.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py:


Variational Laplace EM for SLDS
===============================

.. GENERATED FROM PYTHON SOURCE LINES 19-197



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_001.png
         :alt: 7 Variatonal Laplace EM for SLDS Tutorial
         :srcset: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_002.png
         :alt: 7 Variatonal Laplace EM for SLDS Tutorial
         :srcset: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_003.png
         :alt: 7 Variatonal Laplace EM for SLDS Tutorial
         :srcset: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_004.png
         :alt: 7 Variatonal Laplace EM for SLDS Tutorial
         :srcset: /auto_examples/images/sphx_glr_7-Variatonal-Laplace-EM-for-SLDS-Tutorial_004.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Fitting SLDS with Laplace-EM, alpha = 0.0

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    ELBO: -9272.6:  93%|#########3| 93/100 [00:34<00:02,  3.35it/s]
    ELBO: -9272.6:  94%|#########3| 94/100 [00:34<00:02,  2.96it/s]
    ELBO: -9255.5:  94%|#########3| 94/100 [00:34<00:02,  2.96it/s]
    ELBO: -9255.5:  95%|#########5| 95/100 [00:34<00:02,  2.46it/s]
    ELBO: -9224.0:  95%|#########5| 95/100 [00:35<00:02,  2.46it/s]
    ELBO: -9224.0:  96%|#########6| 96/100 [00:35<00:01,  2.81it/s]
    ELBO: -9248.2:  96%|#########6| 96/100 [00:35<00:01,  2.81it/s]
    ELBO: -9248.2:  97%|#########7| 97/100 [00:35<00:01,  2.80it/s]
    ELBO: -9230.3:  97%|#########7| 97/100 [00:36<00:01,  2.80it/s]
    ELBO: -9230.3:  98%|#########8| 98/100 [00:36<00:00,  2.40it/s]
    ELBO: -9269.9:  98%|#########8| 98/100 [00:36<00:00,  2.40it/s]
    ELBO: -9269.9:  99%|#########9| 99/100 [00:36<00:00,  2.67it/s]
    ELBO: -9330.5:  99%|#########9| 99/100 [00:36<00:00,  2.67it/s]
    ELBO: -9330.5: 100%|##########| 100/100 [00:36<00:00,  2.60it/s]
    ELBO: -9330.5: 100%|##########| 100/100 [00:36<00:00,  2.72it/s]
    Fitting SLDS with Laplace-EM, alpha = 0.25

      0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -20525.9:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -9730.8:   0%|          | 0/100 [00:00<?, ?it/s] 
    ELBO: -9730.8:   1%|1         | 1/100 [00:00<00:46,  2.15it/s]
    ELBO: -9459.0:   1%|1         | 1/100 [00:00<00:46,  2.15it/s]
    ELBO: -9459.0:   2%|2         | 2/100 [00:00<00:30,  3.24it/s]
    ELBO: -9467.0:   2%|2         | 2/100 [00:01<00:30,  3.24it/s]
    ELBO: -9467.0:   3%|3         | 3/100 [00:01<00:33,  2.91it/s]
    ELBO: -9418.5:   3%|3         | 3/100 [00:01<00:33,  2.91it/s]
    ELBO: -9418.5:   4%|4         | 4/100 [00:01<00:40,  2.39it/s]
    ELBO: -9464.4:   4%|4         | 4/100 [00:01<00:40,  2.39it/s]
    ELBO: -9464.4:   5%|5         | 5/100 [00:01<00:30,  3.08it/s]
    ELBO: -9327.2:   5%|5         | 5/100 [00:01<00:30,  3.08it/s]
    ELBO: -9327.2:   6%|6         | 6/100 [00:01<00:26,  3.50it/s]
    ELBO: -9359.9:   6%|6         | 6/100 [00:02<00:26,  3.50it/s]
    ELBO: -9359.9:   7%|7         | 7/100 [00:02<00:25,  3.62it/s]
    ELBO: -9315.1:   7%|7         | 7/100 [00:02<00:25,  3.62it/s]
    ELBO: -9315.1:   8%|8         | 8/100 [00:02<00:30,  3.02it/s]
    ELBO: -9338.5:   8%|8         | 8/100 [00:02<00:30,  3.02it/s]
    ELBO: -9338.5:   9%|9         | 9/100 [00:02<00:26,  3.48it/s]
    ELBO: -9342.1:   9%|9         | 9/100 [00:03<00:26,  3.48it/s]
    ELBO: -9342.1:  10%|#         | 10/100 [00:03<00:28,  3.21it/s]
    ELBO: -9320.1:  10%|#         | 10/100 [00:03<00:28,  3.21it/s]
    ELBO: -9320.1:  11%|#1        | 11/100 [00:03<00:36,  2.41it/s]
    ELBO: -9286.4:  11%|#1        | 11/100 [00:04<00:36,  2.41it/s]
    ELBO: -9286.4:  12%|#2        | 12/100 [00:04<00:30,  2.90it/s]
    ELBO: -9302.7:  12%|#2        | 12/100 [00:04<00:30,  2.90it/s]
    ELBO: -9302.7:  13%|#3        | 13/100 [00:04<00:30,  2.84it/s]
    ELBO: -9257.7:  13%|#3        | 13/100 [00:04<00:30,  2.84it/s]
    ELBO: -9257.7:  14%|#4        | 14/100 [00:04<00:36,  2.38it/s]
    ELBO: -9293.8:  14%|#4        | 14/100 [00:05<00:36,  2.38it/s]
    ELBO: -9293.8:  15%|#5        | 15/100 [00:05<00:27,  3.05it/s]
    ELBO: -9226.1:  15%|#5        | 15/100 [00:05<00:27,  3.05it/s]
    ELBO: -9226.1:  16%|#6        | 16/100 [00:05<00:30,  2.75it/s]
    ELBO: -9255.8:  16%|#6        | 16/100 [00:06<00:30,  2.75it/s]
    ELBO: -9255.8:  17%|#7        | 17/100 [00:06<00:35,  2.34it/s]
    ELBO: -9212.9:  17%|#7        | 17/100 [00:06<00:35,  2.34it/s]
    ELBO: -9212.9:  18%|#8        | 18/100 [00:06<00:28,  2.86it/s]
    ELBO: -9331.4:  18%|#8        | 18/100 [00:06<00:28,  2.86it/s]
    ELBO: -9331.4:  19%|#9        | 19/100 [00:06<00:34,  2.36it/s]
    ELBO: -9298.6:  19%|#9        | 19/100 [00:07<00:34,  2.36it/s]
    ELBO: -9298.6:  20%|##        | 20/100 [00:07<00:33,  2.38it/s]
    ELBO: -9326.5:  20%|##        | 20/100 [00:07<00:33,  2.38it/s]
    ELBO: -9326.5:  21%|##1       | 21/100 [00:07<00:27,  2.91it/s]
    ELBO: -9326.7:  21%|##1       | 21/100 [00:07<00:27,  2.91it/s]
    ELBO: -9326.7:  22%|##2       | 22/100 [00:07<00:29,  2.64it/s]
    ELBO: -9243.2:  22%|##2       | 22/100 [00:08<00:29,  2.64it/s]
    ELBO: -9243.2:  23%|##3       | 23/100 [00:08<00:33,  2.27it/s]
    ELBO: -9318.2:  23%|##3       | 23/100 [00:08<00:33,  2.27it/s]
    ELBO: -9318.2:  24%|##4       | 24/100 [00:08<00:29,  2.59it/s]
    ELBO: -9279.4:  24%|##4       | 24/100 [00:09<00:29,  2.59it/s]
    ELBO: -9279.4:  25%|##5       | 25/100 [00:09<00:27,  2.72it/s]
    ELBO: -9310.4:  25%|##5       | 25/100 [00:09<00:27,  2.72it/s]
    ELBO: -9310.4:  26%|##6       | 26/100 [00:09<00:29,  2.48it/s]
    ELBO: -9302.6:  26%|##6       | 26/100 [00:09<00:29,  2.48it/s]
    ELBO: -9302.6:  27%|##7       | 27/100 [00:09<00:24,  3.02it/s]
    ELBO: -9297.2:  27%|##7       | 27/100 [00:10<00:24,  3.02it/s]
    ELBO: -9297.2:  28%|##8       | 28/100 [00:10<00:26,  2.74it/s]
    ELBO: -9269.4:  28%|##8       | 28/100 [00:10<00:26,  2.74it/s]
    ELBO: -9269.4:  29%|##9       | 29/100 [00:10<00:30,  2.34it/s]
    ELBO: -9244.2:  29%|##9       | 29/100 [00:10<00:30,  2.34it/s]
    ELBO: -9244.2:  30%|###       | 30/100 [00:10<00:24,  2.91it/s]
    ELBO: -9315.3:  30%|###       | 30/100 [00:11<00:24,  2.91it/s]
    ELBO: -9315.3:  31%|###1      | 31/100 [00:11<00:20,  3.41it/s]
    ELBO: -9272.7:  31%|###1      | 31/100 [00:11<00:20,  3.41it/s]
    ELBO: -9272.7:  32%|###2      | 32/100 [00:11<00:18,  3.68it/s]
    ELBO: -9304.7:  32%|###2      | 32/100 [00:11<00:18,  3.68it/s]
    ELBO: -9304.7:  33%|###3      | 33/100 [00:11<00:20,  3.33it/s]
    ELBO: -9296.8:  33%|###3      | 33/100 [00:11<00:20,  3.33it/s]
    ELBO: -9296.8:  34%|###4      | 34/100 [00:11<00:19,  3.31it/s]
