follows: - `python memorize.py` +`python memorize.py` - The code will use default parameter value (q) used in the code. +The code will use default parameter value (q) used in the code. + +---- + +# Experiments with Duolingo data + +## Pre-processing + +Convert to Python `dict` by `user_id, lexeme_id` and pruning it for reading it: + + python dataset2dict.py ./data/raw/duolingo.csv ./data/duo_dict.dill --success_prob 0.99 --max_days 30 + python process_raw_data.py ./data/raw/duolingo.csv ./data/duolingo_reduced.csv + +## Plots + +See the notebook `plots.ipynb`. diff --git a/dataset2dict.py b/dataset2dict.py new file mode 100644 index 0000000..8cb9d52 --- /dev/null +++ b/dataset2dict.py @@ -0,0 +1,136 @@ +#!/usr/bin/env python +import pandas as pd +import dill +import click +import os +from collections import defaultdict +import datetime +import numpy as np +import multiprocessing as MP + +_df_indexed = None + +TIME_SCALE = 24 * 60 * 60 + + +def _column_worker(params): + idx, success_prob = params + if idx == 0: + return _df_indexed.groupby(level=[0, 1]).p_recall.transform( + lambda x: np.cumsum([0] + [1 if r >= success_prob else 0 for r in x])[:-1]) + elif idx == 1: + return _df_indexed.groupby(level=[0, 1]).p_recall.transform( + lambda x: np.cumsum([0] + [1 if r < success_prob else 0 for r in x][:-1])) + elif idx == 2: + return _df_indexed.groupby(level=[0, 1]).p_recall.transform( + lambda x: np.arange(len(x))) + + +def add_user_lexeme_columns(success_prob): + """Adds 'n_correct', 'n_wrong', 'n_total' column to the data-frame.""" + + if "history_seen" in _df_indexed.columns: + _df_indexed['n_correct'] = _df_indexed['history_correct'] + _df_indexed['n_total'] = _df_indexed['history_seen'] + _df_indexed['n_wrong']= _df_indexed['n_total']-_df_indexed['n_correct'] + return + print("No meta info on total number of exercises") + with MP.Pool(3) as pool: + n_correct, n_wrong, n_total = pool.map(_column_worker, + [(ii, success_prob) + for ii in range(3)]) + + _df_indexed['n_correct'] = n_correct + _df_indexed['n_wrong'] = n_wrong + _df_indexed['n_total'] = n_total + + +def convert_csv_to_dict(csv_path, + dictionary_output, + max_days, + success_prob, + force=False): + """Pre-process the CSV file and save as a dictionary.""" + + if os.path.exists(dictionary_output) and not force: + print('{} already exists and not being forced to over-write it.'.format(dictionary_output)) + return + + start_time = datetime.datetime.now() + + def elapsed(): + return (datetime.datetime.now() - start_time).seconds + + df = pd.read_csv(csv_path) + + # Hack to avoid passing df_indexed as a argument to the worker function + + if 'n_correct' not in df.columns: + print('Calculating n_wrong, n_correct and n_total') + global _df_indexed + # Only mergesort is stable sort. + _df_indexed = df.set_index(['user_id', 'lexeme_id']).sort_values('timestamp').sort_index(kind='mergesort') + + add_user_lexeme_columns(success_prob) + + df = _df_indexed.reset_index().sort_values('timestamp') + + # Drop all intervals larger than 30 days. + df = df[df.delta < TIME_SCALE * max_days] + + # results = dill.load(open(results_path, 'rb')) + + # map_lexeme = results['map_lexeme'] + # alpha = results['alpha'] + # beta = results['beta'] + # lexeme_difficulty = results['lexeme_difficulty'] + + # n_0 = [lexeme_difficulty[map_lexeme[x]] for x in df.lexeme_id] + # df['n_0'] = np.abs(n_0) + # df['n_t'] = df['n_0'] * (alpha[0] ** df['n_correct']) * (beta[0] ** df['n_wrong']) + # df['m_t'] = np.exp(-df['n_t'] * df['delta'] / TIME_SCALE) + + op_dict = defaultdict(lambda: defaultdict(lambda: [])) + + for ii in range(df.shape[0]): + row = df.iloc[ii] + u_id, l_id = row.user_id, row.lexeme_id + delta = row.delta / TIME_SCALE + + op_dict[u_id][l_id].append({ + 'delta_scaled' : delta, + 'n_wrong' : row.n_wrong, + 'n_correct' : row.n_correct, + 'p_recall' : row.p_recall, + # 'n_0' : row.n_0, + 'timestamp' : row.timestamp, + # 'm_t' : row.m_t, + # 'n_t' : row.n_t, + 'user_id' : u_id, + 'lexeme_id' : l_id + }) + + if ii % 100000 == 0: + print('Done {:0.2f}%\tElapsed = {} sec'.format(100. * ii / df.shape[0], elapsed())) + + print('Writing {} ...'.format(dictionary_output)) + dill.dump(op_dict, open(dictionary_output, 'wb')) + print('Done.') + + +@click.command() +@click.argument('csv_file') +@click.argument('output_dill') +@click.option('--success_prob', 'success_prob', default=0.6, type=float, help='At what recall probability is the trial considered successful.') +@click.option('--max_days', 'max_days', default=30, help='Maximum number of days before a revision.') +@click.option('--force/--no-force', 'force', default=False, help='Force overwrite of existing files.') +def run(csv_file, output_dill, success_prob, max_days, force): + """Converts the CSV_FILE from Duolingo format to a dictionary and saves it in OUTPUT_DILL + after reading the results of Half-Life regression from RESULTS_PATH.""" + convert_csv_to_dict(csv_path=csv_file, dictionary_output=output_dill, + max_days=max_days, success_prob=success_prob, + force=force) + + +if __name__ == '__main__': + run() diff --git a/plot_utils.py b/plot_utils.py new file mode 100644 index 0000000..79ff7db --- /dev/null +++ b/plot_utils.py @@ -0,0 +1,79 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib + +SPINE_COLOR = 'grey' +def latexify(fig_width=None, fig_height=None, columns=1, largeFonts=False,font_scale=1): + """Set up matplotlib's RC params for LaTeX plotting. + Call this before plotting a figure. + + Parameters + ---------- + fig_width : float, optional, inches + fig_height : float, optional, inches + columns : {1, 2} + """ + + # code adapted from http://www.scipy.org/Cookbook/Matplotlib/LaTeX_Examples + + # Width and max height in inches for IEEE journals taken from + # computer.org/cms/Computer.org/Journal%20templates/transactions_art_guide.pdf + + assert(columns in [1,2]) + + if fig_width is None: + fig_width = 3.39 if columns == 1 else 6.9 # width in inches + + if fig_height is None: + golden_mean = (np.sqrt(5)-1.0)/2.0 # Aesthetic ratio + fig_height = fig_width*golden_mean # height in inches + + MAX_HEIGHT_INCHES = 8.0 + if fig_height > MAX_HEIGHT_INCHES: + print("WARNING: fig_height too large:" + fig_height + + "so will reduce to" + MAX_HEIGHT_INCHES + "inches.") + fig_height = MAX_HEIGHT_INCHES + + params = {'backend': 'ps', + 'text.latex.preamble': ['\\usepackage{gensymb}'], + 'axes.labelsize': font_scale*10 if largeFonts else font_scale*7, # fontsize for x and y labels (was 10) + 'axes.titlesize': font_scale*10 if largeFonts else font_scale*7, + 'font.size': font_scale*10 if largeFonts else font_scale*7, # was 10 + 'legend.fontsize': font_scale*10 if largeFonts else font_scale*7, # was 10 + 'xtick.labelsize': font_scale*10 if largeFonts else font_scale*7, + 'ytick.labelsize': font_scale*10 if largeFonts else font_scale*7, + 'text.usetex': True, + 'figure.figsize': [fig_width,fig_height], + 'font.family': 'serif', + 'xtick.minor.size': 0.5, + 'xtick.major.pad': 1.5, + 'xtick.major.size': 1, + 'ytick.minor.size': 0.5, + 'ytick.major.pad': 1.5, + 'ytick.major.size': 1, + 'lines.linewidth': 0.9, + 'lines.markersize': 0.1, + 'hatch.linewidth': 0.5 + } + + matplotlib.rcParams.update(params) + plt.rcParams.update(params) + + +def format_axes(ax): + + for spine in ['top', 'right']: + ax.spines[spine].set_visible(False) + + for spine in ['left', 'bottom']: + ax.spines[spine].set_color(SPINE_COLOR) + ax.spines[spine].set_linewidth(0.5) + + ax.xaxis.set_ticks_position('bottom') + ax.yaxis.set_ticks_position('left') + + for axis in [ax.xaxis, ax.yaxis]: + axis.set_tick_params(direction='out', color=SPINE_COLOR) + + return ax + diff --git a/plots.ipynb b/plots.ipynb new file mode 100644 index 0000000..e0ecc7d --- /dev/null +++ b/plots.ipynb @@ -0,0 +1,6597 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import numpy as np\n", + "from os import path\n", + "\n", + "import multiprocessing as MP\n", + "import sys\n", + "from collections import defaultdict\n", + "from scipy.stats import spearmanr, kendalltau, mannwhitneyu\n", + "import datetime\n", + "import matplotlib as mpl\n", + "import dill" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sns.set_style(\"ticks\")\n", + "sns.set_context(\"paper\", font_scale=2.5, rc={\"lines.linewidth\": 3,\n", + " 'lines.markersize': 10,\n", + " 'legend.fontsize': 24})\n", + "sns.set_palette(\"Set1\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Data location" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Functions and constants to run the experiments are defined here." