diff --git a/collab/foraging/toolkit/derive.py b/collab/foraging/toolkit/derive.py
index 3e520272..aed06974 100644
--- a/collab/foraging/toolkit/derive.py
+++ b/collab/foraging/toolkit/derive.py
@@ -38,15 +38,23 @@ def _generate_combined_DF(
 
     :param predictors_and_scoress: dictionary of computed predictors/scores
     :param dropna: set to `True` to drop NaN elements from final DataFrame
-    :param add_scaled_values: set to `True` to scale the predictor/score columns and
+    :param add_scaled_values: set to `True` to scale the predictor/score columns using empirical CDF and
         add the values as additional columns in final DataFrame
     :return: final, flattened DataFrame containing all computed predictors as columns
     """
-    list_DFs = [_generate_DF_from_nestedList(p) for p in predictors_and_scores.values()]
-    combinedDF = list_DFs[0]
 
-    for i in range(1, len(list_DFs)):
-        combinedDF = combinedDF.merge(list_DFs[i], how="inner")
+    dict_DFs = {
+        key: _generate_DF_from_nestedList(predictors_and_scores[key])
+        for key in predictors_and_scores.keys()
+    }
+    combinedDF = pd.concat(
+        [dict_DFs[key][[key]] for key in dict_DFs.keys()], axis=1
+    )  # only combining predictor/score columns on index
+
+    # list_DFs = [_generate_DF_from_nestedList(p) for p in predictors_and_scores.values()]
+    # combinedDF = list_DFs[0]
+    # for i in range(1, len(list_DFs)):
+    #     combinedDF = combinedDF.merge(list_DFs[i], how="inner")
 
     if dropna:
         og_frames = len(combinedDF)
@@ -55,21 +63,17 @@ def _generate_combined_DF(
         if dropped_frames:
             warnings.warn(
                 f"""
-                      Dropped {dropped_frames}/{og_frames} frames from `derivedDF` due to NaN values.
-                      Missing values can arise when computations depend on next/previous step positions
-                      that are unavailable. See documentation of the corresponding predictor/score generating
-                      functions for more information.
+                      Dropped {dropped_frames}/{og_frames} (~{100*dropped_frames/og_frames:.2f}%) rows from `derivedDF`
+                      due to NaN values. Missing values can arise when computations depend on next/previous positions
+                      that are unavailable. See documentation of the corresponding predictor/score generating functions
+                      for more information.
                       """
             )
 
     # scale predictor columns
     if add_scaled_values:
         for key in predictors_and_scores.keys():
-            column_min = combinedDF[key].min()
-            column_max = combinedDF[key].max()
-            combinedDF[f"{key}_scaled"] = (combinedDF[key] - column_min) / (
-                column_max - column_min
-            )
+            combinedDF[f"{key}_scaled"] = combinedDF[key].rank(method="dense", pct=True)
 
     return combinedDF
 
@@ -106,8 +110,8 @@ def derive_predictors_and_scores(
                 "nextStep_squared" : {"nonlinearity_exponent" : 2},
             }
     :param dropna: set to `True` to drop NaN elements from the final DataFrame
-    :param add_scaled_values: set to `True` to compute scaled predictor scores
-        and add them as additional columns in final DataFrame
+    :param add_scaled_values: set to `True` to compute scaled predictors/scores using empirical
+        CDF and add them as additional columns in final DataFrame
     :return: final, flattened DataFrame containing all computed predictors as columns
     """
 
@@ -117,9 +121,11 @@ def derive_predictors_and_scores(
     foragers_object.score_kwargs = score_kwargs
 
     # generate local_windows and add to object
+    start = time.time()
     local_windows = generate_local_windows(foragers_object)
     foragers_object.local_windows = local_windows
-
+    end = time.time()
+    derivation_logger.info(f"Local windows completed in {end-start:.2f} seconds.")
     derived_quantities = {}
 
     # calculate predictors
@@ -150,8 +156,10 @@ def derive_predictors_and_scores(
     foragers_object.derived_quantities = derived_quantities
 
     # generate combined DF
+    start = time.time()
     derivedDF = _generate_combined_DF(derived_quantities, dropna, add_scaled_values)
-
+    end = time.time()
+    derivation_logger.info(f"derivedDF generated in {end-start:.2f} seconds.")