    ELBO: -9281.1:  34%|###4      | 34/100 [00:12<00:19,  3.31it/s]
    ELBO: -9281.1:  35%|###5      | 35/100 [00:12<00:23,  2.71it/s]
    ELBO: -9306.7:  35%|###5      | 35/100 [00:12<00:23,  2.71it/s]
    ELBO: -9306.7:  36%|###6      | 36/100 [00:12<00:20,  3.19it/s]
    ELBO: -9259.4:  36%|###6      | 36/100 [00:13<00:20,  3.19it/s]
    ELBO: -9259.4:  37%|###7      | 37/100 [00:13<00:21,  2.97it/s]
    ELBO: -9270.1:  37%|###7      | 37/100 [00:13<00:21,  2.97it/s]
    ELBO: -9270.1:  38%|###8      | 38/100 [00:13<00:25,  2.46it/s]
    ELBO: -9189.8:  38%|###8      | 38/100 [00:13<00:25,  2.46it/s]
    ELBO: -9189.8:  39%|###9      | 39/100 [00:13<00:19,  3.14it/s]
    ELBO: -9305.6:  39%|###9      | 39/100 [00:14<00:19,  3.14it/s]
    ELBO: -9305.6:  40%|####      | 40/100 [00:14<00:23,  2.53it/s]
    ELBO: -9315.3:  40%|####      | 40/100 [00:14<00:23,  2.53it/s]
    ELBO: -9315.3:  41%|####1     | 41/100 [00:14<00:26,  2.23it/s]
    ELBO: -9300.6:  41%|####1     | 41/100 [00:15<00:26,  2.23it/s]
    ELBO: -9300.6:  42%|####2     | 42/100 [00:15<00:20,  2.82it/s]
    ELBO: -9281.6:  42%|####2     | 42/100 [00:15<00:20,  2.82it/s]
    ELBO: -9281.6:  43%|####3     | 43/100 [00:15<00:25,  2.27it/s]
    ELBO: -9271.9:  43%|####3     | 43/100 [00:16<00:25,  2.27it/s]
    ELBO: -9271.9:  44%|####4     | 44/100 [00:16<00:23,  2.37it/s]
    ELBO: -9288.9:  44%|####4     | 44/100 [00:16<00:23,  2.37it/s]
    ELBO: -9288.9:  45%|####5     | 45/100 [00:16<00:19,  2.82it/s]
    ELBO: -9245.1:  45%|####5     | 45/100 [00:16<00:19,  2.82it/s]
    ELBO: -9245.1:  46%|####6     | 46/100 [00:16<00:20,  2.65it/s]
    ELBO: -9315.0:  46%|####6     | 46/100 [00:16<00:20,  2.65it/s]
    ELBO: -9315.0:  47%|####6     | 47/100 [00:16<00:16,  3.26it/s]
    ELBO: -9313.0:  47%|####6     | 47/100 [00:17<00:16,  3.26it/s]
    ELBO: -9313.0:  48%|####8     | 48/100 [00:17<00:20,  2.56it/s]
    ELBO: -9273.9:  48%|####8     | 48/100 [00:17<00:20,  2.56it/s]
    ELBO: -9273.9:  49%|####9     | 49/100 [00:17<00:15,  3.20it/s]
    ELBO: -9293.3:  49%|####9     | 49/100 [00:17<00:15,  3.20it/s]
    ELBO: -9293.3:  50%|#####     | 50/100 [00:17<00:16,  3.06it/s]
    ELBO: -9257.2:  50%|#####     | 50/100 [00:18<00:16,  3.06it/s]
    ELBO: -9257.2:  51%|#####1    | 51/100 [00:18<00:12,  3.81it/s]
    ELBO: -9286.9:  51%|#####1    | 51/100 [00:18<00:12,  3.81it/s]
    ELBO: -9286.9:  52%|#####2    | 52/100 [00:18<00:17,  2.79it/s]
    ELBO: -9206.9:  52%|#####2    | 52/100 [00:19<00:17,  2.79it/s]
    ELBO: -9206.9:  53%|#####3    | 53/100 [00:19<00:19,  2.37it/s]
    ELBO: -9305.9:  53%|#####3    | 53/100 [00:19<00:19,  2.37it/s]
    ELBO: -9305.9:  54%|#####4    | 54/100 [00:19<00:15,  3.05it/s]
    ELBO: -9252.3:  54%|#####4    | 54/100 [00:19<00:15,  3.05it/s]
    ELBO: -9252.3:  55%|#####5    | 55/100 [00:19<00:19,  2.35it/s]
    ELBO: -9282.8:  55%|#####5    | 55/100 [00:20<00:19,  2.35it/s]
    ELBO: -9282.8:  56%|#####6    | 56/100 [00:20<00:15,  2.79it/s]
    ELBO: -9245.2:  56%|#####6    | 56/100 [00:20<00:15,  2.79it/s]
    ELBO: -9245.2:  57%|#####6    | 57/100 [00:20<00:15,  2.84it/s]
    ELBO: -9276.0:  57%|#####6    | 57/100 [00:20<00:15,  2.84it/s]
    ELBO: -9276.0:  58%|#####8    | 58/100 [00:20<00:12,  3.23it/s]
    ELBO: -9321.5:  58%|#####8    | 58/100 [00:20<00:12,  3.23it/s]
    ELBO: -9321.5:  59%|#####8    | 59/100 [00:20<00:10,  3.83it/s]
    ELBO: -9306.4:  59%|#####8    | 59/100 [00:21<00:10,  3.83it/s]
    ELBO: -9306.4:  60%|######    | 60/100 [00:21<00:09,  4.25it/s]
    ELBO: -9313.8:  60%|######    | 60/100 [00:21<00:09,  4.25it/s]
    ELBO: -9313.8:  61%|######1   | 61/100 [00:21<00:10,  3.55it/s]
    ELBO: -9271.9:  61%|######1   | 61/100 [00:21<00:10,  3.55it/s]
    ELBO: -9271.9:  62%|######2   | 62/100 [00:21<00:08,  4.26it/s]
    ELBO: -9325.5:  62%|######2   | 62/100 [00:22<00:08,  4.26it/s]
    ELBO: -9325.5:  63%|######3   | 63/100 [00:22<00:12,  3.05it/s]
    ELBO: -9352.3:  63%|######3   | 63/100 [00:22<00:12,  3.05it/s]
    ELBO: -9352.3:  64%|######4   | 64/100 [00:22<00:09,  3.73it/s]
    ELBO: -9229.2:  64%|######4   | 64/100 [00:22<00:09,  3.73it/s]
    ELBO: -9229.2:  65%|######5   | 65/100 [00:22<00:13,  2.66it/s]
    ELBO: -9329.8:  65%|######5   | 65/100 [00:23<00:13,  2.66it/s]
    ELBO: -9329.8:  66%|######6   | 66/100 [00:23<00:13,  2.44it/s]
    ELBO: -9301.4:  66%|######6   | 66/100 [00:23<00:13,  2.44it/s]
    ELBO: -9301.4:  67%|######7   | 67/100 [00:23<00:13,  2.49it/s]
    ELBO: -9240.6:  67%|######7   | 67/100 [00:23<00:13,  2.49it/s]
    ELBO: -9240.6:  68%|######8   | 68/100 [00:23<00:11,  2.87it/s]
    ELBO: -9313.3:  68%|######8   | 68/100 [00:24<00:11,  2.87it/s]
    ELBO: -9313.3:  69%|######9   | 69/100 [00:24<00:11,  2.64it/s]
    ELBO: -9315.7:  69%|######9   | 69/100 [00:24<00:11,  2.64it/s]
    ELBO: -9315.7:  70%|#######   | 70/100 [00:24<00:13,  2.28it/s]
    ELBO: -9314.9:  70%|#######   | 70/100 [00:25<00:13,  2.28it/s]
    ELBO: -9314.9:  71%|#######1  | 71/100 [00:25<00:10,  2.77it/s]
    ELBO: -9317.4:  71%|#######1  | 71/100 [00:25<00:10,  2.77it/s]
    ELBO: -9317.4:  72%|#######2  | 72/100 [00:25<00:10,  2.77it/s]
    ELBO: -9276.6:  72%|#######2  | 72/100 [00:26<00:10,  2.77it/s]
    ELBO: -9276.6:  73%|#######3  | 73/100 [00:26<00:11,  2.32it/s]
    ELBO: -9300.9:  73%|#######3  | 73/100 [00:26<00:11,  2.32it/s]
    ELBO: -9300.9:  74%|#######4  | 74/100 [00:26<00:09,  2.87it/s]
    ELBO: -9301.0:  74%|#######4  | 74/100 [00:26<00:09,  2.87it/s]
    ELBO: -9301.0:  75%|#######5  | 75/100 [00:26<00:09,  2.78it/s]
    ELBO: -9286.7:  75%|#######5  | 75/100 [00:27<00:09,  2.78it/s]
    ELBO: -9286.7:  76%|#######6  | 76/100 [00:27<00:09,  2.42it/s]
    ELBO: -9288.2:  76%|#######6  | 76/100 [00:27<00:09,  2.42it/s]
    ELBO: -9288.2:  77%|#######7  | 77/100 [00:27<00:07,  3.03it/s]
    ELBO: -9298.2:  77%|#######7  | 77/100 [00:27<00:07,  3.03it/s]
    ELBO: -9298.2:  78%|#######8  | 78/100 [00:27<00:08,  2.53it/s]
    ELBO: -9281.7:  78%|#######8  | 78/100 [00:28<00:08,  2.53it/s]
    ELBO: -9281.7:  79%|#######9  | 79/100 [00:28<00:06,  3.03it/s]
    ELBO: -9320.1:  79%|#######9  | 79/100 [00:28<00:06,  3.03it/s]
    ELBO: -9320.1:  80%|########  | 80/100 [00:28<00:06,  2.97it/s]
    ELBO: -9251.6:  80%|########  | 80/100 [00:28<00:06,  2.97it/s]
    ELBO: -9251.6:  81%|########1 | 81/100 [00:28<00:07,  2.43it/s]
    ELBO: -9331.4:  81%|########1 | 81/100 [00:29<00:07,  2.43it/s]
    ELBO: -9331.4:  82%|########2 | 82/100 [00:29<00:06,  2.94it/s]
    ELBO: -9337.5:  82%|########2 | 82/100 [00:29<00:06,  2.94it/s]
    ELBO: -9337.5:  83%|########2 | 83/100 [00:29<00:05,  2.86it/s]