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run -i spaced_rep_code.py\n", + "%run -i plot_utils.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Data files should be kept at these paths." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "raw_data = \"./data/duolingo_reduced.csv\"\n", + "dict_data = \"./data/duo_dict.dill\"\n", + "\n", + "model_weights_file = \"power.duolingo.weights\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Load Data" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15.9 s, sys: 1.65 s, total: 17.5 s\n", + "Wall time: 17.5 s\n" + ] + } + ], + "source": [ + "%%time\n", + "df_duo = pd.read_csv(raw_data)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "df_duo['lexeme_comp'] = df_duo['learning_language']+\":\"+df_duo['lexeme_string']\n", + "convert = df_duo[['lexeme_comp','lexeme_id']].set_index('lexeme_comp').to_dict()['lexeme_id']" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 226 ms, sys: 3.11 ms, total: 229 ms\n", + "Wall time: 228 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "results_duo = pd.read_csv(open(model_weights_file, 'rb'),\n", + " sep=\"\\t\",\n", + " names=['label','value'],\n", + " header=None)\n", + "\n", + "results_duo = results_duo.set_index(\"label\")\n", + "\n", + "B = results_duo.loc[\"B\"]\n", + "start = 5\n", + "\n", + "duo_lexeme_difficulty = 2**(-(results_duo[start:]+results_duo.loc['bias']))\n", + "new_index = []\n", + "for ind in duo_lexeme_difficulty.index:\n", + " new_index.append(convert[ind])\n", + " \n", + "duo_lexeme_difficulty['new_index'] = new_index\n", + "duo_lexeme_difficulty.set_index('new_index',inplace=True)\n", + "\n", + "duo_map_lexeme = dict([(l_id,ind) for ind, l_id in enumerate(duo_lexeme_difficulty.index)])\n", + "\n", + "duo_lexeme_difficulty = duo_lexeme_difficulty['value'].tolist()\n", + "duo_alpha = (-2**(-results_duo.loc['right'])+1).iloc[0]\n", + "duo_beta = (2**(-results_duo.loc['wrong'])-1).iloc[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 53.5 s, sys: 8.15 s, total: 1min 1s\n", + "Wall time: 1min 1s\n" + ] + } + ], + "source": [ + "%%time\n", + "duo_dict = dill.load(open(dict_data, 'rb'))" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "107867" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(duo_dict)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 19.5 s, sys: 182 ms, total: 19.7 s\n", + "Wall time: 19.7 s\n" + ] + } + ], + "source": [ + "%%time\n", + "duo_pairs = get_unique_user_lexeme(duo_dict)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 10s, sys: 4.52 s, total: 1min 15s\n", + "Wall time: 1min 14s\n" + ] + } + ], + "source": [ + "%%time\n", + "initial_cond = df_duo[[\"lexeme_id\",\"user_id\",\"timestamp\"]].groupby([\"lexeme_id\",\"user_id\"]).min()[\"timestamp\"]\n", + "initial_cond = initial_cond.to_dict()\n", + "df_duo_index_set = df_duo.copy().set_index([\"lexeme_id\",\"user_id\",\"timestamp\"])\n", + "df_duo_index_set.sort_index(inplace=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 4h 17min 59s, sys: 57.8 s, total: 4h 18min 57s\n", + "Wall time: 4h 18min 11s\n" + ] + } + ], + "source": [ + "%%time\n", + "total_correct = []\n", + "total_seen = []\n", + "for ind, (u_id,l_id) in enumerate(duo_pairs):\n", + " for item in duo_dict[u_id][l_id]:\n", + " time = initial_cond[(l_id,u_id)]\n", + " correct = df_duo_index_set[\"history_correct\"].loc[(l_id,u_id,time)].tolist()[0]\n", + " seen = df_duo_index_set[\"history_seen\"].loc[(l_id,u_id,time)].tolist()[0]\n", + " total_correct.append(correct)\n", + " total_seen.append(seen)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2019-01-10T23:22:00.165905 0 / 5291058\n", + "2019-01-10T23:22:03.177796 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in duo_dict[u_id][l_id]:\n", + " time = initial_cond[(l_id,u_id)]\n", + " correct = df_duo_index_set[\"history_correct\"].loc[(l_id,u_id,time)].tolist()[0]\n", + " seen = df_duo_index_set[\"history_seen\"].loc[(l_id,u_id,time)].tolist()[0]\n", + " #print(correct, seen)\n", + " temp = None\n", + " if l_id not in temp_duo_map_lexeme:\n", + " temp_duo_map_lexeme[l_id] = duo_lexeme_difficulty[duo_map_lexeme[l_id]]\n", + " temp = temp_duo_map_lexeme[l_id]\n", + " item['n_0'] =temp*\\\n", + " 2**(-(right*correct+\\\n", + " wrong*(seen-correct)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2.51 s, sys: 682 ms, total: 3.19 s\n", + "Wall time: 3.19 s\n" + ] + } + ], + "source": [ + "%%time\n", + "training_pairs = get_training_pairs(duo_dict, duo_pairs)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "25.28% of sequences can be used for training/testing.\n" + ] + } + ], + "source": [ + "print('{:.2f}% of sequences can be used for training/testing.'\n", + " .format(len(training_pairs) / len(duo_pairs) * 100.))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2min 3s, sys: 59.3 s, total: 3min 2s\n", + "Wall time: 3min 12s\n" + ] + } + ], + "source": [ + "%%time\n", + "duo_stats_99 = calc_user_LL_dict(duo_dict, duo_alpha, duo_beta, duo_lexeme_difficulty, duo_map_lexeme, \n", + " success_prob=0.99, pairs=duo_pairs, verbose=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 45.5 s, sys: 35.3 s, total: 1min 20s\n", + "Wall time: 1min 25s\n" + ] + } + ], + "source": [ + "%%time\n", + "with warnings.catch_warnings():\n", + " warnings.filterwarnings('error')\n", + " duo_stats_training = calc_user_LL_dict(\n", + " duo_dict, duo_alpha, duo_beta, duo_lexeme_difficulty, duo_map_lexeme, \n", + " success_prob=0.99, training=True, pairs=training_pairs, verbose=False,\n", + " n_procs=None\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2min 32s, sys: 58.1 s, total: 3min 31s\n", + "Wall time: 8min 35s\n" + ] + } + ], + "source": [ + "%%time\n", + "threshold_LL = calc_LL_dict_threshold(duo_dict, alpha=duo_alpha, beta=duo_beta, pairs=duo_pairs, \n", + " lexeme_difficulty=duo_lexeme_difficulty, map_lexeme=duo_map_lexeme,\n", + " success_prob=0.99, verbose=False)\n", + "merge_with_thres_LL(duo_stats_99, threshold_LL, pairs=duo_pairs)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 25.4 s, sys: 1min 13s, total: 1min 38s\n", + "Wall time: 3min 5s\n" + ] + } + ], + "source": [ + "%%time\n", + "threshold_LL_training = calc_user_LL_dict_threshold(\n", + " duo_dict, alpha=duo_alpha, beta=duo_beta, pairs=training_pairs, \n", + " lexeme_difficulty=duo_lexeme_difficulty, map_lexeme=duo_map_lexeme,\n", + " success_prob=0.99, verbose=False, training=True)\n", + "\n", + "merge_with_thres_LL(duo_stats_training, threshold_LL_training, pairs=training_pairs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 13.8 s, sys: 3.12 s, total: 16.9 s\n", + "Wall time: 16.9 s\n" + ] + } + ], + "source": [ + "%%time\n", + "duo_durations = get_all_durations(duo_dict, duo_pairs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "73317 / 1337453 = 5.48% sequences selected.