     # save to object
     foragers_object.derivedDF = derivedDF
 
diff --git a/docs/experimental/collab_tests/derive_predictors.ipynb b/docs/experimental/collab_tests/derive_predictors.ipynb
index c0310299..a3e0295a 100644
--- a/docs/experimental/collab_tests/derive_predictors.ipynb
+++ b/docs/experimental/collab_tests/derive_predictors.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -23,8 +23,8 @@
     "\n",
     "smoke_test = \"CI\" in os.environ\n",
     "\n",
-    "num_svi_iters = 400 if not smoke_test else 4\n",
-    "num_samples = 1000 if not smoke_test else 10"
+    "num_svi_iters = 400 if not smoke_test else 10\n",
+    "num_samples = 1000 if not smoke_test else 50"
    ]
   },
   {
@@ -88,19 +88,21 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "2024-09-18 17:54:02,666 - vicsek completed in 0.83 seconds.\n",
-      "2024-09-18 17:54:03,557 - vicsek_large_sigma completed in 0.88 seconds.\n",
-      "2024-09-18 17:54:05,462 - pairwiseCopying completed in 1.90 seconds.\n",
-      "2024-09-18 17:54:06,493 - proximity completed in 1.02 seconds.\n",
-      "2024-09-18 17:54:06,668 - nextStep_linear completed in 0.17 seconds.\n",
-      "2024-09-18 17:54:06,838 - nextStep_sublinear completed in 0.16 seconds.\n",
-      "/home/rafal/s78projects/collab-creatures/collab/foraging/toolkit/derive.py:56: UserWarning: \n",
-      "                      Dropped 8277/25075 frames from `derivedDF` due to NaN values.\n",
-      "                      Missing values can arise when computations depend on next/previous step positions\n",
-      "                      that are unavailable. See documentation of the corresponding predictor/score generating\n",
-      "                      functions for more information.\n",
+      "2024-12-31 06:33:59,402 - Local windows completed in 0.18 seconds.\n",
+      "2024-12-31 06:33:59,703 - vicsek completed in 0.30 seconds.\n",
+      "2024-12-31 06:33:59,995 - vicsek_large_sigma completed in 0.29 seconds.\n",
+      "2024-12-31 06:34:00,386 - pairwiseCopying completed in 0.39 seconds.\n",
+      "2024-12-31 06:34:00,628 - proximity completed in 0.24 seconds.\n",
+      "2024-12-31 06:34:00,670 - nextStep_linear completed in 0.04 seconds.\n",
+      "2024-12-31 06:34:00,705 - nextStep_sublinear completed in 0.03 seconds.\n",
+      "/home/rafal/s78projects/collab-creatures/collab/foraging/toolkit/derive.py:64: UserWarning: \n",
+      "                      Dropped 8277/25075 (~33.01%) rows from `derivedDF`\n",
+      "                      due to NaN values. Missing values can arise when computations depend on next/previous positions\n",
+      "                      that are unavailable. See documentation of the corresponding predictor/score generating functions\n",
+      "                      for more information.\n",
       "                      \n",
-      "  warnings.warn(\n"
+      "  warnings.warn(\n",
+      "2024-12-31 06:34:00,739 - derivedDF generated in 0.03 seconds.\n"
      ]
     }
    ],
@@ -189,16 +191,10 @@
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
-       "      <th>x</th>\n",
-       "      <th>y</th>\n",
-       "      <th>distance_to_forager</th>\n",
-       "      <th>time</th>\n",
-       "      <th>forager</th>\n",
        "      <th>vicsek</th>\n",
        "      <th>vicsek_large_sigma</th>\n",
        "      <th>pairwiseCopying</th>\n",
        "      <th>proximity</th>\n",
-       "      <th>distance_to_next_step</th>\n",
        "      <th>nextStep_linear</th>\n",
        "      <th>nextStep_sublinear</th>\n",
        "      <th>vicsek_scaled</th>\n",
@@ -211,109 +207,79 @@
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
-       "      <th>697</th>\n",