    ELBO: -9321.6:  83%|########2 | 83/100 [00:29<00:05,  2.86it/s]
    ELBO: -9321.6:  84%|########4 | 84/100 [00:29<00:05,  2.71it/s]
    ELBO: -9304.5:  84%|########4 | 84/100 [00:30<00:05,  2.71it/s]
    ELBO: -9304.5:  85%|########5 | 85/100 [00:30<00:05,  3.00it/s]
    ELBO: -9284.6:  85%|########5 | 85/100 [00:30<00:05,  3.00it/s]
    ELBO: -9284.6:  86%|########6 | 86/100 [00:30<00:04,  3.35it/s]
    ELBO: -9277.9:  86%|########6 | 86/100 [00:30<00:04,  3.35it/s]
    ELBO: -9277.9:  87%|########7 | 87/100 [00:30<00:03,  3.37it/s]
    ELBO: -9260.7:  87%|########7 | 87/100 [00:31<00:03,  3.37it/s]
    ELBO: -9260.7:  88%|########8 | 88/100 [00:31<00:04,  2.68it/s]
    ELBO: -9308.0:  88%|########8 | 88/100 [00:31<00:04,  2.68it/s]
    ELBO: -9308.0:  89%|########9 | 89/100 [00:31<00:03,  3.43it/s]
    ELBO: -9310.3:  89%|########9 | 89/100 [00:31<00:03,  3.43it/s]
    ELBO: -9310.3:  90%|######### | 90/100 [00:31<00:03,  2.70it/s]
    ELBO: -9286.8:  90%|######### | 90/100 [00:32<00:03,  2.70it/s]
    ELBO: -9286.8:  91%|#########1| 91/100 [00:32<00:02,  3.12it/s]
    ELBO: -9360.7:  91%|#########1| 91/100 [00:32<00:02,  3.12it/s]
    ELBO: -9360.7:  92%|#########2| 92/100 [00:32<00:02,  3.71it/s]
    ELBO: -9298.6:  92%|#########2| 92/100 [00:32<00:02,  3.71it/s]
    ELBO: -9298.6:  93%|#########3| 93/100 [00:32<00:02,  3.15it/s]
    ELBO: -9258.1:  93%|#########3| 93/100 [00:33<00:02,  3.15it/s]
    ELBO: -9258.1:  94%|#########3| 94/100 [00:33<00:01,  3.05it/s]
    ELBO: -9248.6:  94%|#########3| 94/100 [00:33<00:01,  3.05it/s]
    ELBO: -9248.6:  95%|#########5| 95/100 [00:33<00:01,  3.59it/s]
    ELBO: -9317.9:  95%|#########5| 95/100 [00:33<00:01,  3.59it/s]
    ELBO: -9272.5:  95%|#########5| 95/100 [00:33<00:01,  3.59it/s]
    ELBO: -9272.5:  97%|#########7| 97/100 [00:33<00:00,  3.89it/s]
    ELBO: -9345.4:  97%|#########7| 97/100 [00:34<00:00,  3.89it/s]
    ELBO: -9345.4:  98%|#########8| 98/100 [00:34<00:00,  3.42it/s]
    ELBO: -9327.8:  98%|#########8| 98/100 [00:34<00:00,  3.42it/s]
    ELBO: -9327.8:  99%|#########9| 99/100 [00:34<00:00,  3.98it/s]
    ELBO: -9316.1:  99%|#########9| 99/100 [00:34<00:00,  3.98it/s]
    ELBO: -9316.1: 100%|##########| 100/100 [00:34<00:00,  4.17it/s]
    ELBO: -9316.1: 100%|##########| 100/100 [00:34<00:00,  2.91it/s]
    Fitting SLDS with Laplace-EM, alpha = 0.5

      0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -20229.3:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -10059.0:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -10059.0:   1%|1         | 1/100 [00:00<00:53,  1.86it/s]
    ELBO: -9641.6:   1%|1         | 1/100 [00:00<00:53,  1.86it/s] 
    ELBO: -9641.6:   2%|2         | 2/100 [00:00<00:38,  2.54it/s]
    ELBO: -9485.2:   2%|2         | 2/100 [00:01<00:38,  2.54it/s]
    ELBO: -9485.2:   3%|3         | 3/100 [00:01<00:35,  2.76it/s]
    ELBO: -9459.5:   3%|3         | 3/100 [00:01<00:35,  2.76it/s]
    ELBO: -9459.5:   4%|4         | 4/100 [00:01<00:35,  2.67it/s]
    ELBO: -9361.6:   4%|4         | 4/100 [00:01<00:35,  2.67it/s]
    ELBO: -9361.6:   5%|5         | 5/100 [00:01<00:35,  2.64it/s]
    ELBO: -9368.2:   5%|5         | 5/100 [00:02<00:35,  2.64it/s]
    ELBO: -9368.2:   6%|6         | 6/100 [00:02<00:38,  2.45it/s]
    ELBO: -9359.9:   6%|6         | 6/100 [00:02<00:38,  2.45it/s]
    ELBO: -9359.9:   7%|7         | 7/100 [00:02<00:43,  2.16it/s]
    ELBO: -9350.5:   7%|7         | 7/100 [00:03<00:43,  2.16it/s]
    ELBO: -9350.5:   8%|8         | 8/100 [00:03<00:33,  2.72it/s]
    ELBO: -9347.4:   8%|8         | 8/100 [00:03<00:33,  2.72it/s]
    ELBO: -9347.4:   9%|9         | 9/100 [00:03<00:34,  2.65it/s]
    ELBO: -9356.5:   9%|9         | 9/100 [00:04<00:34,  2.65it/s]
    ELBO: -9356.5:  10%|#         | 10/100 [00:04<00:39,  2.26it/s]
    ELBO: -9341.0:  10%|#         | 10/100 [00:04<00:39,  2.26it/s]
    ELBO: -9341.0:  11%|#1        | 11/100 [00:04<00:31,  2.85it/s]
    ELBO: -9344.6:  11%|#1        | 11/100 [00:04<00:31,  2.85it/s]
    ELBO: -9344.6:  12%|#2        | 12/100 [00:04<00:31,  2.75it/s]
    ELBO: -9395.1:  12%|#2        | 12/100 [00:05<00:31,  2.75it/s]
    ELBO: -9395.1:  13%|#3        | 13/100 [00:05<00:37,  2.33it/s]
    ELBO: -9336.8:  13%|#3        | 13/100 [00:05<00:37,  2.33it/s]
    ELBO: -9336.8:  14%|#4        | 14/100 [00:05<00:31,  2.69it/s]
    ELBO: -9289.4:  14%|#4        | 14/100 [00:05<00:31,  2.69it/s]
    ELBO: -9289.4:  15%|#5        | 15/100 [00:05<00:34,  2.48it/s]
    ELBO: -9302.4:  15%|#5        | 15/100 [00:06<00:34,  2.48it/s]
    ELBO: -9302.4:  16%|#6        | 16/100 [00:06<00:35,  2.34it/s]
    ELBO: -9301.9:  16%|#6        | 16/100 [00:06<00:35,  2.34it/s]
    ELBO: -9301.9:  17%|#7        | 17/100 [00:06<00:28,  2.87it/s]
    ELBO: -9329.7:  17%|#7        | 17/100 [00:07<00:28,  2.87it/s]
    ELBO: -9329.7:  18%|#8        | 18/100 [00:07<00:31,  2.64it/s]
    ELBO: -9317.5:  18%|#8        | 18/100 [00:07<00:31,  2.64it/s]
    ELBO: -9317.5:  19%|#9        | 19/100 [00:07<00:35,  2.30it/s]
    ELBO: -9310.7:  19%|#9        | 19/100 [00:07<00:35,  2.30it/s]
    ELBO: -9310.7:  20%|##        | 20/100 [00:07<00:27,  2.96it/s]
    ELBO: -9288.4:  20%|##        | 20/100 [00:08<00:27,  2.96it/s]
    ELBO: -9288.4:  21%|##1       | 21/100 [00:08<00:32,  2.45it/s]
    ELBO: -9316.8:  21%|##1       | 21/100 [00:08<00:32,  2.45it/s]
    ELBO: -9316.8:  22%|##2       | 22/100 [00:08<00:33,  2.32it/s]
    ELBO: -9279.1:  22%|##2       | 22/100 [00:09<00:33,  2.32it/s]
    ELBO: -9279.1:  23%|##3       | 23/100 [00:09<00:30,  2.56it/s]
    ELBO: -9302.6:  23%|##3       | 23/100 [00:09<00:30,  2.56it/s]
    ELBO: -9302.6:  24%|##4       | 24/100 [00:09<00:32,  2.36it/s]
    ELBO: -9290.1:  24%|##4       | 24/100 [00:10<00:32,  2.36it/s]
    ELBO: -9290.1:  25%|##5       | 25/100 [00:10<00:32,  2.28it/s]
    ELBO: -9279.4:  25%|##5       | 25/100 [00:10<00:32,  2.28it/s]
    ELBO: -9279.4:  26%|##6       | 26/100 [00:10<00:34,  2.15it/s]
    ELBO: -9312.6:  26%|##6       | 26/100 [00:10<00:34,  2.15it/s]
    ELBO: -9312.6:  27%|##7       | 27/100 [00:10<00:28,  2.53it/s]
    ELBO: -9271.7:  27%|##7       | 27/100 [00:11<00:28,  2.53it/s]
    ELBO: -9271.7:  28%|##8       | 28/100 [00:11<00:25,  2.86it/s]
    ELBO: -9305.0:  28%|##8       | 28/100 [00:11<00:25,  2.86it/s]
    ELBO: -9305.0:  29%|##9       | 29/100 [00:11<00:29,  2.40it/s]
    ELBO: -9311.4:  29%|##9       | 29/100 [00:11<00:29,  2.40it/s]
    ELBO: -9311.4:  30%|###       | 30/100 [00:11<00:22,  3.05it/s]
    ELBO: -9274.6:  30%|###       | 30/100 [00:12<00:22,  3.05it/s]
    ELBO: -9274.6:  31%|###1      | 31/100 [00:12<00:24,  2.78it/s]
    ELBO: -9313.9:  31%|###1      | 31/100 [00:12<00:24,  2.78it/s]