\n", + "CPU times: user 1.42 s, sys: 53.4 ms, total: 1.47 s\n", + "Wall time: 1.47 s\n" + ] + } + ], + "source": [ + "%%time\n", + "# Different sequences be chosen for different T\n", + "# The paper contains plots correspondnig to T \\in {3, 5, 7}\n", + "middle_dur_pairs = filter_by_duration(\n", + " durations_dict=duo_durations, \n", + " pairs=training_pairs, \n", + " T=3, alpha=0.1,\n", + " verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Calculate the metric" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 33s, sys: 6.67 s, total: 1min 40s\n", + "Wall time: 1min 40s\n" + ] + } + ], + "source": [ + "%%time\n", + "duo_forgetting_rate = calc_empirical_forgetting_rate(duo_dict, pairs=duo_pairs, no_norm=False)\n", + "base = calc_empirical_forgetting_rate(duo_dict, pairs=duo_pairs, return_base=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 121 ms, sys: 7.67 s, total: 7.79 s\n", + "Wall time: 12.2 s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "perf = duo_forgetting_rate\n", + "with_exact_reps = True\n", + "quantile = 0.25\n", + "with_training = True\n", + "\n", + "def top_k_reps_worker(reps):\n", + " max_reps = None if not with_exact_reps else reps + 1\n", + " stats_dict = duo_stats_99 if not with_training else duo_stats_training\n", + " # pairs = duo_pairs if not with_training else training_pairs\n", + " pairs = duo_pairs if not with_training else middle_dur_pairs\n", + " return reps, calc_top_k_perf(stats_dict, perf, pairs=pairs, quantile=quantile,\n", + " min_reps=reps, max_reps=max_reps, with_overall=True,\n", + " only_finite=False, with_threshold=True)\n", + "\n", + "reps_range = np.arange(1 if not with_training else 2, 8)\n", + "\n", + "# For performance\n", + "with MP.Pool(9) as pool:\n", + " top_k_99_reps = pool.map(top_k_reps_worker, reps_range)\n", + "\n", + "# For debugging\n", + "# top_k_99_reps = []\n", + "# for i in reps_range:\n", + "# top_k_99_reps.append(top_k_reps_worker(i))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2 MEM vs. Threshold MannwhitneyuResult(statistic=11505201.5, pvalue=1.1061918181801826e-07)\n", + "2 MEM vs. Uniform MannwhitneyuResult(statistic=12086002.0, pvalue=0.13714228906507603)\n", + "3 MEM vs. Threshold MannwhitneyuResult(statistic=6378420.0, pvalue=8.348829333034287e-32)\n", + "3 MEM vs. Uniform MannwhitneyuResult(statistic=6609413.5, pvalue=4.9564904131029064e-21)\n", + "4 MEM vs. Threshold MannwhitneyuResult(statistic=3464683.5, pvalue=2.7758587040052677e-20)\n", + "4 MEM vs. Uniform MannwhitneyuResult(statistic=3506376.5, pvalue=1.1489852105295113e-17)\n", + "5 MEM vs. Threshold MannwhitneyuResult(statistic=1561159.5, pvalue=1.2872524730984318e-08)\n", + "5 MEM vs. Uniform MannwhitneyuResult(statistic=1482814.0, pvalue=9.724375865400268e-16)\n", + "6 MEM vs. Threshold MannwhitneyuResult(statistic=712996.5, pvalue=0.036465675149430866)\n", + "6 MEM vs. Uniform MannwhitneyuResult(statistic=681236.5, pvalue=0.00014813991865410945)\n", + "7 MEM vs. Threshold MannwhitneyuResult(statistic=375957.0, pvalue=0.2854285834275138)\n", + "7 MEM vs. Uniform MannwhitneyuResult(statistic=368384.0, pvalue=0.09948268495401996)\n" + ] + } + ], + "source": [ + "stats = {}\n", + "for i in range(len(top_k_99_reps)): \n", + " mem_thresh = mannwhitneyu(top_k_99_reps[i][1]['perf_top_threshold'],\n", + " top_k_99_reps[i][1]['perf_top_mem'])\n", + " mem_unif = mannwhitneyu(\n", + " top_k_99_reps[i][1]['perf_top_mem'],top_k_99_reps[i][1]['perf_top_unif'])\n", + " stats[top_k_99_reps[i][0]]=(mem_thresh, mem_unif)\n", + " print(top_k_99_reps[i][0],\"MEM vs. Threshold\", stats[top_k_99_reps[i][0]][0])\n", + " print(top_k_99_reps[i][0],\"MEM vs. Uniform\", stats[top_k_99_reps[i][0]][1])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 0.4)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# T=7.0 alpha=0.1\n", + "# latexify(fig_width=2,largeFonts=False,columns=2,font_scale=1.0)\n", + "latexify(fig_width=3.4, largeFonts=True)\n", + "\n", + "plot_perf_by_reps_boxed(top_k_99_reps, with_threshold=True, std=False, \n", + " max_rev=7, median=True, stats=stats)\n", + "\n", + "format_axes(plt.gca())\n", + "plt.ylabel(\"$\\hat{n}$\")\n", + "plt.xlabel(\"\\# reviews\")\n", + "\n", + "plt.ylim(0, 0.4)\n", + "# plt.savefig(plot_path('empirical_p_recall_duo_new_boxed_split_T_3.pdf'), bbox_inches='tight',pad_inches=0)\n", + "# plt.savefig(plot_path('empirical_p_recall_duo_new_boxed.pdf'), bbox_inches='tight',pad_inches=0)\n", + "#plt.xlim(0,6*2+)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "205750 / 1337453 = 15.38% sequences selected.\n" + ] + } + ], + "source": [ + "middle_dur_pairs = filter_by_duration(\n", + " durations_dict=duo_durations, \n", + " pairs=training_pairs, \n", + " T=8, alpha=0.4,\n", + " verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of users = 322\n", + "CPU times: user 104 ms, sys: 6.59 ms, total: 110 ms\n", + "Wall time: 107 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "users = list(map(lambda f:f[0], middle_dur_pairs))\n", + "\n", + "from collections import OrderedDict\n", + "users_ = {}\n", + "for u in users:\n", + " if u in users_:\n", + " users_[u] += 1\n", + " else:\n", + " users_[u] = 0\n", + "users_ = OrderedDict(sorted(users_.items(), key=lambda x: -x[1]))\n", + "\n", + "users_ = OrderedDict(filter(lambda x: x[1]>70, users_.items()))\n", + "print('Number of users = ', len(users_))" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Completed = 0.0\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/scipy/stats/stats.py:3013: RuntimeWarning: invalid value encountered in double_scalars\n", + " prob = _betai(0.5*df, 0.5, df/(df+t_squared))\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/scipy/stats/stats.py:2998: RuntimeWarning: Mean of empty slice.\n", + " mx = x.mean()\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/numpy/core/_methods.py:85: RuntimeWarning: invalid value encountered in double_scalars\n", + " ret = ret.dtype.type(ret / rcount)\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/scipy/stats/stats.py:2999: RuntimeWarning: Mean of empty slice.\n", + " my = y.mean()\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/scipy/stats/stats.py:3003: RuntimeWarning: invalid value encountered in double_scalars\n", + " r = r_num / r_den\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Completed = 0.3105590062111801\n", + "Completed = 0.6211180124223602\n", + "Completed = 0.9316770186335404\n", + "CPU times: user 10.3 s, sys: 130 ms, total: 10.5 s\n", + "Wall time: 10.5 s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "results = []\n", + "for ind, u in enumerate(users_):\n", + " if ind % 100 == 0:\n", + " print(\"Completed = \", ind / len(users_))\n", + " \n", + " middle_dur_pairs_users = filter_by_users(middle_dur_pairs, [u], False) \n", + " perf = duo_forgetting_rate\n", + " with_exact_reps = True\n", + " with_training = True\n", + " threshold = 1.0\n", + " \n", + " def top_k_reps_worker(reps):\n", + " max_reps = None if not with_exact_reps else reps + 1\n", + " stats_dict = duo_stats_99 if not with_training else duo_stats_training\n", + " # pairs = duo_pairs if not with_training else training_pairs\n", + " pairs = middle_dur_pairs_users\n", + " return reps, calc_top_memorize(stats_dict, perf, pairs=pairs, \n", + " min_reps=reps, max_reps=max_reps, with_overall=True,\n", + " only_finite=True, with_threshold=True)\n", + "\n", + " reps_range = np.arange(1 if not with_training else 2, 10)\n", + "\n", + " # For performance\n", + " #with MP.Pool(9) as pool:\n", + " # top_k_99_reps = pool.map(top_k_reps_worker, reps_range)\n", + " #\n", + " # For debugging\n", + " top_k_99_reps = []\n", + " for i in reps_range:\n", + " reps, (corr_mem, corr_uniform, corr_thresh) = top_k_reps_worker(i)\n", + " if corr_mem[1] < threshold:\n", + " results.append((u, reps, corr_mem[0], \"Memorize\" ))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/seaborn/categorical.py:3666: UserWarning: The `factorplot` function has been renamed to `catplot`. The original name will be removed in a future release. Please update your code. Note that the default `kind` in `factorplot` (`'point'`) has changed `'strip'` in `catplot`.