-       "      <td>19</td>\n",
-       "      <td>19</td>\n",
-       "      <td>15.000000</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
+       "      <th>969</th>\n",
        "      <td>2.333703e-25</td>\n",
        "      <td>0.006069</td>\n",
        "      <td>2.015709e-11</td>\n",
        "      <td>0.000072</td>\n",
-       "      <td>14.000000</td>\n",
-       "      <td>0.125000</td>\n",
-       "      <td>0.064586</td>\n",
-       "      <td>2.333601e-25</td>\n",
-       "      <td>0.003619</td>\n",
-       "      <td>2.015709e-11</td>\n",
-       "      <td>0.428935</td>\n",
        "      <td>0.125000</td>\n",
        "      <td>0.064586</td>\n",
+       "      <td>0.022189</td>\n",
+       "      <td>0.022346</td>\n",
+       "      <td>0.136897</td>\n",
+       "      <td>0.130953</td>\n",
+       "      <td>0.189130</td>\n",
+       "      <td>0.189204</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>698</th>\n",
-       "      <td>20</td>\n",
-       "      <td>14</td>\n",
-       "      <td>14.866069</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
+       "      <th>1014</th>\n",
        "      <td>9.256047e-21</td>\n",
        "      <td>0.015739</td>\n",
        "      <td>8.391062e-14</td>\n",
        "      <td>0.000009</td>\n",
-       "      <td>13.928388</td>\n",
-       "      <td>0.129476</td>\n",
-       "      <td>0.066981</td>\n",
-       "      <td>9.256047e-21</td>\n",
-       "      <td>0.013313</td>\n",
-       "      <td>8.391062e-14</td>\n",
-       "      <td>0.428899</td>\n",
        "      <td>0.129476</td>\n",
        "      <td>0.066981</td>\n",
+       "      <td>0.115898</td>\n",
+       "      <td>0.117573</td>\n",
+       "      <td>0.084757</td>\n",
+       "      <td>0.050936</td>\n",
+       "      <td>0.197826</td>\n",
+       "      <td>0.197928</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>699</th>\n",
-       "      <td>20</td>\n",
-       "      <td>15</td>\n",
-       "      <td>14.560220</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
+       "      <th>1015</th>\n",
        "      <td>2.267917e-21</td>\n",
        "      <td>0.013868</td>\n",
        "      <td>2.174845e-13</td>\n",
        "      <td>0.000018</td>\n",
-       "      <td>13.601471</td>\n",
-       "      <td>0.149908</td>\n",
-       "      <td>0.077996</td>\n",
-       "      <td>2.267917e-21</td>\n",
-       "      <td>0.011437</td>\n",
-       "      <td>2.174845e-13</td>\n",
-       "      <td>0.428904</td>\n",
        "      <td>0.149908</td>\n",
        "      <td>0.077996</td>\n",
+       "      <td>0.102255</td>\n",
+       "      <td>0.103811</td>\n",
+       "      <td>0.091555</td>\n",
+       "      <td>0.069721</td>\n",
+       "      <td>0.229891</td>\n",
+       "      <td>0.230098</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>700</th>\n",
-       "      <td>20</td>\n",
-       "      <td>16</td>\n",
-       "      <td>14.317821</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
+       "      <th>1016</th>\n",
        "      <td>4.450581e-22</td>\n",
        "      <td>0.011977</td>\n",
        "      <td>1.117982e-12</td>\n",
        "      <td>0.000034</td>\n",
-       "      <td>13.341664</td>\n",
-       "      <td>0.166146</td>\n",
-       "      <td>0.086844</td>\n",
-       "      <td>4.450581e-22</td>\n",
-       "      <td>0.009542</td>\n",
-       "      <td>1.117982e-12</td>\n",
-       "      <td>0.428913</td>\n",
        "      <td>0.166146</td>\n",
        "      <td>0.086844</td>\n",
+       "      <td>0.086529</td>\n",
+       "      <td>0.087754</td>\n",
+       "      <td>0.105962</td>\n",
+       "      <td>0.093443</td>\n",
+       "      <td>0.258152</td>\n",