    ELBO: -9313.9:  32%|###2      | 32/100 [00:12<00:24,  2.74it/s]
    ELBO: -9284.2:  32%|###2      | 32/100 [00:12<00:24,  2.74it/s]
    ELBO: -9284.2:  33%|###3      | 33/100 [00:12<00:24,  2.75it/s]
    ELBO: -9289.7:  33%|###3      | 33/100 [00:13<00:24,  2.75it/s]
    ELBO: -9289.7:  34%|###4      | 34/100 [00:13<00:19,  3.46it/s]
    ELBO: -9275.2:  34%|###4      | 34/100 [00:13<00:19,  3.46it/s]
    ELBO: -9275.2:  35%|###5      | 35/100 [00:13<00:16,  4.01it/s]
    ELBO: -9205.7:  35%|###5      | 35/100 [00:13<00:16,  4.01it/s]
    ELBO: -9205.7:  36%|###6      | 36/100 [00:13<00:17,  3.67it/s]
    ELBO: -9275.3:  36%|###6      | 36/100 [00:13<00:17,  3.67it/s]
    ELBO: -9275.3:  37%|###7      | 37/100 [00:13<00:14,  4.47it/s]
    ELBO: -9322.0:  37%|###7      | 37/100 [00:14<00:14,  4.47it/s]
    ELBO: -9322.0:  38%|###8      | 38/100 [00:14<00:17,  3.49it/s]
    ELBO: -9317.7:  38%|###8      | 38/100 [00:14<00:17,  3.49it/s]
    ELBO: -9317.7:  39%|###9      | 39/100 [00:14<00:19,  3.20it/s]
    ELBO: -9313.1:  39%|###9      | 39/100 [00:14<00:19,  3.20it/s]
    ELBO: -9313.1:  40%|####      | 40/100 [00:14<00:16,  3.71it/s]
    ELBO: -9243.0:  40%|####      | 40/100 [00:15<00:16,  3.71it/s]
    ELBO: -9243.0:  41%|####1     | 41/100 [00:15<00:19,  3.03it/s]
    ELBO: -9319.4:  41%|####1     | 41/100 [00:15<00:19,  3.03it/s]
    ELBO: -9319.4:  42%|####2     | 42/100 [00:15<00:19,  2.95it/s]
    ELBO: -9329.2:  42%|####2     | 42/100 [00:15<00:19,  2.95it/s]
    ELBO: -9329.2:  43%|####3     | 43/100 [00:15<00:20,  2.78it/s]
    ELBO: -9277.2:  43%|####3     | 43/100 [00:16<00:20,  2.78it/s]
    ELBO: -9277.2:  44%|####4     | 44/100 [00:16<00:20,  2.79it/s]
    ELBO: -9284.2:  44%|####4     | 44/100 [00:16<00:20,  2.79it/s]
    ELBO: -9284.2:  45%|####5     | 45/100 [00:16<00:23,  2.34it/s]
    ELBO: -9266.8:  45%|####5     | 45/100 [00:16<00:23,  2.34it/s]
    ELBO: -9266.8:  46%|####6     | 46/100 [00:16<00:18,  2.92it/s]
    ELBO: -9295.8:  46%|####6     | 46/100 [00:17<00:18,  2.92it/s]
    ELBO: -9295.8:  47%|####6     | 47/100 [00:17<00:19,  2.76it/s]
    ELBO: -9356.9:  47%|####6     | 47/100 [00:17<00:19,  2.76it/s]
    ELBO: -9356.9:  48%|####8     | 48/100 [00:17<00:21,  2.37it/s]
    ELBO: -9277.6:  48%|####8     | 48/100 [00:18<00:21,  2.37it/s]
    ELBO: -9277.6:  49%|####9     | 49/100 [00:18<00:16,  3.06it/s]
    ELBO: -9265.5:  49%|####9     | 49/100 [00:18<00:16,  3.06it/s]
    ELBO: -9265.5:  50%|#####     | 50/100 [00:18<00:21,  2.37it/s]
    ELBO: -9229.5:  50%|#####     | 50/100 [00:18<00:21,  2.37it/s]
    ELBO: -9229.5:  51%|#####1    | 51/100 [00:18<00:18,  2.63it/s]
    ELBO: -9322.1:  51%|#####1    | 51/100 [00:19<00:18,  2.63it/s]
    ELBO: -9322.1:  52%|#####2    | 52/100 [00:19<00:17,  2.76it/s]
    ELBO: -9264.0:  52%|#####2    | 52/100 [00:19<00:17,  2.76it/s]
    ELBO: -9264.0:  53%|#####3    | 53/100 [00:19<00:18,  2.55it/s]
    ELBO: -9329.0:  53%|#####3    | 53/100 [00:19<00:18,  2.55it/s]
    ELBO: -9329.0:  54%|#####4    | 54/100 [00:19<00:15,  3.04it/s]
    ELBO: -9306.3:  54%|#####4    | 54/100 [00:20<00:15,  3.04it/s]
    ELBO: -9306.3:  55%|#####5    | 55/100 [00:20<00:15,  2.96it/s]
    ELBO: -9229.0:  55%|#####5    | 55/100 [00:20<00:15,  2.96it/s]
    ELBO: -9229.0:  56%|#####6    | 56/100 [00:20<00:17,  2.48it/s]
    ELBO: -9297.2:  56%|#####6    | 56/100 [00:20<00:17,  2.48it/s]
    ELBO: -9297.2:  57%|#####6    | 57/100 [00:20<00:14,  3.05it/s]
    ELBO: -9292.5:  57%|#####6    | 57/100 [00:21<00:14,  3.05it/s]
    ELBO: -9292.5:  58%|#####8    | 58/100 [00:21<00:14,  2.91it/s]
    ELBO: -9268.6:  58%|#####8    | 58/100 [00:21<00:14,  2.91it/s]
    ELBO: -9268.6:  59%|#####8    | 59/100 [00:21<00:14,  2.78it/s]
    ELBO: -9270.2:  59%|#####8    | 59/100 [00:21<00:14,  2.78it/s]
    ELBO: -9270.2:  60%|######    | 60/100 [00:21<00:12,  3.10it/s]
    ELBO: -9324.0:  60%|######    | 60/100 [00:22<00:12,  3.10it/s]
    ELBO: -9324.0:  61%|######1   | 61/100 [00:22<00:14,  2.73it/s]
    ELBO: -9221.7:  61%|######1   | 61/100 [00:22<00:14,  2.73it/s]
    ELBO: -9221.7:  62%|######2   | 62/100 [00:22<00:11,  3.24it/s]
    ELBO: -9248.1:  62%|######2   | 62/100 [00:23<00:11,  3.24it/s]
    ELBO: -9248.1:  63%|######3   | 63/100 [00:23<00:12,  2.87it/s]
    ELBO: -9345.6:  63%|######3   | 63/100 [00:23<00:12,  2.87it/s]
    ELBO: -9345.6:  64%|######4   | 64/100 [00:23<00:13,  2.58it/s]
    ELBO: -9252.2:  64%|######4   | 64/100 [00:23<00:13,  2.58it/s]
    ELBO: -9252.2:  65%|######5   | 65/100 [00:23<00:11,  3.03it/s]
    ELBO: -9281.6:  65%|######5   | 65/100 [00:24<00:11,  3.03it/s]
    ELBO: -9281.6:  66%|######6   | 66/100 [00:24<00:12,  2.76it/s]
    ELBO: -9290.6:  66%|######6   | 66/100 [00:24<00:12,  2.76it/s]
    ELBO: -9290.6:  67%|######7   | 67/100 [00:24<00:09,  3.41it/s]
    ELBO: -9253.3:  67%|######7   | 67/100 [00:24<00:09,  3.41it/s]
    ELBO: -9253.3:  68%|######8   | 68/100 [00:24<00:10,  2.95it/s]
    ELBO: -9326.7:  68%|######8   | 68/100 [00:25<00:10,  2.95it/s]
    ELBO: -9326.7:  69%|######9   | 69/100 [00:25<00:12,  2.46it/s]
    ELBO: -9271.4:  69%|######9   | 69/100 [00:25<00:12,  2.46it/s]
    ELBO: -9271.4:  70%|#######   | 70/100 [00:25<00:09,  3.07it/s]
    ELBO: -9297.2:  70%|#######   | 70/100 [00:25<00:09,  3.07it/s]
    ELBO: -9297.2:  71%|#######1  | 71/100 [00:25<00:07,  3.68it/s]
    ELBO: -9261.5:  71%|#######1  | 71/100 [00:25<00:07,  3.68it/s]
    ELBO: -9261.5:  72%|#######2  | 72/100 [00:25<00:07,  3.73it/s]
    ELBO: -9258.7:  72%|#######2  | 72/100 [00:26<00:07,  3.73it/s]
    ELBO: -9258.7:  73%|#######3  | 73/100 [00:26<00:06,  4.18it/s]
    ELBO: -9345.0:  73%|#######3  | 73/100 [00:26<00:06,  4.18it/s]
    ELBO: -9345.0:  74%|#######4  | 74/100 [00:26<00:07,  3.31it/s]
    ELBO: -9296.7:  74%|#######4  | 74/100 [00:26<00:07,  3.31it/s]
    ELBO: -9296.7:  75%|#######5  | 75/100 [00:26<00:06,  3.87it/s]
    ELBO: -9328.1:  75%|#######5  | 75/100 [00:27<00:06,  3.87it/s]
    ELBO: -9328.1:  76%|#######6  | 76/100 [00:27<00:08,  2.88it/s]
    ELBO: -9325.2:  76%|#######6  | 76/100 [00:27<00:08,  2.88it/s]
    ELBO: -9325.2:  77%|#######7  | 77/100 [00:27<00:06,  3.58it/s]
    ELBO: -9284.5:  77%|#######7  | 77/100 [00:27<00:06,  3.58it/s]
    ELBO: -9284.5:  78%|#######8  | 78/100 [00:27<00:06,  3.23it/s]
    ELBO: -9273.8:  78%|#######8  | 78/100 [00:27<00:06,  3.23it/s]
    ELBO: -9273.8:  79%|#######9  | 79/100 [00:27<00:05,  3.87it/s]
    ELBO: -9261.2:  79%|#######9  | 79/100 [00:28<00:05,  3.87it/s]
    ELBO: -9261.2:  80%|########  | 80/100 [00:28<00:06,  3.22it/s]
    ELBO: -9304.7:  80%|########  | 80/100 [00:28<00:06,  3.22it/s]