\n", + " warnings.warn(msg)\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/seaborn/categorical.py:3672: UserWarning: The `size` paramter has been renamed to `height`; please update your code.\n", + " warnings.warn(msg, UserWarning)\n", + "/home/utkarshu/miniconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1706: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "c1, c2, c3 = sns.color_palette(\"Set2\",n_colors=3)\n", + "df = pd.DataFrame(results, columns=[\"user\", \"Repetitions\", \n", + " \"Pearson Correlation\\nCoefficient\", \"Policy\"])\n", + "#df.plot(\"reps\",\"correlation\",kind=\"bar\")\n", + "df = df[df['Repetitions']<8]\n", + "df = df[df[\"Policy\"]==\"Memorize\"]\n", + "sns.factorplot(\"Repetitions\", \"Pearson Correlation\\nCoefficient\",hue=\"Policy\", data=df, size=2.2,\n", + " aspect=2, legend=False, estimator=np.median, ci=68,capsize=.2,#,hue_order=[\"Memorize\", \"Threshold\",\"Uniform\"],\n", + " palette=sns.color_palette(\"Set2\",n_colors=3), linestyles=[\"\"])\n", + "plt.hlines(0,-1,7, linestyle=\"--\")\n", + "#plt.legend(loc=9, ncol=3)\n", + "#plt.savefig(plot_path('user_n_perf_all.pdf'), \n", + "# bbox_inches='tight',pad_inches=0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/process_raw_data.py b/process_raw_data.py new file mode 100644 index 0000000..0cfab83 --- /dev/null +++ b/process_raw_data.py @@ -0,0 +1,59 @@ +"""Script to convert Duolingo dataset to have one entry per session with the student.""" +import click +import pandas as pd +import numpy as np + + +@click.command() +@click.argument('in_csv') +@click.argument('out_csv') +def cmd(in_csv, out_csv): + """Read in the raw data from IN_CSV, process it to keep only one entry + per session with binary recall signal, and save the output in OUT_CSV.""" + + print('Reading input ...') + raw_df = pd.read_csv(in_csv) + + print('Processing data ...') + raw_df.sort_values("timestamp", inplace=True) + + sess_seen = raw_df.groupby("lexeme_id").mean()['session_seen'] + first_review = raw_df.groupby(["lexeme_id", "user_id"]).first() + first_review['history_seen'] /= sess_seen + first_review['history_correct'] /= sess_seen + + new_df = raw_df.copy() + new_df['session_correct'] = (raw_df['session_correct'] / raw_df['session_seen']) > 0.99 + new_df['session_seen'] = 1 + new_df.sort_values(["user_id", "lexeme_id", "timestamp"], inplace=True) + new_df.reset_index(inplace=True) + new_df.drop("index", axis=1, inplace=True) + + current_u = None + current_l = None + result = [] + for _index, row in new_df.iterrows(): + if current_u != row['user_id'] or current_l != row['lexeme_id']: + history_seen = int(np.round(row['history_seen'] / sess_seen[row['lexeme_id']])) + history_correct = int(np.round(row['history_correct'] / sess_seen[row['lexeme_id']])) + row['history_seen'] = history_seen + row['history_correct'] = history_correct + else: + row['history_seen'] = history_seen + row['history_correct'] = history_correct + result.append(row) + current_u = row['user_id'] + current_l = row['lexeme_id'] + history_seen += row['session_seen'] + history_correct += row['session_correct'] + + cleaned_df = pd.DataFrame(result) + cleaned_df['session_correct'] = cleaned_df['session_correct'].astype("int") + + print('Writing output ...') + cleaned_df.to_csv(out_csv, index=False) + print('Done.') + + +if __name__ == '__main__': + cmd() diff --git a/spaced_rep_code.py b/spaced_rep_code.py new file mode 100644 index 0000000..1fae976 --- /dev/null +++ b/spaced_rep_code.py @@ -0,0 +1,1052 @@ +"""This file contains functions which are used to generate the log-likelihood for +different memory models and other code required to run the experiments in the +manuscript.""" + +import bisect +import heapq +import multiprocessing as MP +import warnings +from collections import OrderedDict, defaultdict + +import numpy as np +import pandas as pd +from scipy.stats import kendalltau, ks_2samp, spearmanr + +import matplotlib.patches as mpatches +import matplotlib.pyplot as plt +import seaborn as sns + +# Constants + +TIME_SCALE = 60 * 60 * 24 + +MODEL_POWER = True +B = [1] +POWER_B = 1 + + +def get_unique_user_lexeme(data_dict): + """Get all unique (user, lexeme) pairs.""" + pairs = set() + for u_id in data_dict.keys(): + pairs.update([(u_id, x) for x in data_dict[u_id].keys()]) + + return sorted(pairs) + + +def max_unif(N, sum_D): + """Find maximum value of N * log(x) - x * sum_D""" + x_max = N / sum_D + return N * np.log(x_max) - sum_D * x_max + + +def max_memorize(n_0, a, b, recalled, Ds, + q_fixed=None, n_max=np.inf, n_min=0, verbose=True): + """Return max_{over q} memorizeLL.""" + + # TODO: Currently, these are not true. + # n_max=1440, n_min=1/36500000 + # maximum forgetting rate is clipped at 1 minute for exp(-1) forgetting and + # minimum forgetting rate is that exp(-1) chance of forgetting after 100,000 years. + + assert len(recalled) == len(Ds), "recalled and t_is are not of the same length." + + N = len(Ds) + n_t = n_0 + log_sum = 0 + int_sum = 0 + + n_ts = [] + m_dts = [] + + not_warned_min, not_warned_max = True, True + + n_correct, n_wrong = 0, 0 + + with warnings.catch_warnings(): + warnings.simplefilter('once' if verbose else 'ignore') + + for D, recall in zip(Ds, recalled): + if MODEL_POWER is False: + m_dt = np.exp(-n_t * D) + else: + m_dt = (1 + POWER_B*D)**(-n_t) + + n_ts.append(n_t) + m_dts.append(m_dt) + + if n_t < 1e-20: + # log_sum += np.log(n_0) + n_correct * np.log(a) + n_wrong * np.log(b) + np.log(D) + int_sum += n_t * (D ** 2) / 2 + else: + if MODEL_POWER is False: + int_sum += D + np.expm1(-n_t * D) / n_t + else: + int_sum += D - ((1 + POWER_B * D) ** (1 - n_t) - 1) / (POWER_B * (1 - n_t)) + + if m_dt >= 1.0: + log_sum = -np.inf + else: + log_sum += np.log1p(-m_dt) + + if recall: + n_t *= (1 - a) + n_correct += 1 + else: + n_t *= (1 + b) + n_wrong += 1 + + n_t = min(n_max, max(n_min, n_t)) + + if n_t == n_max and not_warned_max: + if verbose: + warnings.warn('Max boundary hit.') + not_warned_max = False + + if n_t == n_min and not_warned_min: + if verbose: + warnings.warn('Min boundary hit.') + not_warned_min = False + + if int_sum != 0: + q_max = 1 / (4 * ((N / 2) / int_sum) ** 2) if q_fixed is None else q_fixed + else: + # If int_sum == 0, then LL should be -inf, not NaN + q_max = 1.0 + + LL = log_sum - (N / 2) * np.log(q_max) - (1 / q_max)**(0.5) * int_sum + + return { + 'q_max' : q_max, + 'n_ts' : n_ts, + 'm_dts' : m_dts, + 'm_mean' : np.mean(m_dts), + 'log_sum' : log_sum, + 'int_sum' : int_sum, + 'LL' : LL, + 'max_boundary_hit' : not not_warned_max, + 'min_boundary_hit' : not not_warned_min, + 'n_max' : n_max, + 