+       "      <td>0.257906</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>701</th>\n",
-       "      <td>20</td>\n",
-       "      <td>17</td>\n",
-       "      <td>14.142136</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
+       "      <th>1017</th>\n",
        "      <td>7.065420e-23</td>\n",
        "      <td>0.010149</td>\n",
        "      <td>5.522924e-12</td>\n",
        "      <td>0.000061</td>\n",
-       "      <td>13.152946</td>\n",
-       "      <td>0.177941</td>\n",
-       "      <td>0.093325</td>\n",
-       "      <td>7.065419e-23</td>\n",
-       "      <td>0.007709</td>\n",
-       "      <td>5.522924e-12</td>\n",
-       "      <td>0.428929</td>\n",
        "      <td>0.177941</td>\n",
        "      <td>0.093325</td>\n",
+       "      <td>0.068792</td>\n",
+       "      <td>0.069626</td>\n",
+       "      <td>0.122552</td>\n",
+       "      <td>0.122524</td>\n",
+       "      <td>0.275543</td>\n",
+       "      <td>0.275354</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
@@ -329,190 +295,141 @@
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>24361</th>\n",
-       "      <td>48</td>\n",
-       "      <td>26</td>\n",
-       "      <td>14.142136</td>\n",
-       "      <td>8</td>\n",
-       "      <td>3</td>\n",
+       "      <th>2426</th>\n",
        "      <td>6.896891e-06</td>\n",
        "      <td>0.343146</td>\n",
        "      <td>7.092926e-05</td>\n",
        "      <td>0.000055</td>\n",
-       "      <td>21.023796</td>\n",
-       "      <td>0.045359</td>\n",
-       "      <td>0.022942</td>\n",
-       "      <td>6.896891e-06</td>\n",
-       "      <td>0.341527</td>\n",
-       "      <td>7.092926e-05</td>\n",
-       "      <td>0.428925</td>\n",
        "      <td>0.045359</td>\n",
        "      <td>0.022942</td>\n",
+       "      <td>0.616186</td>\n",
+       "      <td>0.628561</td>\n",
+       "      <td>0.461145</td>\n",
+       "      <td>0.115841</td>\n",
+       "      <td>0.055435</td>\n",
+       "      <td>0.055616</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>24362</th>\n",
-       "      <td>48</td>\n",
-       "      <td>27</td>\n",
-       "      <td>14.317821</td>\n",
-       "      <td>8</td>\n",
-       "      <td>3</td>\n",
+       "      <th>2427</th>\n",
        "      <td>3.240315e-06</td>\n",
        "      <td>0.320592</td>\n",
        "      <td>5.465289e-05</td>\n",
        "      <td>0.000049</td>\n",
-       "      <td>21.095023</td>\n",
-       "      <td>0.042124</td>\n",
-       "      <td>0.021289</td>\n",
-       "      <td>3.240315e-06</td>\n",
-       "      <td>0.318918</td>\n",
-       "      <td>5.465289e-05</td>\n",
-       "      <td>0.428922</td>\n",
        "      <td>0.042124</td>\n",
        "      <td>0.021289</td>\n",
+       "      <td>0.596295</td>\n",
+       "      <td>0.608435</td>\n",
+       "      <td>0.449295</td>\n",
+       "      <td>0.111867</td>\n",
+       "      <td>0.051087</td>\n",
+       "      <td>0.051254</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>24363</th>\n",
-       "      <td>48</td>\n",
-       "      <td>28</td>\n",
-       "      <td>14.560220</td>\n",
-       "      <td>8</td>\n",
-       "      <td>3</td>\n",
+       "      <th>2428</th>\n",
        "      <td>1.320367e-06</td>\n",
        "      <td>0.295708</td>\n",
        "      <td>3.876775e-05</td>\n",
        "      <td>0.000041</td>\n",
-       "      <td>21.213203</td>\n",
-       "      <td>0.036758</td>\n",
-       "      <td>0.018551</td>\n",
-       "      <td>1.320367e-06</td>\n",
-       "      <td>0.293972</td>\n",
-       "      <td>3.876775e-05</td>\n",
-       "      <td>0.428917</td>\n",
        "      <td>0.036758</td>\n",