    ELBO: -9304.7:  81%|########1 | 81/100 [00:28<00:07,  2.51it/s]
    ELBO: -9343.6:  81%|########1 | 81/100 [00:29<00:07,  2.51it/s]
    ELBO: -9343.6:  82%|########2 | 82/100 [00:29<00:06,  2.97it/s]
    ELBO: -9271.8:  82%|########2 | 82/100 [00:29<00:06,  2.97it/s]
    ELBO: -9271.8:  83%|########2 | 83/100 [00:29<00:06,  2.78it/s]
    ELBO: -9225.0:  83%|########2 | 83/100 [00:29<00:06,  2.78it/s]
    ELBO: -9225.0:  84%|########4 | 84/100 [00:29<00:04,  3.33it/s]
    ELBO: -9273.3:  84%|########4 | 84/100 [00:30<00:04,  3.33it/s]
    ELBO: -9273.3:  85%|########5 | 85/100 [00:30<00:05,  2.76it/s]
    ELBO: -9342.6:  85%|########5 | 85/100 [00:30<00:05,  2.76it/s]
    ELBO: -9342.6:  86%|########6 | 86/100 [00:30<00:06,  2.32it/s]
    ELBO: -9290.5:  86%|########6 | 86/100 [00:30<00:06,  2.32it/s]
    ELBO: -9290.5:  87%|########7 | 87/100 [00:30<00:04,  2.83it/s]
    ELBO: -9303.9:  87%|########7 | 87/100 [00:31<00:04,  2.83it/s]
    ELBO: -9303.9:  88%|########8 | 88/100 [00:31<00:04,  2.84it/s]
    ELBO: -9274.2:  88%|########8 | 88/100 [00:31<00:04,  2.84it/s]
    ELBO: -9274.2:  89%|########9 | 89/100 [00:31<00:04,  2.64it/s]
    ELBO: -9265.6:  89%|########9 | 89/100 [00:31<00:04,  2.64it/s]
    ELBO: -9265.6:  90%|######### | 90/100 [00:31<00:02,  3.34it/s]
    ELBO: -9293.6:  90%|######### | 90/100 [00:32<00:02,  3.34it/s]
    ELBO: -9293.6:  91%|#########1| 91/100 [00:32<00:03,  2.90it/s]
    ELBO: -9277.9:  91%|#########1| 91/100 [00:32<00:03,  2.90it/s]
    ELBO: -9277.9:  92%|#########2| 92/100 [00:32<00:02,  3.45it/s]
    ELBO: -9279.5:  92%|#########2| 92/100 [00:32<00:02,  3.45it/s]
    ELBO: -9279.5:  93%|#########3| 93/100 [00:32<00:02,  2.75it/s]
    ELBO: -9279.8:  93%|#########3| 93/100 [00:33<00:02,  2.75it/s]
    ELBO: -9279.8:  94%|#########3| 94/100 [00:33<00:01,  3.39it/s]
    ELBO: -9321.5:  94%|#########3| 94/100 [00:33<00:01,  3.39it/s]
    ELBO: -9321.5:  95%|#########5| 95/100 [00:33<00:01,  2.52it/s]
    ELBO: -9289.4:  95%|#########5| 95/100 [00:33<00:01,  2.52it/s]
    ELBO: -9326.5:  95%|#########5| 95/100 [00:34<00:01,  2.52it/s]
    ELBO: -9326.5:  97%|#########7| 97/100 [00:34<00:01,  2.94it/s]
    ELBO: -9319.6:  97%|#########7| 97/100 [00:34<00:01,  2.94it/s]
    ELBO: -9319.6:  98%|#########8| 98/100 [00:34<00:00,  2.76it/s]
    ELBO: -9310.9:  98%|#########8| 98/100 [00:34<00:00,  2.76it/s]
    ELBO: -9310.9:  99%|#########9| 99/100 [00:34<00:00,  3.39it/s]
    ELBO: -9269.4:  99%|#########9| 99/100 [00:35<00:00,  3.39it/s]
    ELBO: -9269.4: 100%|##########| 100/100 [00:35<00:00,  2.93it/s]
    ELBO: -9269.4: 100%|##########| 100/100 [00:35<00:00,  2.83it/s]
    Fitting SLDS with Laplace-EM, alpha = 0.75

      0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -20071.8:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -10650.1:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -10650.1:   1%|1         | 1/100 [00:00<00:43,  2.28it/s]
    ELBO: -10204.1:   1%|1         | 1/100 [00:00<00:43,  2.28it/s]
    ELBO: -10204.1:   2%|2         | 2/100 [00:00<00:40,  2.39it/s]
    ELBO: -9931.4:   2%|2         | 2/100 [00:01<00:40,  2.39it/s] 
    ELBO: -9931.4:   3%|3         | 3/100 [00:01<00:39,  2.45it/s]
    ELBO: -9722.7:   3%|3         | 3/100 [00:01<00:39,  2.45it/s]
    ELBO: -9722.7:   4%|4         | 4/100 [00:01<00:37,  2.58it/s]
    ELBO: -9621.0:   4%|4         | 4/100 [00:01<00:37,  2.58it/s]
    ELBO: -9621.0:   5%|5         | 5/100 [00:01<00:37,  2.57it/s]
    ELBO: -9609.7:   5%|5         | 5/100 [00:02<00:37,  2.57it/s]
    ELBO: -9609.7:   6%|6         | 6/100 [00:02<00:40,  2.35it/s]
    ELBO: -9579.9:   6%|6         | 6/100 [00:02<00:40,  2.35it/s]
    ELBO: -9579.9:   7%|7         | 7/100 [00:02<00:42,  2.20it/s]
    ELBO: -9527.3:   7%|7         | 7/100 [00:03<00:42,  2.20it/s]
    ELBO: -9527.3:   8%|8         | 8/100 [00:03<00:34,  2.65it/s]
    ELBO: -9469.6:   8%|8         | 8/100 [00:03<00:34,  2.65it/s]
    ELBO: -9469.6:   9%|9         | 9/100 [00:03<00:33,  2.70it/s]
    ELBO: -9531.3:   9%|9         | 9/100 [00:04<00:33,  2.70it/s]
    ELBO: -9531.3:  10%|#         | 10/100 [00:04<00:39,  2.29it/s]
    ELBO: -9511.3:  10%|#         | 10/100 [00:04<00:39,  2.29it/s]
    ELBO: -9511.3:  11%|#1        | 11/100 [00:04<00:32,  2.72it/s]
    ELBO: -9483.6:  11%|#1        | 11/100 [00:04<00:32,  2.72it/s]
    ELBO: -9483.6:  12%|#2        | 12/100 [00:04<00:34,  2.53it/s]
    ELBO: -9500.2:  12%|#2        | 12/100 [00:05<00:34,  2.53it/s]
    ELBO: -9500.2:  13%|#3        | 13/100 [00:05<00:33,  2.62it/s]
    ELBO: -9473.1:  13%|#3        | 13/100 [00:05<00:33,  2.62it/s]
    ELBO: -9473.1:  14%|#4        | 14/100 [00:05<00:28,  3.05it/s]
    ELBO: -9440.0:  14%|#4        | 14/100 [00:05<00:28,  3.05it/s]
    ELBO: -9478.1:  14%|#4        | 14/100 [00:06<00:28,  3.05it/s]
    ELBO: -9478.1:  16%|#6        | 16/100 [00:06<00:27,  3.02it/s]
    ELBO: -9428.3:  16%|#6        | 16/100 [00:06<00:27,  3.02it/s]
    ELBO: -9428.3:  17%|#7        | 17/100 [00:06<00:24,  3.45it/s]
    ELBO: -9426.0:  17%|#7        | 17/100 [00:06<00:24,  3.45it/s]
    ELBO: -9426.0:  18%|#8        | 18/100 [00:06<00:25,  3.22it/s]
    ELBO: -9457.7:  18%|#8        | 18/100 [00:06<00:25,  3.22it/s]
    ELBO: -9457.7:  19%|#9        | 19/100 [00:06<00:26,  3.01it/s]
    ELBO: -9437.3:  19%|#9        | 19/100 [00:07<00:26,  3.01it/s]
    ELBO: -9437.3:  20%|##        | 20/100 [00:07<00:23,  3.39it/s]
    ELBO: -9417.3:  20%|##        | 20/100 [00:07<00:23,  3.39it/s]
    ELBO: -9417.3:  21%|##1       | 21/100 [00:07<00:30,  2.59it/s]
    ELBO: -9464.4:  21%|##1       | 21/100 [00:07<00:30,  2.59it/s]
    ELBO: -9464.4:  22%|##2       | 22/100 [00:07<00:24,  3.21it/s]
    ELBO: -9467.7:  22%|##2       | 22/100 [00:08<00:24,  3.21it/s]
    ELBO: -9467.7:  23%|##3       | 23/100 [00:08<00:21,  3.63it/s]
    ELBO: -9536.9:  23%|##3       | 23/100 [00:08<00:21,  3.63it/s]
    ELBO: -9536.9:  24%|##4       | 24/100 [00:08<00:23,  3.30it/s]
    ELBO: -9430.2:  24%|##4       | 24/100 [00:09<00:23,  3.30it/s]
    ELBO: -9430.2:  25%|##5       | 25/100 [00:09<00:28,  2.59it/s]
    ELBO: -9382.8:  25%|##5       | 25/100 [00:09<00:28,  2.59it/s]
    ELBO: -9382.8:  26%|##6       | 26/100 [00:09<00:23,  3.15it/s]
    ELBO: -9441.2:  26%|##6       | 26/100 [00:09<00:23,  3.15it/s]
    ELBO: -9441.2:  27%|##7       | 27/100 [00:09<00:25,  2.91it/s]
    ELBO: -9426.4:  27%|##7       | 27/100 [00:10<00:25,  2.91it/s]
    ELBO: -9426.4:  28%|##8       | 28/100 [00:10<00:27,  2.62it/s]
    ELBO: -9420.4:  28%|##8       | 28/100 [00:10<00:27,  2.62it/s]
    ELBO: -9420.4:  29%|##9       | 29/100 [00:10<00:28,  2.47it/s]
    ELBO: -9411.3:  29%|##9       | 29/100 [00:11<00:28,  2.47it/s]