'n_min' : n_min + } + + +def get_training_pairs(data_dict, pairs): + """Returns the subset of pairs which have more than 3 reviews, i.e. + the set for which we will be able to perform training using `n-1` reviews + and testing for the last review.""" + + training_pairs = [] + for u_id, l_id in pairs: + if len(data_dict[u_id][l_id]) >= 3: + training_pairs.append((u_id, l_id)) + + return training_pairs + + +def calc_ll_arr(method, data_arr, alpha=None, beta=None, + success_prob=0.49, eps=1e-10, + all_mem_output=False, verbose=True): + """Calculate LL for a given user_id, lexeme_id pair's data_arr.""" + n_0 = data_arr[0]['n_0'] + + if method == 'uniform': + sum_D = max(sum(x['delta_scaled'] for x in data_arr), eps) + N = len(data_arr) + return max_unif(N, sum_D) + elif method == 'memorize': + recalled = np.asarray([x['p_recall'] > success_prob for x in data_arr]) + deltas = np.asarray([x['delta_scaled'] for x in data_arr]) + deltas = np.where(deltas <= 0, eps, deltas) + op = max_memorize(n_0, alpha, beta, recalled, deltas, verbose=verbose) + if not all_mem_output: + return op['LL'] + else: + return op + else: + raise ValueError("Invalid method: {}".format(method)) + + +def calc_user_LL_dict(data_dict, alpha, beta, lexeme_difficulty, map_lexeme, + success_prob=0.49, n_procs=None, pairs=None, verbose=True, + training=False): + """Calculate LL while assuming that the LL factors are the same per user + instead of setting them for each (user, lexeme) pair. + + If `training` is True, then the LL calculation is done only for the + first n-1 entries instead of for all events in the sequence. + """ + + u_l_dict = defaultdict(lambda: defaultdict(lambda: {})) + + lexeme_difficulty = np.abs(lexeme_difficulty) + + global stat_worker + def stat_worker(params): + u_id = params + data_per_lexeme = data_dict[u_id] + + n_0s = [] + Ns, sumDs = [], [] + log_sums, int_sums = [], [] + all_mem_op = [] + + # The tests for all lexemes. + all_tests = [] + + lexeme_ids = sorted(data_per_lexeme.keys()) + valid_lexeme_ids = [] + + for l_id in lexeme_ids: + arr = data_per_lexeme[l_id] + + if training: + if len(arr) < 3: + # Cannot calculate the LL for sequences shorter than 3 + # elements if we are looking to train + test with these + # sequences. + continue + else: + # Ignore the last review, which we will use for testing. + all_tests.append(arr[-1]) + # Append the test before truncating arr + arr = arr[:-1] + + valid_lexeme_ids.append(l_id) + n_0 = arr[0]['n_0'] + n_0s.append(n_0) + Ns.append(len(arr)) + sumDs.append(sum(x['delta_scaled'] for x in arr)) + mem_res = calc_ll_arr('memorize', arr, + alpha=alpha, beta=beta, + success_prob=success_prob, all_mem_output=True, + verbose=verbose) + log_sums.append(mem_res['log_sum']) + int_sums.append(mem_res['int_sum']) + all_mem_op.append(mem_res) + + c_unif = np.sum(Ns) / np.sum(sumDs) + q_max = 1 / (4 * ((np.sum(Ns) / 2) / np.sum(int_sums)) ** 2) + res = {} + for idx, l_id in enumerate(valid_lexeme_ids): + res[l_id] = { + 'uniform_LL': Ns[idx] * np.log(c_unif) - sumDs[idx] * c_unif, + 'memorize_LL': log_sums[idx] + Ns[idx] * np.log(q_max) / 2 - (1 / q_max)**(0.5) * int_sums[idx], + 'mem_op': all_mem_op[idx], + 'q_max': q_max, + 'c_unif': c_unif + } + + if training: + res[l_id]['test'] = all_tests[idx] + + return u_id, res + + if n_procs is None: + n_procs = MP.cpu_count() + + user_ids = sorted(set([u_id for u_id, _ in pairs])) + + with MP.Pool(n_procs) as pool: + if n_procs > 1: + map_func = pool.map + else: + # This aids debugging. + map_func = map + + for u_id, res in map_func(stat_worker, user_ids): + u_l_dict[u_id] = res + + return u_l_dict + + +def max_threshold(n_0, a, b, recalled, Ds, w, p, + alpha_fixed=None, n_max=np.inf, n_min=0, verbose=True): + """Return max_{over a} threshold-LL, unless alpha_fixed is provided. + In that case, the LL is calculated for the given alpha. + + Note (relationship of the symbols with those used in the paper): + - p is m_{th} in the paper. + - alpha (also alpha_max) is c in the paper + - w is 1/\zeta in the paper. + """ + + assert len(recalled) == len(Ds), "recalled and t_is are not of the same length." + + N = len(Ds) + n_t = n_0 + log_sum = 0 + int_sum = 0 + + n_ts = [] + m_dts = [] + tau_dts = [] + not_warned_min, not_warned_max = True, True + + n_correct, n_wrong = 0, 0 + + sum_third = 0 + sum_second = 0 + with warnings.catch_warnings(): + warnings.simplefilter('once' if verbose else 'ignore') + + for D, recall in zip(Ds, recalled): + if MODEL_POWER is True: + tau = (np.exp(-np.log(p) / n_t) - 1) / B[0] + else: + tau = -np.log(p) / n_t + if n_t < 1e-20 and p != 1.0: + raise Exception("P should be 1 when n_t is not finite") + # When n_t is too small, p should also be 1. + elif n_t < 1e-20 and p == 1.0: + D_ = np.max([D, 0.0001]) + else: + D_ = np.max([D - tau, 0.0001]) + sum_third += w * np.expm1(-D_ / w) + sum_second += -D_ / w + + n_ts.append(n_t) + m_dts.append(np.exp(-n_t * D)) + tau_dts.append(tau) + + if recall: + n_t *= a + n_correct += 1 + else: + n_t *= b + n_wrong += 1 + + n_t = min(n_max, max(n_min, n_t)) + + if n_t == n_max and not_warned_max: + if verbose: + warnings.warn('Max boundary hit.') + not_warned_max = False + + if n_t == n_min and not_warned_min: + if verbose: + warnings.warn('Min boundary hit.') + not_warned_min = False + + if alpha_fixed is None: + alpha_max = -N / sum_third + else: + alpha_max = alpha_fixed + + LL = N * np.log(np.max([alpha_max, 0.0001])) + sum_second + alpha_max * sum_third + if np.isfinite(LL).sum() == 0: + raise Exception("LL is not finite") + + return { + 'alpha_max': alpha_max, + 'n_ts': n_ts, + 'm_dts': m_dts, + 'm_mean': np.mean(m_dts), + 'log_sum': log_sum, + 'int_sum': int_sum, + 'LL': LL, + 'max_boundary_hit': not not_warned_max, + 'min_boundary_hit': not not_warned_min, + 'n_max': n_max, + 'n_min': n_min, + 'p': p, + 'w': w, + + 'sum_second': sum_second, # sum_i -D_i / w + 'sum_third': sum_third, # sum_i w * (exp(-D_i / w) - 1) + 'N': N + } + + +def calc_ll_arr_thres( + method, data_arr, alpha=None, beta=None, + success_prob=0.49, eps=1e-10, w_range=None, p_range=None, + verbose=True, all_thres_output=True, alpha_fixed=None): + + assert method == 'threshold', "This function only computes the max_threshold LL." + + n_0 = data_arr[0]['n_0'] + recalled = np.asarray([x['p_recall'] > success_prob for x in data_arr]) + deltas = np.asarray([x['delta_scaled'] for x in data_arr]) + deltas = np.where(deltas <= 0, eps, deltas) + best_LL = None + + if w_range is None: + w_range = [0.01, 0.1, 1, 10, 100] + + n_is = [n_0] + + with warnings.catch_warnings(): + warnings.simplefilter('once' if verbose else 'ignore') + for x in data_arr: + if x['p_recall'] > success_prob: + n_is.append(n_is[-1] * alpha) + else: + n_is.append(n_is[-1] * beta) + + # Remove the last n_t + n_is = np.array(n_is[:-1]) + + if p_range is None: + # In most cases p_ == 1, the np.unique limits useless iterations. + if (n_is < 1e-20).sum() > 0: + p_range = [1.0] + else: + p_ = np.exp(-deltas * n_is).max() + p_range = np.unique(np.linspace(p_, 1, 4)) + + for w in w_range: + for p in p_range: + op = max_threshold(n_0, a=alpha, b=beta, recalled=recalled, + Ds=deltas, p=p, w=w, verbose=verbose, + alpha_fixed=alpha_fixed) + if best_LL is None or best_LL['LL'] < op['LL']: + best_LL = op + + if all_thres_output: + return best_LL + else: + return best_LL['LL'] + + +def calc_LL_dict_threshold(data_dict, alpha, beta, pairs, + lexeme_difficulty, map_lexeme, success_prob=0.49, + p_range=None, w_range=None, + n_procs=None, verbose=True): + """Calculate the