        "      <td>0.018551</td>\n",
+       "      <td>0.575039</td>\n",
+       "      <td>0.586459</td>\n",
+       "      <td>0.436822</td>\n",
+       "      <td>0.102294</td>\n",
+       "      <td>0.041848</td>\n",
+       "      <td>0.041985</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>24364</th>\n",
-       "      <td>48</td>\n",
-       "      <td>29</td>\n",
-       "      <td>14.866069</td>\n",
-       "      <td>8</td>\n",
-       "      <td>3</td>\n",
+       "      <th>2429</th>\n",
        "      <td>4.706635e-07</td>\n",
        "      <td>0.269491</td>\n",
        "      <td>2.563767e-05</td>\n",
        "      <td>0.000032</td>\n",
-       "      <td>21.377558</td>\n",
-       "      <td>0.029295</td>\n",
-       "      <td>0.014756</td>\n",
-       "      <td>4.706635e-07</td>\n",
-       "      <td>0.267690</td>\n",
-       "      <td>2.563767e-05</td>\n",
-       "      <td>0.428912</td>\n",
        "      <td>0.029295</td>\n",
        "      <td>0.014756</td>\n",
+       "      <td>0.548470</td>\n",
+       "      <td>0.559822</td>\n",
+       "      <td>0.419858</td>\n",
+       "      <td>0.091035</td>\n",
+       "      <td>0.029891</td>\n",
+       "      <td>0.029989</td>\n",
        "    </tr>\n",
        "    <tr>\n",
-       "      <th>24365</th>\n",
-       "      <td>49</td>\n",
-       "      <td>24</td>\n",
-       "      <td>15.000000</td>\n",
-       "      <td>8</td>\n",
-       "      <td>3</td>\n",
+       "      <th>2474</th>\n",
        "      <td>4.289158e-06</td>\n",
        "      <td>0.328786</td>\n",
        "      <td>1.919096e-05</td>\n",
        "      <td>0.000021</td>\n",
-       "      <td>22.022716</td>\n",
-       "      <td>0.000000</td>\n",
-       "      <td>0.000000</td>\n",
-       "      <td>4.289158e-06</td>\n",
-       "      <td>0.327132</td>\n",
-       "      <td>1.919096e-05</td>\n",
-       "      <td>0.428906</td>\n",
        "      <td>0.000000</td>\n",
        "      <td>0.000000</td>\n",
+       "      <td>0.603332</td>\n",
+       "      <td>0.615612</td>\n",
+       "      <td>0.408257</td>\n",
+       "      <td>0.076766</td>\n",
+       "      <td>0.000543</td>\n",
+       "      <td>0.000545</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
-       "<p>16798 rows × 18 columns</p>\n",
+       "<p>16798 rows × 12 columns</p>\n",
        "</div>"
       ],
       "text/plain": [
-       "        x   y  distance_to_forager  time  forager        vicsek  \\\n",
-       "697    19  19            15.000000     1        0  2.333703e-25   \n",
-       "698    20  14            14.866069     1        0  9.256047e-21   \n",
-       "699    20  15            14.560220     1        0  2.267917e-21   \n",
-       "700    20  16            14.317821     1        0  4.450581e-22   \n",
-       "701    20  17            14.142136     1        0  7.065420e-23   \n",
-       "...    ..  ..                  ...   ...      ...           ...   \n",
-       "24361  48  26            14.142136     8        3  6.896891e-06   \n",
-       "24362  48  27            14.317821     8        3  3.240315e-06   \n",
-       "24363  48  28            14.560220     8        3  1.320367e-06   \n",
-       "24364  48  29            14.866069     8        3  4.706635e-07   \n",
-       "24365  49  24            15.000000     8        3  4.289158e-06   \n",
+       "            vicsek  vicsek_large_sigma  pairwiseCopying  proximity  \\\n",
+       "969   2.333703e-25            0.006069     2.015709e-11   0.000072   \n",
+       "1014  9.256047e-21            0.015739     8.391062e-14   0.000009   \n",
+       "1015  2.267917e-21            0.013868     2.174845e-13   0.000018   \n",