    ELBO: -9411.3:  30%|###       | 30/100 [00:11<00:30,  2.30it/s]
    ELBO: -9441.7:  30%|###       | 30/100 [00:11<00:30,  2.30it/s]
    ELBO: -9441.7:  31%|###1      | 31/100 [00:11<00:26,  2.57it/s]
    ELBO: -9426.5:  31%|###1      | 31/100 [00:11<00:26,  2.57it/s]
    ELBO: -9426.5:  32%|###2      | 32/100 [00:11<00:24,  2.75it/s]
    ELBO: -9411.3:  32%|###2      | 32/100 [00:11<00:24,  2.75it/s]
    ELBO: -9411.3:  33%|###3      | 33/100 [00:11<00:21,  3.14it/s]
    ELBO: -9400.1:  33%|###3      | 33/100 [00:11<00:21,  3.14it/s]
    ELBO: -9400.1:  34%|###4      | 34/100 [00:11<00:17,  3.87it/s]
    ELBO: -9425.9:  34%|###4      | 34/100 [00:12<00:17,  3.87it/s]
    ELBO: -9425.9:  35%|###5      | 35/100 [00:12<00:13,  4.69it/s]
    ELBO: -9437.9:  35%|###5      | 35/100 [00:12<00:13,  4.69it/s]
    ELBO: -9437.9:  36%|###6      | 36/100 [00:12<00:15,  4.16it/s]
    ELBO: -9437.1:  36%|###6      | 36/100 [00:12<00:15,  4.16it/s]
    ELBO: -9437.1:  37%|###7      | 37/100 [00:12<00:19,  3.16it/s]
    ELBO: -9449.6:  37%|###7      | 37/100 [00:13<00:19,  3.16it/s]
    ELBO: -9449.6:  38%|###8      | 38/100 [00:13<00:24,  2.55it/s]
    ELBO: -9390.5:  38%|###8      | 38/100 [00:13<00:24,  2.55it/s]
    ELBO: -9390.5:  39%|###9      | 39/100 [00:13<00:23,  2.59it/s]
    ELBO: -9387.7:  39%|###9      | 39/100 [00:14<00:23,  2.59it/s]
    ELBO: -9387.7:  40%|####      | 40/100 [00:14<00:22,  2.68it/s]
    ELBO: -9360.7:  40%|####      | 40/100 [00:14<00:22,  2.68it/s]
    ELBO: -9360.7:  41%|####1     | 41/100 [00:14<00:23,  2.52it/s]
    ELBO: -9378.8:  41%|####1     | 41/100 [00:15<00:23,  2.52it/s]
    ELBO: -9378.8:  42%|####2     | 42/100 [00:15<00:26,  2.21it/s]
    ELBO: -9371.4:  42%|####2     | 42/100 [00:15<00:26,  2.21it/s]
    ELBO: -9371.4:  43%|####3     | 43/100 [00:15<00:26,  2.14it/s]
    ELBO: -9374.8:  43%|####3     | 43/100 [00:16<00:26,  2.14it/s]
    ELBO: -9374.8:  44%|####4     | 44/100 [00:16<00:27,  2.06it/s]
    ELBO: -9388.3:  44%|####4     | 44/100 [00:16<00:27,  2.06it/s]
    ELBO: -9388.3:  45%|####5     | 45/100 [00:16<00:23,  2.33it/s]
    ELBO: -9424.3:  45%|####5     | 45/100 [00:16<00:23,  2.33it/s]
    ELBO: -9424.3:  46%|####6     | 46/100 [00:16<00:23,  2.31it/s]
    ELBO: -9412.2:  46%|####6     | 46/100 [00:17<00:23,  2.31it/s]
    ELBO: -9412.2:  47%|####6     | 47/100 [00:17<00:21,  2.41it/s]
    ELBO: -9416.5:  47%|####6     | 47/100 [00:17<00:21,  2.41it/s]
    ELBO: -9416.5:  48%|####8     | 48/100 [00:17<00:18,  2.81it/s]
    ELBO: -9374.9:  48%|####8     | 48/100 [00:18<00:18,  2.81it/s]
    ELBO: -9374.9:  49%|####9     | 49/100 [00:18<00:22,  2.22it/s]
    ELBO: -9448.4:  49%|####9     | 49/100 [00:18<00:22,  2.22it/s]
    ELBO: -9448.4:  50%|#####     | 50/100 [00:18<00:18,  2.72it/s]
    ELBO: -9413.7:  50%|#####     | 50/100 [00:18<00:18,  2.72it/s]
    ELBO: -9413.7:  51%|#####1    | 51/100 [00:18<00:19,  2.51it/s]
    ELBO: -9418.1:  51%|#####1    | 51/100 [00:19<00:19,  2.51it/s]
    ELBO: -9418.1:  52%|#####2    | 52/100 [00:19<00:15,  3.00it/s]
    ELBO: -9438.5:  52%|#####2    | 52/100 [00:19<00:15,  3.00it/s]
    ELBO: -9438.5:  53%|#####3    | 53/100 [00:19<00:17,  2.64it/s]
    ELBO: -9402.8:  53%|#####3    | 53/100 [00:19<00:17,  2.64it/s]
    ELBO: -9402.8:  54%|#####4    | 54/100 [00:19<00:14,  3.27it/s]
    ELBO: -9429.1:  54%|#####4    | 54/100 [00:19<00:14,  3.27it/s]
    ELBO: -9429.1:  55%|#####5    | 55/100 [00:19<00:11,  4.04it/s]
    ELBO: -9399.2:  55%|#####5    | 55/100 [00:19<00:11,  4.04it/s]
    ELBO: -9439.9:  55%|#####5    | 55/100 [00:19<00:11,  4.04it/s]
    ELBO: -9439.9:  57%|#####6    | 57/100 [00:19<00:07,  5.57it/s]
    ELBO: -9453.5:  57%|#####6    | 57/100 [00:20<00:07,  5.57it/s]
    ELBO: -9453.5:  58%|#####8    | 58/100 [00:20<00:10,  3.94it/s]
    ELBO: -9369.6:  58%|#####8    | 58/100 [00:20<00:10,  3.94it/s]
    ELBO: -9369.6:  59%|#####8    | 59/100 [00:20<00:09,  4.29it/s]
    ELBO: -9355.8:  59%|#####8    | 59/100 [00:21<00:09,  4.29it/s]
    ELBO: -9355.8:  60%|######    | 60/100 [00:21<00:10,  3.68it/s]
    ELBO: -9402.1:  60%|######    | 60/100 [00:21<00:10,  3.68it/s]
    ELBO: -9402.1:  61%|######1   | 61/100 [00:21<00:14,  2.75it/s]
    ELBO: -9407.6:  61%|######1   | 61/100 [00:21<00:14,  2.75it/s]
    ELBO: -9407.6:  62%|######2   | 62/100 [00:21<00:11,  3.29it/s]
    ELBO: -9457.4:  62%|######2   | 62/100 [00:22<00:11,  3.29it/s]
    ELBO: -9457.4:  63%|######3   | 63/100 [00:22<00:12,  3.00it/s]
    ELBO: -9351.8:  63%|######3   | 63/100 [00:22<00:12,  3.00it/s]
    ELBO: -9351.8:  64%|######4   | 64/100 [00:22<00:14,  2.47it/s]
    ELBO: -9453.1:  64%|######4   | 64/100 [00:23<00:14,  2.47it/s]
    ELBO: -9453.1:  65%|######5   | 65/100 [00:23<00:14,  2.35it/s]
    ELBO: -9457.1:  65%|######5   | 65/100 [00:23<00:14,  2.35it/s]
    ELBO: -9457.1:  66%|######6   | 66/100 [00:23<00:11,  3.02it/s]
    ELBO: -9434.3:  66%|######6   | 66/100 [00:23<00:11,  3.02it/s]
    ELBO: -9434.3:  67%|######7   | 67/100 [00:23<00:12,  2.69it/s]
    ELBO: -9400.7:  67%|######7   | 67/100 [00:24<00:12,  2.69it/s]
    ELBO: -9400.7:  68%|######8   | 68/100 [00:24<00:13,  2.32it/s]
    ELBO: -9412.5:  68%|######8   | 68/100 [00:24<00:13,  2.32it/s]
    ELBO: -9412.5:  69%|######9   | 69/100 [00:24<00:10,  2.86it/s]
    ELBO: -9464.4:  69%|######9   | 69/100 [00:24<00:10,  2.86it/s]
    ELBO: -9464.4:  70%|#######   | 70/100 [00:24<00:10,  2.79it/s]
    ELBO: -9425.0:  70%|#######   | 70/100 [00:25<00:10,  2.79it/s]
    ELBO: -9425.0:  71%|#######1  | 71/100 [00:25<00:10,  2.75it/s]
    ELBO: -9432.9:  71%|#######1  | 71/100 [00:25<00:10,  2.75it/s]
    ELBO: -9432.9:  72%|#######2  | 72/100 [00:25<00:09,  2.98it/s]
    ELBO: -9449.3:  72%|#######2  | 72/100 [00:26<00:09,  2.98it/s]
    ELBO: -9449.3:  73%|#######3  | 73/100 [00:26<00:11,  2.44it/s]
    ELBO: -9433.1:  73%|#######3  | 73/100 [00:26<00:11,  2.44it/s]
    ELBO: -9433.1:  74%|#######4  | 74/100 [00:26<00:08,  3.07it/s]
    ELBO: -9459.2:  74%|#######4  | 74/100 [00:26<00:08,  3.07it/s]
    ELBO: -9459.2:  75%|#######5  | 75/100 [00:26<00:08,  2.86it/s]
    ELBO: -9423.2:  75%|#######5  | 75/100 [00:27<00:08,  2.86it/s]
    ELBO: -9423.2:  76%|#######6  | 76/100 [00:27<00:09,  2.40it/s]
    ELBO: -9422.7:  76%|#######6  | 76/100 [00:27<00:09,  2.40it/s]
    ELBO: -9422.7:  77%|#######7  | 77/100 [00:27<00:08,  2.59it/s]
    ELBO: -9421.3:  77%|#######7  | 77/100 [00:27<00:08,  2.59it/s]
    ELBO: -9421.3:  78%|#######8  | 78/100 [00:27<00:08,  2.69it/s]
    ELBO: -9438.0:  78%|#######8  | 78/100 [00:28<00:08,  2.69it/s]
    ELBO: -9438.0:  79%|#######9  | 79/100 [00:28<00:07,  2.63it/s]