LL of the threshold model optimized for each (user, item) + pair.""" + u_l_dict = defaultdict(lambda: {}) + + lexeme_difficulty = np.abs(lexeme_difficulty) + + global _max_threshold_worker + def _max_threshold_worker(params): + u_id, l_id = params + arr = data_dict[u_id][l_id] + op = calc_ll_arr_thres('threshold', arr, alpha=alpha, beta=beta, + success_prob=success_prob, all_thres_output=True, + verbose=verbose) + return u_id, l_id, {'threshold_op': op, 'threshold_LL': op['LL']} + + if n_procs is None: + n_procs = MP.cpu_count() + + with MP.Pool() as pool: + for u_id, l_id, res in pool.map(_max_threshold_worker, pairs): + u_l_dict[u_id][l_id] = res + + return u_l_dict + + +def calc_user_ll_arr_thres( + method, user_data_dict, alpha=None, beta=None, + success_prob=0.49, eps=1e-10, w_range_init=None, p_range_init=None, + training=False, verbose=True, all_thres_output=True): + """Calculates the best-LL for a given user, by computing it across all + items the user has touched. + + If `training` is True, then only consider the first 'n - 1' reviews + of the user/lexme pairs, ignoring sequences smaller than 2. + """ + + assert method == 'threshold', "This function only computes the max_threshold LL." + + total_sum_second = defaultdict(lambda: 0) + total_sum_third = defaultdict(lambda: 0) + total_N = 0 + p_ = 0.0 + + if w_range_init is None: + w_range = [0.01, 0.1, 1, 10, 100] + else: + w_range = w_range_init + + if p_range_init is None: + for l_id in user_data_dict.keys(): + data_arr = user_data_dict[l_id] + + n_0 = data_arr[0]['n_0'] + deltas = np.asarray([x['delta_scaled'] for x in data_arr]) + deltas = np.where(deltas <= 0, eps, deltas) + + n_is = [n_0] + + with warnings.catch_warnings(): + warnings.simplefilter('once' if verbose else 'ignore') + for x in data_arr: + if x['p_recall'] > success_prob: + n_is.append(n_is[-1] * alpha) + else: + n_is.append(n_is[-1] * beta) + + # Remove the last n_t + n_is = np.array(n_is[:-1]) + + # In most cases p_ == 1, the np.unique limits useless iterations. + if (n_is < 1e-20).sum() > 0: + p_ = 1.0 + else: + p_ = max(p_, np.exp(-deltas * n_is).max()) + + if p_ < 1.0: + p_range = np.linspace(p_, 1, 4) + else: + # if p_ == 1.0, then no point taking linspace. + p_range = [p_] + else: + p_range = p_range_init + + for l_id in user_data_dict.keys(): + data_arr = user_data_dict[l_id] + + if training: + if len(data_arr) < 3: + # Cannot calculate the LL for training and have a test unless + # there are at least 3 reviews. + continue + else: + # Calculate the LL only using the first 'n-1' reviews. + data_arr = data_arr[:-1] + + total_N += len(data_arr) + + n_0 = data_arr[0]['n_0'] + recalled = np.asarray([x['p_recall'] > success_prob for x in data_arr]) + deltas = np.asarray([x['delta_scaled'] for x in data_arr]) + deltas = np.where(deltas <= 0, eps, deltas) + + for w in w_range: + for p in p_range: + op = max_threshold(n_0, a=alpha, b=beta, recalled=recalled, + Ds=deltas, p=p, w=w, verbose=verbose) + total_sum_second[w, p] += op['sum_second'] + total_sum_third[w, p] += op['sum_third'] + + best_LL = None + for w, p in total_sum_second.keys(): + alpha_max_user = - total_sum_third[w, p] / total_N + LL = total_N * alpha_max_user + total_sum_second[w, p] + alpha_max_user * total_sum_third[w, p] + if best_LL is None or best_LL['LL'] < LL: + best_LL = { + 'LL': LL, + 'w': w, + 'p': p, + 'sum_third': total_sum_third[w, p], + 'sum_second': total_sum_second[w, p], + 'alpha_max_user': alpha_max_user + } + + if all_thres_output: + return best_LL + else: + return best_LL['LL'] + + +def calc_user_LL_dict_threshold(data_dict, alpha, beta, pairs, + lexeme_difficulty, map_lexeme, success_prob=0.49, + p_range=None, w_range=None, training=False, + n_procs=None, verbose=True): + """Calculate the LL of the threshold model optimized for each user. + + if `training` is True, then it computes the likelihood only for the first + `n - 1` entries instead of for all 'n' reviews. + """ + + u_l_dict = defaultdict(lambda: {}) + + lexeme_difficulty = np.abs(lexeme_difficulty) + + if n_procs is None: + n_procs = MP.cpu_count() + + global _max_user_c_worker + def _max_user_c_worker(params): + u_id = params + best_LL = calc_user_ll_arr_thres('threshold', + user_data_dict=data_dict[u_id], + alpha=alpha, beta=beta, + success_prob=success_prob, + training=training, + all_thres_output=True, + verbose=verbose) + return u_id, best_LL + + with MP.Pool() as pool: + u_best_alpha = dict(pool.map(_max_user_c_worker, data_dict.keys())) + + global _max_user_threshold_worker + def _max_user_threshold_worker(params): + u_id, l_id = params + alpha_max_user = u_best_alpha[u_id]['alpha_max_user'] + + w_range = [u_best_alpha[u_id]['w']] + p_range = [u_best_alpha[u_id]['p']] + + arr = data_dict[u_id][l_id] + if training: + assert len(arr) >= 3, "Are you using `training_pairs` instead of" \ + " all pairs in the call?" + test = arr[-1] + # Append the test before truncating arr + arr = arr[:-1] + + op = calc_ll_arr_thres('threshold', arr, alpha=alpha, beta=beta, + success_prob=success_prob, + all_thres_output=True, verbose=verbose, + alpha_fixed=alpha_max_user, w_range=w_range, + p_range=p_range) + res = {'threshold_op': op, 'threshold_LL': op['LL']} + + if training: + res['test'] = test + + return u_id, l_id, res + + with MP.Pool() as pool: + for u_id, l_id, res in pool.map(_max_user_threshold_worker, pairs): + u_l_dict[u_id][l_id] = res + + return u_l_dict + + +def merge_with_thres_LL(other_LL, thres_LL, pairs): + """Merge the dictionaries containing the threshold-LL and other thresholds. + Other_LL will be modified in place. + """ + + for u_id, l_id in pairs: + for key in thres_LL[u_id][l_id]: + other_LL[u_id][l_id][key] = thres_LL[u_id][l_id][key] + + return None + + +def get_all_durations(data_dict, pairs): + """Generates all durations from the LL_dict or the data_dict.""" + + def _get_duration(user_id, item_id): + """Generates test/train/total duration for the given user_id, item_id pair.""" + session = data_dict[user_id][item_id] + session_length = len(session) + + if session_length > 2: + train_duration = session[-2]['timestamp'] - session[0]['timestamp'] + test_duration = session[-1]['timestamp'] - session[-2]['timestamp'] + else: + train_duration = None + test_duration = None + + if session_length > 1: + total_duration = session[-1]['timestamp'] - session[0]['timestamp'] + else: + total_duration = None + + return { + 'train_duration': train_duration, + 'test_duration': test_duration, + 'total_duration': total_duration, + 'session_length': session_length, + } + + dur_dict = defaultdict(lambda: {}) + for u_id, i_id in pairs: + dur_dict[u_id][i_id] = _get_duration(u_id, i_id) + + return dur_dict + + +def filter_by_duration(durations_dict, pairs, T, alpha, verbose=False): + """Filter the (u_id, l_id) by selecting those which have the duration in + [(1 - alpha) * T, (1 + alpha) * T].""" + filtered_pairs = [] + + for u_id, l_id in pairs: + train_duration = durations_dict[u_id][l_id]['train_duration'] / TIME_SCALE + if (1 - alpha) * T <= train_duration <= (1 + alpha) * T: + filtered_pairs.append((u_id, l_id)) + + count = len(filtered_pairs) + + total = len(pairs) + if verbose: + print('{} / {} = {:.2f}% sequences selected.' + .format(count, total, count / total * 100.)) + + return filtered_pairs + + +def filter_by_users(pairs, users_, verbose=False): + """Filter the (u_id, l_id) by selecting those which have u_id \in users_.""" + filtered_pairs = [] + + for u_id, l_id in pairs: + if u_id in users_: + filtered_pairs.append((u_id, l_id)) + + count = len(filtered_pairs) + + total = len(pairs) + if verbose: + print('{} / {} = {:.2f}% sequences selected.' + .format(count, total, count / total * 100.)) + + return filtered_pairs + + +def calc_empirical_forgetting_rate(data_dict, pairs, return_base=False, no_norm=False): + u_l_dict = defaultdict(lambda: defaultdict(lambda: None)) + + base = {} + base_count = {} + for u_id, l_id in pairs: + first_session = data_dict[u_id][l_id][0] + res = (- np.log(max(0.01, min(0.99, first_session['p_recall'] + 1e-10))) / (first_session['delta_scaled'] + 0.1)) + if l_id not in base: + base[l_id] = res + base_count[l_id] = 1 + else: + base[l_id]+=res + base_count[l_id] += 1 + if return_base: + return dict([(l_id, base[l_id] / base_count[l_id]) for l_id in base.keys()]) + for u_id, l_id in pairs: + last_session = data_dict[u_id][l_id][-1] + u_l_dict[u_id][l_id] = - np.log(max(0.01, min(0.99, last_session['p_recall'] + 1e-10))) / (last_session['delta_scaled'] + 0.1) + if not no_norm: + u_l_dict[u_id][l_id] = (u_l_dict[u_id][l_id]) / (base[l_id] / base_count[l_id]) + else: + u_l_dict[u_id][l_id] = u_l_dict[u_id][l_id] + + return u_l_dict + + +def calc_top_k_perf(LL_dict, perf, pairs, quantile=0.25, min_reps=0, + max_reps=None, with_overall=False, with_threshold=False, + only_finite=True, with_uniform=True, whis=1.5): + """Calculates the average and median performance of people in the + top quantile by log-likelihood of following either strategy.""" + + def check_u_l(u_id, l_id): + return (not only_finite or np.isfinite(perf[u_id][l_id])) and \ + (min_reps <= 1 or len(LL_dict[u_id][l_id]['mem_op']['n_ts']) >= min_reps) and \ + (max_reps is None or len(LL_dict[u_id][l_id]['mem_op']['n_ts']) < max_reps) + + # global _get_top_k + def _get_top_k(key): + sorted_by_ll = sorted((LL_dict[u_id][l_id][key], u_id, l_id) + for u_id, l_id in pairs + if check_u_l(u_id, l_id)) + # print("counts {}".format(len(sorted_by_ll))) + # Taking the quantile after limiting to only valid pairs. + K = int(quantile * len(sorted_by_ll)) + # print("K: {}".format(K), quantile, len(sorted_by_ll[-K:]), len(sorted_by_ll[-K:])) + return sorted_by_ll[-K:], sorted_by_ll[:K] + + top_memorize_LL, bottom_memorize_LL = _get_top_k('memorize_LL') + + top_common_u_l = set() + bottom_common_u_l = set() + if with_uniform: + top_uniform_LL, bottom_uniform_LL = _get_top_k('uniform_LL') + top_common_u_l = set([(u_id, l_id) for _, u_id, l_id in top_uniform_LL]).intersection( + [(u_id, l_id) for _, u_id, l_id in top_memorize_LL]) + + bottom_common_u_l = set([(u_id, l_id) for _, u_id, l_id in bottom_uniform_LL]).intersection( + [(u_id, l_id) for _, u_id, l_id in bottom_memorize_LL]) + + if with_threshold: + top_threshold_LL, bottom_threshold_LL = _get_top_k('threshold_LL') + + # If we have already calculated a common set, then calculate + # intersection with that set. Otherwise, take the intersection with + # memorize directly. + if not with_uniform: + top_common_u_l = set([(u_id, l_id) for _, u_id, l_id in top_threshold_LL]).intersection( + [(u_id, l_id) for _, u_id, l_id in top_memorize_LL]) + + bottom_common_u_l = set([(u_id, l_id) for _, u_id, l_id in bottom_threshold_LL]).intersection( + [(u_id, l_id) for _, u_id, l_id in bottom_memorize_LL]) + else: + top_common_u_l = top_common_u_l.intersection( + [(u_id, l_id) for _, u_id, l_id in top_threshold_LL]) + bottom_common_u_l = bottom_common_u_l.intersection( + [(u_id, l_id) for _, u_id, l_id in bottom_threshold_LL]) + + # global _perf_top_k + def _perf_top_k(top_ll): + return [perf[u_id][l_id] + for _, u_id, l_id in top_ll + if (u_id, l_id) not in top_common_u_l] + + def _perf_top_k_elem(top_ll): + return [(u_id, l_id) + for _, u_id, l_id in top_ll + if (u_id, l_id) not in top_common_u_l] + + def _perf_bottom_k(bottom_ll): + return [perf[u_id][l_id] + for _, u_id, l_id in bottom_ll + if (u_id, l_id) not in bottom_common_u_l] + + # Selecting only non-unique (u_id, l_id) from the top 25% of both. + # Because several times, the same user, lexeme pair have likelihood in the + # top 25%. + # print("common {}".format(len(top_common_u_l))) + perf_top_mem = _perf_top_k(top_memorize_LL) + perf_top_mem_elem = _perf_top_k_elem(top_memorize_LL) + perf_bottom_mem = _perf_bottom_k(bottom_memorize_LL) + + perc = [0.1, 0.2, 0.25, 0.30, 0.40, 0.5, 0.6, 0.7, 0.75, 0.8, 0.9] + + res = { + 'mem_top': pd.Series(perf_top_mem).describe(percentiles=perc), + 'mem_top_elem': perf_top_mem_elem, + 'mem_bottom': pd.Series(perf_bottom_mem).describe(percentiles=perc), + 'top_memorize_LL': top_memorize_LL, + 'bottom_memorize_LL': bottom_memorize_LL, + + 'perf_top_mem': perf_top_mem, + + 'top_common_u_l': top_common_u_l, + 'bottom_common_u_l': bottom_common_u_l + } + + mem_min_whis = res['mem_top']['25%'] - (res['mem_top']['75%'] - res['mem_top']['25%']) * whis + ind = np.asarray(perf_top_mem) < mem_min_whis + if ind.sum() == 0: + res['mem_top'].loc['min_whis'] = np.asarray(perf_top_mem).min() + else: + res['mem_top'].loc['min_whis'] = np.asarray(perf_top_mem)[ind].max() + + mem_max_whis = res['mem_top']['75%'] + (res['mem_top']['75%'] - res['mem_top']['25%']) * whis + ind = np.asarray(perf_top_mem) > mem_max_whis + if ind.sum() == 0: + res['mem_top'].loc['max_whis'] = np.asarray(perf_top_mem).max() + else: + res['mem_top'].loc['max_whis'] = np.asarray(perf_top_mem)[ind].min() + + if with_uniform: + perf_top_unif = _perf_top_k(top_uniform_LL) + perf_top_unif_elem = _perf_top_k_elem(top_uniform_LL) + perf_bottom_unif = _perf_bottom_k(bottom_uniform_LL) + + res.update({ + 'unif_top': pd.Series(perf_top_unif).describe(percentiles=perc), + 'unif_top_elem': perf_top_unif_elem, + 'unif_bottom': pd.Series(perf_bottom_unif).describe(percentiles=perc), + 'top_uniform_LL': top_uniform_LL, + 'bottom_uniform_LL': bottom_uniform_LL, + 'perf_top_unif': perf_top_unif, + }) + + uni_min_whis = res['unif_top']['25%'] - (res['unif_top']['75%'] - res['unif_top']['25%']) * whis + ind = np.asarray(perf_top_unif) < uni_min_whis + if ind.sum() == 0: + res['unif_top'].loc['min_whis'] = np.asarray(perf_top_mem).min() + else: + res['unif_top'].loc['min_whis'] = np.asarray(perf_top_mem)[ind].max() + + uni_max_whis = res['unif_top']['75%'] + (res['unif_top']['75%'] - res['unif_top']['25%']) * whis + ind = np.asarray(perf_top_unif) > uni_max_whis + if ind.sum() ==0: + res['unif_top'].loc['max_whis'] = np.asarray(perf_top_unif).max() + else: + res['unif_top'].loc['max_whis'] = np.asarray(perf_top_unif)[ind].min() + + if with_threshold: + perf_top_threshold = _perf_top_k(top_threshold_LL) + perf_top_threshold_elem = _perf_top_k_elem(top_threshold_LL) + perf_bottom_threshold = _perf_bottom_k(bottom_threshold_LL) + + res.update({ + 'threshold_top': pd.Series(perf_top_threshold).describe(percentiles=perc), + 'threshold_top_elem': perf_top_threshold_elem, + 'threshold_bottom': pd.Series(perf_bottom_threshold).describe(percentiles=perc), + 'top_threshold_LL': top_threshold_LL, + 'bottom_threshold_LL': bottom_threshold_LL, + 'perf_top_threshold': perf_top_threshold, + }) + + thr_min_whis = res['threshold_top']['25%'] - (res['threshold_top']['75%'] - res['threshold_top']['25%']) * whis + ind = np.asarray(perf_top_threshold) thr_max_whis + if ind.sum() == 0: + res['threshold_top'].loc['max_whis'] = np.asarray(perf_top_threshold).max() + else: + res['threshold_top'].loc['max_whis'] = np.asarray(perf_top_threshold)[ind].min() + if with_overall: + res['unif_top_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in top_uniform_LL).describe() + res['mem_top_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in