Sparse-criteo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparse Logistic Regression with Criteo's dataset\n",
    "\n",
    "Criteo released a 1TB dataset of logs on click advertisements.  There are 13 numeric columns and 26 text columns with varying levels of entropy (some have only a few categories, some have millions).  There is also a single predictor column of if someone clicked the advertisement or not.\n",
    "\n",
    "To handle the text columns we hash each down and then encode as a sparse matrix.  We then hand this distributed sparse array to dask-glm's LogisticRegression estimator to try to see if we can build a model to determine if we can predict clicks.\n",
    "\n",
    "This notebook stresses the following capabailities:\n",
    "\n",
    "1.  Loading data from parquet files\n",
    "2.  Parallel data munging, both with dask.dataframe and with custom operations on dask.delayed\n",
    "3.  Sparse arrays\n",
    "4.  Parallelizing those sparse arrays with dask.array\n",
    "5.  Mixing both dense arrays (for the numeric columns) and sparse arrays (for the categorical columns) in the same dask.array\n",
    "5.  dask-glm's algorithms for logistic regression\n",
    "\n",
    "\n",
    "### Future work\n",
    "\n",
    "1.  Use regularizations in the face of non-differentiable points\n",
    "2.  Profile and speed up sparse tensordot calls\n",
    "4.  Run on larger dataset on a single machine to stress spill-to-disk behaviors\n",
    "5.  Run on a cluster to measure scalability\n",
    "5.  Handle low number of output labels well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Client: scheduler='tcp://localhost:8786' processes=4 cores=8>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from dask.distributed import Client\n",
    "client = Client('localhost:8786')\n",
    "client"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><strong>Dask DataFrame Structure:</strong></div>\n",
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>click</th>\n",
       "      <th>numeric_0</th>\n",
       "      <th>numeric_1</th>\n",
       "      <th>numeric_2</th>\n",
       "      <th>numeric_3</th>\n",
       "      <th>numeric_4</th>\n",
       "      <th>numeric_5</th>\n",
       "      <th>numeric_6</th>\n",
       "      <th>numeric_7</th>\n",
       "      <th>numeric_8</th>\n",
       "      <th>numeric_9</th>\n",
       "      <th>numeric_10</th>\n",
       "      <th>numeric_11</th>\n",
       "      <th>numeric_12</th>\n",
       "      <th>category_0</th>\n",
       "      <th>category_1</th>\n",
       "      <th>category_2</th>\n",
       "      <th>category_3</th>\n",
       "      <th>category_4</th>\n",
       "      <th>category_5</th>\n",
       "      <th>category_6</th>\n",
       "      <th>category_7</th>\n",
       "      <th>category_8</th>\n",
       "      <th>category_9</th>\n",
       "      <th>category_10</th>\n",
       "      <th>category_11</th>\n",
       "      <th>category_12</th>\n",
       "      <th>category_13</th>\n",
       "      <th>category_14</th>\n",
       "      <th>category_15</th>\n",
       "      <th>category_16</th>\n",
       "      <th>category_17</th>\n",
       "      <th>category_18</th>\n",
       "      <th>category_19</th>\n",
       "      <th>category_20</th>\n",
       "      <th>category_21</th>\n",
       "      <th>category_22</th>\n",
       "      <th>category_23</th>\n",
       "      <th>category_24</th>\n",
       "      <th>category_25</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>npartitions=778</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>None</th>\n",
       "      <td>int64</td>\n",
       "      <td>float64</td>\n",
       "      <td>float64</td>\n",
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       "      <td>object</td>\n",
       "      <td>object</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>None</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>None</th>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "<div>Dask Name: read-parquet, 778 tasks</div>"
      ],
      "text/plain": [
       "Dask DataFrame Structure:\n",
       "                 click numeric_0 numeric_1 numeric_2 numeric_3 numeric_4 numeric_5 numeric_6 numeric_7 numeric_8 numeric_9 numeric_10 numeric_11 numeric_12 category_0 category_1 category_2 category_3 category_4 category_5 category_6 category_7 category_8 category_9 category_10 category_11 category_12 category_13 category_14 category_15 category_16 category_17 category_18 category_19 category_20 category_21 category_22 category_23 category_24 category_25\n",
       "npartitions=778                                                                                                                                                                                                                                                                                                                                                                                                                                                          \n",
       "None             int64   float64   float64   float64   float64   float64   float64   float64     int64     int64   float64    float64    float64    float64     object     object     object     object     object     object     object     object     object     object      object      object      object      object      object      object      object      object      object      object      object      object      object      object      object      object\n",
       "None               ...       ...       ...       ...       ...       ...       ...       ...       ...       ...       ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...\n",
       "...                ...       ...       ...       ...       ...       ...       ...       ...       ...       ...       ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...\n",
       "None               ...       ...       ...       ...       ...       ...       ...       ...       ...       ...       ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...\n",
       "None               ...       ...       ...       ...       ...       ...       ...       ...       ...       ...       ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...        ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...         ...\n",