    ELBO: -9385.5:  79%|#######9  | 79/100 [00:28<00:07,  2.63it/s]
    ELBO: -9385.5:  80%|########  | 80/100 [00:28<00:07,  2.71it/s]
    ELBO: -9399.5:  80%|########  | 80/100 [00:28<00:07,  2.71it/s]
    ELBO: -9399.5:  81%|########1 | 81/100 [00:28<00:05,  3.44it/s]
    ELBO: -9387.7:  81%|########1 | 81/100 [00:28<00:05,  3.44it/s]
    ELBO: -9387.7:  82%|########2 | 82/100 [00:28<00:04,  3.95it/s]
    ELBO: -9409.6:  82%|########2 | 82/100 [00:29<00:04,  3.95it/s]
    ELBO: -9409.6:  83%|########2 | 83/100 [00:29<00:03,  4.33it/s]
    ELBO: -9421.6:  83%|########2 | 83/100 [00:29<00:03,  4.33it/s]
    ELBO: -9421.6:  84%|########4 | 84/100 [00:29<00:04,  3.35it/s]
    ELBO: -9347.3:  84%|########4 | 84/100 [00:29<00:04,  3.35it/s]
    ELBO: -9347.3:  85%|########5 | 85/100 [00:29<00:03,  3.85it/s]
    ELBO: -9347.3:  85%|########5 | 85/100 [00:30<00:03,  3.85it/s]
    ELBO: -9347.3:  86%|########6 | 86/100 [00:30<00:04,  2.85it/s]
    ELBO: -9375.3:  86%|########6 | 86/100 [00:30<00:04,  2.85it/s]
    ELBO: -9375.3:  87%|########7 | 87/100 [00:30<00:05,  2.58it/s]
    ELBO: -9416.3:  87%|########7 | 87/100 [00:30<00:05,  2.58it/s]
    ELBO: -9416.3:  88%|########8 | 88/100 [00:30<00:04,  2.89it/s]
    ELBO: -9342.8:  88%|########8 | 88/100 [00:31<00:04,  2.89it/s]
    ELBO: -9342.8:  89%|########9 | 89/100 [00:31<00:04,  2.68it/s]
    ELBO: -9334.5:  89%|########9 | 89/100 [00:32<00:04,  2.68it/s]
    ELBO: -9334.5:  90%|######### | 90/100 [00:32<00:04,  2.31it/s]
    ELBO: -9364.5:  90%|######### | 90/100 [00:32<00:04,  2.31it/s]
    ELBO: -9364.5:  91%|#########1| 91/100 [00:32<00:03,  2.88it/s]
    ELBO: -9326.3:  91%|#########1| 91/100 [00:32<00:03,  2.88it/s]
    ELBO: -9326.3:  92%|#########2| 92/100 [00:32<00:02,  2.74it/s]
    ELBO: -9311.2:  92%|#########2| 92/100 [00:33<00:02,  2.74it/s]
    ELBO: -9311.2:  93%|#########3| 93/100 [00:33<00:02,  2.37it/s]
    ELBO: -9315.2:  93%|#########3| 93/100 [00:33<00:02,  2.37it/s]
    ELBO: -9315.2:  94%|#########3| 94/100 [00:33<00:02,  2.94it/s]
    ELBO: -9321.8:  94%|#########3| 94/100 [00:33<00:02,  2.94it/s]
    ELBO: -9321.8:  95%|#########5| 95/100 [00:33<00:02,  2.30it/s]
    ELBO: -9321.3:  95%|#########5| 95/100 [00:34<00:02,  2.30it/s]
    ELBO: -9321.3:  96%|#########6| 96/100 [00:34<00:01,  2.79it/s]
    ELBO: -9296.7:  96%|#########6| 96/100 [00:34<00:01,  2.79it/s]
    ELBO: -9296.7:  97%|#########7| 97/100 [00:34<00:01,  2.23it/s]
    ELBO: -9315.9:  97%|#########7| 97/100 [00:34<00:01,  2.23it/s]
    ELBO: -9315.9:  98%|#########8| 98/100 [00:34<00:00,  2.87it/s]
    ELBO: -9273.3:  98%|#########8| 98/100 [00:35<00:00,  2.87it/s]
    ELBO: -9273.3:  99%|#########9| 99/100 [00:35<00:00,  2.40it/s]
    ELBO: -9296.8:  99%|#########9| 99/100 [00:36<00:00,  2.40it/s]
    ELBO: -9296.8: 100%|##########| 100/100 [00:36<00:00,  2.16it/s]
    ELBO: -9296.8: 100%|##########| 100/100 [00:36<00:00,  2.78it/s]
    Fitting SLDS with Laplace-EM, alpha = 0.9

      0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -20312.0:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -11010.5:   0%|          | 0/100 [00:00<?, ?it/s]
    ELBO: -11010.5:   1%|1         | 1/100 [00:00<00:49,  1.98it/s]
    ELBO: -10711.4:   1%|1         | 1/100 [00:00<00:49,  1.98it/s]
    ELBO: -10711.4:   2%|2         | 2/100 [00:00<00:48,  2.03it/s]
    ELBO: -10477.9:   2%|2         | 2/100 [00:01<00:48,  2.03it/s]
    ELBO: -10477.9:   3%|3         | 3/100 [00:01<00:33,  2.86it/s]
    ELBO: -10322.0:   3%|3         | 3/100 [00:01<00:33,  2.86it/s]
    ELBO: -10322.0:   4%|4         | 4/100 [00:01<00:34,  2.75it/s]
    ELBO: -10182.2:   4%|4         | 4/100 [00:01<00:34,  2.75it/s]
    ELBO: -10182.2:   5%|5         | 5/100 [00:01<00:32,  2.96it/s]
    ELBO: -10058.4:   5%|5         | 5/100 [00:02<00:32,  2.96it/s]
    ELBO: -10058.4:   6%|6         | 6/100 [00:02<00:37,  2.53it/s]
    ELBO: -9969.4:   6%|6         | 6/100 [00:02<00:37,  2.53it/s] 
    ELBO: -9969.4:   7%|7         | 7/100 [00:02<00:31,  2.98it/s]
    ELBO: -9864.2:   7%|7         | 7/100 [00:02<00:31,  2.98it/s]
    ELBO: -9864.2:   8%|8         | 8/100 [00:02<00:31,  2.94it/s]
    ELBO: -9821.8:   8%|8         | 8/100 [00:03<00:31,  2.94it/s]
    ELBO: -9821.8:   9%|9         | 9/100 [00:03<00:38,  2.36it/s]
    ELBO: -9775.3:   9%|9         | 9/100 [00:03<00:38,  2.36it/s]
    ELBO: -9775.3:  10%|#         | 10/100 [00:03<00:30,  2.93it/s]
    ELBO: -9699.4:  10%|#         | 10/100 [00:03<00:30,  2.93it/s]
    ELBO: -9699.4:  11%|#1        | 11/100 [00:03<00:26,  3.33it/s]
    ELBO: -9696.7:  11%|#1        | 11/100 [00:04<00:26,  3.33it/s]
    ELBO: -9696.7:  12%|#2        | 12/100 [00:04<00:32,  2.71it/s]
    ELBO: -9644.1:  12%|#2        | 12/100 [00:04<00:32,  2.71it/s]
    ELBO: -9644.1:  13%|#3        | 13/100 [00:04<00:31,  2.79it/s]
    ELBO: -9620.2:  13%|#3        | 13/100 [00:05<00:31,  2.79it/s]
    ELBO: -9620.2:  14%|#4        | 14/100 [00:05<00:28,  3.02it/s]
    ELBO: -9538.2:  14%|#4        | 14/100 [00:05<00:28,  3.02it/s]
    ELBO: -9538.2:  15%|#5        | 15/100 [00:05<00:31,  2.68it/s]
    ELBO: -9541.1:  15%|#5        | 15/100 [00:06<00:31,  2.68it/s]
    ELBO: -9541.1:  16%|#6        | 16/100 [00:06<00:35,  2.39it/s]
    ELBO: -9564.1:  16%|#6        | 16/100 [00:06<00:35,  2.39it/s]
    ELBO: -9564.1:  17%|#7        | 17/100 [00:06<00:33,  2.51it/s]
    ELBO: -9532.7:  17%|#7        | 17/100 [00:06<00:33,  2.51it/s]
    ELBO: -9532.7:  18%|#8        | 18/100 [00:06<00:34,  2.38it/s]
    ELBO: -9507.4:  18%|#8        | 18/100 [00:07<00:34,  2.38it/s]
    ELBO: -9507.4:  19%|#9        | 19/100 [00:07<00:29,  2.71it/s]
    ELBO: -9508.2:  19%|#9        | 19/100 [00:07<00:29,  2.71it/s]
    ELBO: -9508.2:  20%|##        | 20/100 [00:07<00:30,  2.62it/s]
    ELBO: -9519.2:  20%|##        | 20/100 [00:07<00:30,  2.62it/s]
    ELBO: -9519.2:  21%|##1       | 21/100 [00:07<00:31,  2.54it/s]
    ELBO: -9498.9:  21%|##1       | 21/100 [00:08<00:31,  2.54it/s]
    ELBO: -9498.9:  22%|##2       | 22/100 [00:08<00:25,  3.06it/s]
    ELBO: -9492.1:  22%|##2       | 22/100 [00:08<00:25,  3.06it/s]
    ELBO: -9492.1:  23%|##3       | 23/100 [00:08<00:27,  2.84it/s]
    ELBO: -9469.6:  23%|##3       | 23/100 [00:08<00:27,  2.84it/s]
    ELBO: -9469.6:  24%|##4       | 24/100 [00:08<00:28,  2.71it/s]
    ELBO: -9530.2:  24%|##4       | 24/100 [00:09<00:28,  2.71it/s]
    ELBO: -9530.2:  25%|##5       | 25/100 [00:09<00:23,  3.17it/s]
    ELBO: -9467.1:  25%|##5       | 25/100 [00:09<00:23,  3.17it/s]
    ELBO: -9467.1:  26%|##6       | 26/100 [00:09<00:25,  2.93it/s]
    ELBO: -9460.2:  26%|##6       | 26/100 [00:09<00:25,  2.93it/s]
    ELBO: -9460.2:  27%|##7       | 27/100 [00:09<00:28,  2.58it/s]