+       "1016  4.450581e-22            0.011977     1.117982e-12   0.000034   \n",
+       "1017  7.065420e-23            0.010149     5.522924e-12   0.000061   \n",
+       "...            ...                 ...              ...        ...   \n",
+       "2426  6.896891e-06            0.343146     7.092926e-05   0.000055   \n",
+       "2427  3.240315e-06            0.320592     5.465289e-05   0.000049   \n",
+       "2428  1.320367e-06            0.295708     3.876775e-05   0.000041   \n",
+       "2429  4.706635e-07            0.269491     2.563767e-05   0.000032   \n",
+       "2474  4.289158e-06            0.328786     1.919096e-05   0.000021   \n",
        "\n",
-       "       vicsek_large_sigma  pairwiseCopying  proximity  distance_to_next_step  \\\n",
-       "697              0.006069     2.015709e-11   0.000072              14.000000   \n",
-       "698              0.015739     8.391062e-14   0.000009              13.928388   \n",
-       "699              0.013868     2.174845e-13   0.000018              13.601471   \n",
-       "700              0.011977     1.117982e-12   0.000034              13.341664   \n",
-       "701              0.010149     5.522924e-12   0.000061              13.152946   \n",
-       "...                   ...              ...        ...                    ...   \n",
-       "24361            0.343146     7.092926e-05   0.000055              21.023796   \n",
-       "24362            0.320592     5.465289e-05   0.000049              21.095023   \n",
-       "24363            0.295708     3.876775e-05   0.000041              21.213203   \n",
-       "24364            0.269491     2.563767e-05   0.000032              21.377558   \n",
-       "24365            0.328786     1.919096e-05   0.000021              22.022716   \n",
+       "      nextStep_linear  nextStep_sublinear  vicsek_scaled  \\\n",
+       "969          0.125000            0.064586       0.022189   \n",
+       "1014         0.129476            0.066981       0.115898   \n",
+       "1015         0.149908            0.077996       0.102255   \n",
+       "1016         0.166146            0.086844       0.086529   \n",
+       "1017         0.177941            0.093325       0.068792   \n",
+       "...               ...                 ...            ...   \n",
+       "2426         0.045359            0.022942       0.616186   \n",
+       "2427         0.042124            0.021289       0.596295   \n",
+       "2428         0.036758            0.018551       0.575039   \n",
+       "2429         0.029295            0.014756       0.548470   \n",
+       "2474         0.000000            0.000000       0.603332   \n",
        "\n",
-       "       nextStep_linear  nextStep_sublinear  vicsek_scaled  \\\n",
-       "697           0.125000            0.064586   2.333601e-25   \n",
-       "698           0.129476            0.066981   9.256047e-21   \n",
-       "699           0.149908            0.077996   2.267917e-21   \n",
-       "700           0.166146            0.086844   4.450581e-22   \n",
-       "701           0.177941            0.093325   7.065419e-23   \n",
-       "...                ...                 ...            ...   \n",
-       "24361         0.045359            0.022942   6.896891e-06   \n",
-       "24362         0.042124            0.021289   3.240315e-06   \n",
-       "24363         0.036758            0.018551   1.320367e-06   \n",
-       "24364         0.029295            0.014756   4.706635e-07   \n",
-       "24365         0.000000            0.000000   4.289158e-06   \n",
+       "      vicsek_large_sigma_scaled  pairwiseCopying_scaled  proximity_scaled  \\\n",
+       "969                    0.022346                0.136897          0.130953   \n",