top_memorize_LL).describe() + + res['unif_bottom_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in bottom_uniform_LL).describe() + res['mem_bottom_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in bottom_memorize_LL).describe() + + if with_threshold: + res['threshold_top_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in top_threshold_LL).describe() + res['threshold_bottom_overall'] = pd.Series(perf[u_id][l_id] for _, u_id, l_id in bottom_threshold_LL).describe() + + return res + + +def calc_top_memorize(LL_dict, perf, pairs, min_reps=0, + max_reps=None, with_overall=False, with_threshold=False, + only_finite=True, with_uniform=True): + """Calculates the average and median performance of people in the + top quantile by log-likelihood of following either strategy.""" + from scipy.stats.stats import pearsonr + + def check_u_l(u_id, l_id): + return (not only_finite or np.isfinite(perf[u_id][l_id])) and \ + (min_reps <= 1 or len(LL_dict[u_id][l_id]['mem_op']['n_ts']) >= min_reps) and \ + (max_reps is None or len(LL_dict[u_id][l_id]['mem_op']['n_ts']) < max_reps) + + quantile = 0.1 + + def _get_top_k(key): + sorted_by_ll = sorted((LL_dict[u_id][l_id][key], u_id, l_id) + for u_id, l_id in pairs + if check_u_l(u_id, l_id)) + K = int(quantile * len(sorted_by_ll)) + restricted = sorted_by_ll[:K] + sorted_by_ll[-K:] + coeff = pearsonr([ll for ll, u_id, l_id in restricted], [perf[u_id][l_id] for _, u_id, l_id in restricted]) + if ~np.isfinite(coeff[0]): + # print("NAN", restricted) + pass + return coeff + + top_memorize_LL = _get_top_k('memorize_LL') + top_uniform_LL = _get_top_k('uniform_LL') + top_threshold_LL = _get_top_k('threshold_LL') + return top_memorize_LL, top_uniform_LL, top_threshold_LL + + +def plot_perf_by_reps_boxed(reps_perf_pairs, median=True, + with_threshold=False, std=False, + max_rev=5, stats=None): + """Produces plots comparing different scheduling techniques.""" + + def mean_var(data, color, positions, hatch): + labels = [] + means = [] + err = [] + for d, pos in zip(data, positions): + confidence = 0.95 + m, se = np.mean(d), stats.sem(d) + n = len(d) + h = se * stats.t._ppf((1 + confidence) / 2., n - 1) + means.append(m) + err.append(h) + labels.append(pos) + plt.errorbar(labels, means, yerr=err, fmt='o', capsize=5, elinewidth=3, capthick=2.5, color=color) + + def boxify(data, color, positions, hatch, w): + boxprops = dict(linewidth=0, color=None, facecolor=color, alpha=0.6) + whiskerprops = dict(linewidth=3, alpha=0.0) + medianprops = dict(linewidth=0.9, color='black') + meanlineprops = dict(linestyle='--', markersize=12.5, color=color) + capprops = dict(linestyle='-', linewidth=3, color='black', alpha=0) + bp = plt.boxplot(data, notch=False, showmeans=False, positions=positions, + boxprops=boxprops, meanprops=meanlineprops, + whiskerprops=whiskerprops, medianprops=medianprops, + capprops=capprops, patch_artist=True, + widths=[w] * len(data)) # a simple case with just one variable to boxplot + for median in bp['medians']: + x, y = median.get_data() + dx = x[1] - x[0] + median.set_data([x[0] + dx / 4, x[1] - dx / 4], y) + + def label_diff(stats, X, Y_1, Y_2, W, repetitions, ind): + for i in range(len(repetitions)): + p_val = stats[int(repetitions[i])][ind][1] + y = 1.1 * max(Y_1[i], Y_2[i]) + + props = { + 'connectionstyle': 'bar', + 'arrowstyle': '-', + 'shrinkA': 0, + 'shrinkB': 0, + 'linewidth': 0.7 + } + + if p_val < 0.05: + plt.gca().annotate("*", xy=(X[i], y + 0.01), zorder=10, fontsize=10) + plt.gca().annotate('', xy=(X[i], y), xytext=(X[i] + 3 * W / 4, y), arrowprops=props) + + plt.figure() + c1, c2, c3 = sns.color_palette("Set2", n_colors=3) + + mem_lows, mem_highs, mem_means, mem_meds, mem_stds, mem_counts, mem_whis_lows, mem_whis_highs, mem_samples = [], [], [], [], [], [], [], [], [] + unif_lows, unif_highs, unif_means, unif_meds, unif_stds, unif_counts, unif_whis_lows, unif_whis_highs, unif_samples = [], [], [], [], [], [], [], [], [] + thres_lows, thres_highs, thres_means, thres_meds, thres_stds, thres_counts, thres_whis_lows, thres_whis_highs, thres_samples = [], [], [], [], [], [], [], [], [] + + for reps, top_k in reps_perf_pairs: + mem_low, mem_high, mem_mean, mem_med, mem_std, mem_count, mem_w_max, mem_w_min = [top_k['mem_top'][x] for x in ['25%', '75%', 'mean', '50%', 'std', 'count', 'max_whis', 'min_whis']] + mem_lows.append(mem_low) + mem_highs.append(mem_high) + mem_means.append(mem_mean) + mem_meds.append(mem_med) + mem_stds.append(mem_std) + mem_counts.append(mem_count) + mem_whis_lows.append(mem_w_min) + mem_whis_highs.append(mem_w_max) + mem_samples.append(top_k['perf_top_mem']) + + unif_low, unif_high, unif_mean, unif_med, unif_std, unif_count, unif_w_max, unif_w_min = [top_k['unif_top'][x] for x in ['25%', '75%', 'mean', '50%', 'std', 'count', 'max_whis', 'min_whis']] + unif_lows.append(unif_low) + unif_highs.append(unif_high) + unif_means.append(unif_mean) + unif_meds.append(unif_med) + unif_stds.append(unif_std) + unif_counts.append(unif_count) + unif_whis_lows.append(unif_w_min) + unif_whis_highs.append(unif_w_max) + unif_samples.append(top_k['perf_top_unif']) + + if with_threshold: + thres_low, thres_high, thres_mean, thres_med, thres_std, thres_count, thres_w_max, thres_w_min = [top_k['threshold_top'][x] for x in ['25%', '75%', 'mean', '50%', 'std', 'count', 'max_whis', 'min_whis']] + thres_lows.append(thres_low) + thres_highs.append(thres_high) + thres_means.append(thres_mean) + thres_meds.append(thres_med) + thres_stds.append(thres_std) + thres_counts.append(thres_count) + thres_whis_lows.append(unif_w_min) + thres_whis_highs.append(unif_w_max) + thres_samples.append(top_k['perf_top_threshold']) + + repetitions = np.array([reps for reps, _ in reps_perf_pairs]) + yerr = np.array(mem_stds) / np.sqrt(np.array(mem_counts)) if std else [(x - y) * 1.57 / np.sqrt(c) for (x, y, c) in zip(mem_highs, mem_lows, mem_counts)] + yerr = np.array(mem_stds) / np.sqrt(np.array(mem_counts)) if std else [(x - y) * 1.57 / np.sqrt(c) for (x, y, c) in zip(mem_highs, mem_lows, mem_counts)] + + W = 4 + w = 0.8 + # print(len(mem_samples), len(mem_samples[0])) + if median is False: + mean_var(mem_samples, color=c1, hatch=r"", positions=(repetitions) * W - w) + mean_var(thres_samples, color=c2, hatch=r"", positions=(repetitions) * W) + mean_var(unif_samples, color=c3, hatch=r"", positions=(repetitions) * W + w) + else: + boxify(thres_samples, color=c2, hatch=r"", positions=(repetitions) * W - w, w=0.75 * w) + boxify(mem_samples, color=c1, hatch=r"", positions=(repetitions) * W, w=0.75 * w) + boxify(unif_samples, color=c3, hatch=r"", positions=(repetitions) * W + w, w=0.75 * w) + + label_diff(stats, repetitions * W - w, thres_highs, mem_highs, w, repetitions, ind=0) + label_diff(stats, repetitions * W, unif_highs, mem_highs, w, repetitions, ind=1) + plt.xticks(repetitions * W, repetitions) + + hMem = mpatches.Patch(facecolor=c1, linewidth=6, hatch=r"", label='Memorize') + hThre = mpatches.Patch(facecolor=c2, linewidth=6, hatch=r'', label='Threshold') + hUni = mpatches.Patch(facecolor=c3, linewidth=6, hatch=r'', label='Uniform') + plt.xlim(repetitions.min() * W - w * 1.5, max_rev * W + w * 1.5) + + if with_threshold: + plt.legend((hThre, hMem, hUni), ('Threshold', '\\textsc{Memorize}', 'Uniform'), loc='upper center', ncol=3, bbox_to_anchor=(0.5, 1.2), handletextpad=0.1, columnspacing=0.5) + else: + plt.legend((hThre, hMem, hUni), ('Threshold', '\\textsc{Memorize}', 'Uniform'), loc='upper center', ncol=2, bbox_to_anchor=(0.5, 1.2)) +