       "Dask Name: read-parquet, 778 tasks"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import dask\n",
    "import dask.dataframe as dd\n",
    "df = dd.read_parquet('day-0-bytes.parquet/', index=False)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sparse\n",
    "import numpy as np\n",
    "from pandas.tools.hashing import hash_pandas_object\n",
    "import dask.array as da\n",
    "\n",
    "\n",
    "def to_sparse(s):\n",
    "    s = hash_pandas_object(s).astype(np.uint8)\n",
    "    rows = np.arange(len(s))\n",
    "    cols = s.values\n",
    "    coords = np.stack([rows, cols], axis=0)\n",
    "    values = np.ones(shape=cols.shape, dtype=np.uint8)\n",
    "    result = sparse.COO(coords, values, shape=(len(s), 2**8),)\n",
    "    return result\n",
    "\n",
    "\n",
    "def to_sparse_df(df):\n",
    "    arrays = [to_sparse(df[c])\n",
    "              for c in df.columns \n",
    "              if c.startswith('category')]\n",
    "    result = sparse.concatenate(arrays, axis=1).sort_indices()\n",
    "    # result.sum_duplicates()\n",
    "    result.has_duplciates = False\n",
    "    return result\n",
    "\n",
    "\n",
    "def df_to_array(df):\n",
    "    dense = df[[c for c in df.columns if c.startswith('num')]]\n",
    "    dense = dense.fillna(0)\n",
    "    dense_array = dense.values\n",
    "    \n",
    "    values = df[[c for c in df.columns if c.startswith('cat')]].to_delayed()\n",
    "    sparse_arrays = [dask.delayed(to_sparse_df)(v) for v in values]\n",
    "    sparse_arrays = [da.from_delayed(x, shape=(np.nan, 2**8 * 26), dtype=np.uint8)\n",
    "                     for x in sparse_arrays]\n",
    "    sparse_array = da.concatenate(sparse_arrays, axis=0)\n",
    "       \n",
    "    return da.concatenate([dense_array, sparse_array], axis=1, allow_unknown_chunksizes=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manage data\n",
    "\n",
    "We do the following:\n",
    "\n",
    "-  Reduce to 100/778 partitions\n",
    "-  Split partitions by a factor of 10 (to increase chunk granularity for admm)\n",
    "-  Randomly split into training and testing data\n",
    "-  Separate `click` column of labels from data \n",
    "-  Convert dataframes to sparse arrays\n",
    "-  Store in memory (or disk as necessary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = dd.concat([df.get_partition(i) for i in range(10)], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train, test = df.random_split([0.9, 0.1])\n",
    "train = train.repartition(npartitions=train.npartitions * 10)\n",
    "test = test.repartition(npartitions=test.npartitions * 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_labels = train['click']\n",
    "del train['click']\n",
    "\n",
    "test_labels = test['click']\n",
    "del test['click']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train = df_to_array(train)\n",
    "test = df_to_array(test)\n",
    "train_labels = train_labels.values\n",
    "test_labels = test_labels.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from dask.distributed import progress\n",
    "\n",
    "train, train_labels, test, test_labels = \\\n",
    "    dask.persist(train, train_labels, test, test_labels)\n",
    "    \n",
    "progress([train, train_labels, test, test_labels])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from dask_glm.estimators import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression(fit_intercept=False, max_iter=20, \n",
    "                        regularizer=None, solver='lbfgs')\n",
    "\n",
    "# TODO\n",
    "# I had to use lbfgs rather than ADMM because my dask.array has two columns\n",
    "# of chunks.  The lbfgs solver uses dask.arrayw while admm really wants\n",
    "# numpy arrays.  Attempts to put single-threaded dask.array inside \n",
    "# of admm have resulted in large overheads\n",
    "\n",
    "# TODO\n",
    "# I had to use no regularization because otherwise we pass through points\n",
    "# near zero where L1 is non-differentiable.  Is there a way to make\n",
    "# us robust to this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.82 s, sys: 20 ms, total: 3.84 s\n",
      "Wall time: 2min 25s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(abstol=0.0001, fit_intercept=False, lamduh=1.0,\n",
       "          max_iter=20, over_relax=1, regularizer=None, reltol=0.01, rho=1,\n",
       "          solver='lbfgs', tol=0.0001)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "lr.fit(train, train_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import roc_auc_score, roc_curve\n",
    "\n",
    "predictions = lr.predict_proba(test).compute()\n",
    "fpr, tpr, _ = roc_curve(test_labels.compute(), predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dm2D6XbDp61PnV+4ArQZBrnzn/dRNmlTglVeaUKPGRbRrV+0Cg56dSl5ERAQg6QTMvO/P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\nxULo2bMhc+YMUMCLiKCRfNE1KwH2Omuoc90b7tZ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1cc873f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8))\n",
    "lw = 2\n",
    "plt.plot(fpr, tpr, color='darkorange', lw=lw, label='ROC curve')\n",
    "plt.plot([0, 1], [0, 1], color='navy', lw=lw, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Receiver operating characteristic example')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Low number of clicks\n",
    "\n",
    "Chris said that this was important"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.030130023190667897"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.click.mean().compute()"
   ]
  }
 ],
 "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": "3.6.0"
  },
  "widgets": {
   "state": {
    "a37a4cd0c05b44a2a76e104e3bc520a7": {
     "views": [
      {
       "cell_index": 10
      }
     ]
    }
   },
   "version": "1.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

task-stream-criteo-lbfgs.html

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        <div class="bk-root">
            <div class="plotdiv" id="e3b87779-e184-4abf-94e7-98fed19af98d"></div>
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            Bokeh.safely(function() {
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