+       "1014                   0.117573                0.084757          0.050936   \n",
+       "1015                   0.103811                0.091555          0.069721   \n",
+       "1016                   0.087754                0.105962          0.093443   \n",
+       "1017                   0.069626                0.122552          0.122524   \n",
+       "...                         ...                     ...               ...   \n",
+       "2426                   0.628561                0.461145          0.115841   \n",
+       "2427                   0.608435                0.449295          0.111867   \n",
+       "2428                   0.586459                0.436822          0.102294   \n",
+       "2429                   0.559822                0.419858          0.091035   \n",
+       "2474                   0.615612                0.408257          0.076766   \n",
        "\n",
-       "       vicsek_large_sigma_scaled  pairwiseCopying_scaled  proximity_scaled  \\\n",
-       "697                     0.003619            2.015709e-11          0.428935   \n",
-       "698                     0.013313            8.391062e-14          0.428899   \n",
-       "699                     0.011437            2.174845e-13          0.428904   \n",
-       "700                     0.009542            1.117982e-12          0.428913   \n",
-       "701                     0.007709            5.522924e-12          0.428929   \n",
-       "...                          ...                     ...               ...   \n",
-       "24361                   0.341527            7.092926e-05          0.428925   \n",
-       "24362                   0.318918            5.465289e-05          0.428922   \n",
-       "24363                   0.293972            3.876775e-05          0.428917   \n",
-       "24364                   0.267690            2.563767e-05          0.428912   \n",
-       "24365                   0.327132            1.919096e-05          0.428906   \n",
+       "      nextStep_linear_scaled  nextStep_sublinear_scaled  \n",
+       "969                 0.189130                   0.189204  \n",
+       "1014                0.197826                   0.197928  \n",
+       "1015                0.229891                   0.230098  \n",
+       "1016                0.258152                   0.257906  \n",
+       "1017                0.275543                   0.275354  \n",
+       "...                      ...                        ...  \n",
+       "2426                0.055435                   0.055616  \n",
+       "2427                0.051087                   0.051254  \n",
+       "2428                0.041848                   0.041985  \n",
+       "2429                0.029891                   0.029989  \n",
+       "2474                0.000543                   0.000545  \n",
        "\n",
-       "       nextStep_linear_scaled  nextStep_sublinear_scaled  \n",
-       "697                  0.125000                   0.064586  \n",
-       "698                  0.129476                   0.066981  \n",
-       "699                  0.149908                   0.077996  \n",
-       "700                  0.166146                   0.086844  \n",
-       "701                  0.177941                   0.093325  \n",
-       "...                       ...                        ...  \n",
-       "24361                0.045359                   0.022942  \n",
-       "24362                0.042124                   0.021289  \n",
-       "24363                0.036758                   0.018551  \n",
-       "24364                0.029295                   0.014756  \n",
-       "24365                0.000000                   0.000000  \n",
-       "\n",
-       "[16798 rows x 18 columns]"
+       "[16798 rows x 12 columns]"
       ]
      },
      "metadata": {},
@@ -717,7 +634,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<graphviz.graphs.Digraph at 0x7f3064806fb0>"
+       "<graphviz.graphs.Digraph at 0x72f411356140>"
       ]
      },
      "execution_count": 6,
@@ -735,6 +652,12 @@
     "# which is not assumed to remain fixed\n",
     "\n",
     "\n",
+    "# note this model is superseded in general\n",
+    "# by HeteroskedasticLinear, which uses the new modeling API\n",
+    "# and sigma is transformed,\n",
+    "# as some scores (Like proximity) can be negative.\n",
+    "\n",
+    "\n",
     "def model_sigmavar(vicsek, pCopying, score):\n",
     "    c_v = pyro.sample(\"c_v\", dist.Normal(0, 0.2))\n",
     "    c_pC = pyro.sample(\"c_pC\", dist.Normal(0, 0.2))\n",
@@ -755,6 +678,7 @@
     "    model_sigmavar,\n",
     "    model_args=(vicsek, pCopying, score),\n",
     "    render_distributions=True,\n",
+    "    # render_deterministic = True  #this will work only with pyro-ppl>-1.9.1\n",
     ")"
    ]
   },
@@ -858,11 +782,10 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "2024-09-18 17:54:42,039 - Starting SVI inference with 500 iterations.\n",
-      "2024-09-18 17:54:44,632 - Elbo loss: 12669.213388544196\n",
-      "2024-09-18 17:55:10,922 - Elbo loss: -2355.1349654016544\n",
-      "2024-09-18 17:55:37,693 - Elbo loss: -2398.5397552511945\n",
-      "2024-09-18 17:55:50,802 - SVI inference completed in 68.76 seconds.\n"
+      "2024-12-31 06:34:03,205 - Starting SVI inference with 400 iterations.\n",
+      "2024-12-31 06:34:03,707 - Elbo loss: 684.5439032013333\n",
+      "2024-12-31 06:34:05,061 - Elbo loss: -1492.0153490718878\n",
+      "2024-12-31 06:34:06,396 - SVI inference completed in 3.19 seconds.\n"
      ]
     },
     {
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@@ -2050,12 +1773,12 @@
      "text": [
       "SVI-based coefficient marginals:\n",
       "Site: c_v\n",
-      "       mean       std        5%      25%       50%       75%       95%\n",
-      "0  0.108677  0.045754  0.032056  0.07872  0.107704  0.138375  0.185095 \n",
+      "       mean       std        5%       25%       50%       75%       95%\n",
+      "0  0.118355  0.049889  0.038431  0.087325  0.118433  0.150479  0.202842 \n",
       "\n",
       "Site: c_pC\n",
-      "       mean       std        5%       25%       50%       75%      95%\n",
-      "0  0.538919  0.050607  0.454856  0.504688  0.539964  0.573062  0.62247 \n",
+      "       mean       std        5%       25%       50%       75%       95%\n",
+      "0  0.543075  0.048916  0.464869  0.509485  0.542105  0.576388  0.625086 \n",
       "\n"
      ]
     }
@@ -2066,7 +1789,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
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+          "x0": 0.5421047210693359,
+          "x1": 0.5421047210693359,
           "xref": "x",
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           "y1": 1,
@@ -6277,10 +6000,10 @@
            "color": "#3283FE",
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           },
-          "name": "Median (0.5399643778800964)",
+          "name": "Median (0.5421047210693359)",
           "type": "line",
-          "x0": 0.5399643778800964,
-          "x1": 0.5399643778800964,
+          "x0": 0.5421047210693359,
+          "x1": 0.5421047210693359,
           "xref": "x2",
           "y0": 0,
           "y1": 1,
@@ -6474,7 +6197,7 @@
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  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "collab",
    "language": "python",
    "name": "python3"
   },