    ELBO: -9435.6:  27%|##7       | 27/100 [00:10<00:28,  2.58it/s]
    ELBO: -9435.6:  28%|##8       | 28/100 [00:10<00:25,  2.79it/s]
    ELBO: -9444.3:  28%|##8       | 28/100 [00:10<00:25,  2.79it/s]
    ELBO: -9444.3:  29%|##9       | 29/100 [00:10<00:24,  2.87it/s]
    ELBO: -9426.0:  29%|##9       | 29/100 [00:11<00:24,  2.87it/s]
    ELBO: -9426.0:  30%|###       | 30/100 [00:11<00:29,  2.39it/s]
    ELBO: -9471.9:  30%|###       | 30/100 [00:11<00:29,  2.39it/s]
    ELBO: -9471.9:  31%|###1      | 31/100 [00:11<00:24,  2.79it/s]
    ELBO: -9423.0:  31%|###1      | 31/100 [00:11<00:24,  2.79it/s]
    ELBO: -9423.0:  32%|###2      | 32/100 [00:11<00:21,  3.18it/s]
    ELBO: -9357.0:  32%|###2      | 32/100 [00:12<00:21,  3.18it/s]
    ELBO: -9357.0:  33%|###3      | 33/100 [00:12<00:23,  2.85it/s]
    ELBO: -9364.0:  33%|###3      | 33/100 [00:12<00:23,  2.85it/s]
    ELBO: -9364.0:  34%|###4      | 34/100 [00:12<00:19,  3.35it/s]
    ELBO: -9359.4:  34%|###4      | 34/100 [00:12<00:19,  3.35it/s]
    ELBO: -9359.4:  35%|###5      | 35/100 [00:12<00:20,  3.10it/s]
    ELBO: -9329.6:  35%|###5      | 35/100 [00:13<00:20,  3.10it/s]
    ELBO: -9329.6:  36%|###6      | 36/100 [00:13<00:25,  2.50it/s]
    ELBO: -9338.6:  36%|###6      | 36/100 [00:13<00:25,  2.50it/s]
    ELBO: -9338.6:  37%|###7      | 37/100 [00:13<00:26,  2.41it/s]
    ELBO: -9396.6:  37%|###7      | 37/100 [00:13<00:26,  2.41it/s]
    ELBO: -9396.6:  38%|###8      | 38/100 [00:13<00:22,  2.76it/s]
    ELBO: -9364.0:  38%|###8      | 38/100 [00:14<00:22,  2.76it/s]
    ELBO: -9364.0:  39%|###9      | 39/100 [00:14<00:22,  2.74it/s]
    ELBO: -9317.1:  39%|###9      | 39/100 [00:14<00:22,  2.74it/s]
    ELBO: -9317.1:  40%|####      | 40/100 [00:14<00:25,  2.34it/s]
    ELBO: -9333.3:  40%|####      | 40/100 [00:15<00:25,  2.34it/s]
    ELBO: -9333.3:  41%|####1     | 41/100 [00:15<00:21,  2.71it/s]
    ELBO: -9349.8:  41%|####1     | 41/100 [00:15<00:21,  2.71it/s]
    ELBO: -9349.8:  42%|####2     | 42/100 [00:15<00:21,  2.70it/s]
    ELBO: -9327.1:  42%|####2     | 42/100 [00:15<00:21,  2.70it/s]
    ELBO: -9327.1:  43%|####3     | 43/100 [00:15<00:22,  2.54it/s]
    ELBO: -9328.1:  43%|####3     | 43/100 [00:16<00:22,  2.54it/s]
    ELBO: -9328.1:  44%|####4     | 44/100 [00:16<00:25,  2.24it/s]
    ELBO: -9352.0:  44%|####4     | 44/100 [00:16<00:25,  2.24it/s]
    ELBO: -9352.0:  45%|####5     | 45/100 [00:16<00:19,  2.88it/s]
    ELBO: -9311.0:  45%|####5     | 45/100 [00:17<00:19,  2.88it/s]
    ELBO: -9311.0:  46%|####6     | 46/100 [00:17<00:20,  2.65it/s]
    ELBO: -9318.6:  46%|####6     | 46/100 [00:17<00:20,  2.65it/s]
    ELBO: -9318.6:  47%|####6     | 47/100 [00:17<00:23,  2.27it/s]
    ELBO: -9335.1:  47%|####6     | 47/100 [00:17<00:23,  2.27it/s]
    ELBO: -9335.1:  48%|####8     | 48/100 [00:17<00:18,  2.76it/s]
    ELBO: -9322.1:  48%|####8     | 48/100 [00:18<00:18,  2.76it/s]
    ELBO: -9322.1:  49%|####9     | 49/100 [00:18<00:18,  2.78it/s]
    ELBO: -9294.3:  49%|####9     | 49/100 [00:18<00:18,  2.78it/s]
    ELBO: -9294.3:  50%|#####     | 50/100 [00:18<00:21,  2.35it/s]
    ELBO: -9295.9:  50%|#####     | 50/100 [00:18<00:21,  2.35it/s]
    ELBO: -9295.9:  51%|#####1    | 51/100 [00:18<00:16,  2.89it/s]
    ELBO: -9277.4:  51%|#####1    | 51/100 [00:19<00:16,  2.89it/s]
    ELBO: -9277.4:  52%|#####2    | 52/100 [00:19<00:17,  2.78it/s]
    ELBO: -9301.1:  52%|#####2    | 52/100 [00:19<00:17,  2.78it/s]
    ELBO: -9301.1:  53%|#####3    | 53/100 [00:19<00:20,  2.34it/s]
    ELBO: -9352.8:  53%|#####3    | 53/100 [00:19<00:20,  2.34it/s]
    ELBO: -9352.8:  54%|#####4    | 54/100 [00:19<00:15,  3.03it/s]
    ELBO: -9302.1:  54%|#####4    | 54/100 [00:20<00:15,  3.03it/s]
    ELBO: -9302.1:  55%|#####5    | 55/100 [00:20<00:18,  2.48it/s]
    ELBO: -9308.8:  55%|#####5    | 55/100 [00:21<00:18,  2.48it/s]
    ELBO: -9308.8:  56%|#####6    | 56/100 [00:21<00:19,  2.20it/s]
    ELBO: -9343.6:  56%|#####6    | 56/100 [00:21<00:19,  2.20it/s]
    ELBO: -9343.6:  57%|#####6    | 57/100 [00:21<00:15,  2.86it/s]
    ELBO: -9280.8:  57%|#####6    | 57/100 [00:21<00:15,  2.86it/s]
    ELBO: -9280.8:  58%|#####8    | 58/100 [00:21<00:17,  2.41it/s]
    ELBO: -9247.2:  58%|#####8    | 58/100 [00:22<00:17,  2.41it/s]
    ELBO: -9247.2:  59%|#####8    | 59/100 [00:22<00:19,  2.14it/s]
    ELBO: -9312.9:  59%|#####8    | 59/100 [00:22<00:19,  2.14it/s]
    ELBO: -9312.9:  60%|######    | 60/100 [00:22<00:15,  2.62it/s]
    ELBO: -9261.4:  60%|######    | 60/100 [00:23<00:15,  2.62it/s]
    ELBO: -9261.4:  61%|######1   | 61/100 [00:23<00:16,  2.31it/s]
    ELBO: -9308.5:  61%|######1   | 61/100 [00:23<00:16,  2.31it/s]
    ELBO: -9308.5:  62%|######2   | 62/100 [00:23<00:16,  2.29it/s]
    ELBO: -9297.6:  62%|######2   | 62/100 [00:23<00:16,  2.29it/s]
    ELBO: -9297.6:  63%|######3   | 63/100 [00:23<00:15,  2.42it/s]
    ELBO: -9273.4:  63%|######3   | 63/100 [00:24<00:15,  2.42it/s]
    ELBO: -9273.4:  64%|######4   | 64/100 [00:24<00:15,  2.36it/s]
    ELBO: -9271.0:  64%|######4   | 64/100 [00:24<00:15,  2.36it/s]
    ELBO: -9271.0:  65%|######5   | 65/100 [00:24<00:14,  2.41it/s]
    ELBO: -9278.4:  65%|######5   | 65/100 [00:24<00:14,  2.41it/s]
    ELBO: -9278.4:  66%|######6   | 66/100 [00:24<00:11,  2.84it/s]
    ELBO: -9341.0:  66%|######6   | 66/100 [00:25<00:11,  2.84it/s]
    ELBO: -9341.0:  67%|######7   | 67/100 [00:25<00:13,  2.53it/s]
    ELBO: -9301.5:  67%|######7   | 67/100 [00:26<00:13,  2.53it/s]
    ELBO: -9301.5:  68%|######8   | 68/100 [00:26<00:14,  2.24it/s]
    ELBO: -9312.0:  68%|######8   | 68/100 [00:26<00:14,  2.24it/s]
    ELBO: -9312.0:  69%|######9   | 69/100 [00:26<00:11,  2.69it/s]
    ELBO: -9302.3:  69%|######9   | 69/100 [00:26<00:11,  2.69it/s]
    ELBO: -9302.3:  70%|#######   | 70/100 [00:26<00:10,  2.78it/s]
    ELBO: -9288.0:  70%|#######   | 70/100 [00:26<00:10,  2.78it/s]
    ELBO: -9288.0:  71%|#######1  | 71/100 [00:26<00:10,  2.73it/s]
    ELBO: -9276.4:  71%|#######1  | 71/100 [00:27<00:10,  2.73it/s]
    ELBO: -9276.4:  72%|#######2  | 72/100 [00:27<00:08,  3.30it/s]
    ELBO: -9300.7:  72%|#######2  | 72/100 [00:27<00:08,  3.30it/s]
    ELBO: -9300.7:  73%|#######3  | 73/100 [00:27<00:07,  3.59it/s]
    ELBO: -9264.2:  73%|#######3  | 73/100 [00:27<00:07,  3.59it/s]
    ELBO: -9264.2:  74%|#######4  | 74/100 [00:27<00:06,  3.76it/s]
    ELBO: -9358.2:  74%|#######4  | 74/100 [00:28<00:06,  3.76it/s]
    ELBO: -9358.2:  75%|#######5  | 75/100 [00:28<00:09,  2.77it/s]
    ELBO: -9321.7:  75%|#######5  | 75/100 [00:28<00:09,  2.77it/s]
    ELBO: -9321.7:  76%|#######6  | 76/100 [00:28<00:06,  3.52it/s]
    ELBO: -9231.1:  76%|#######6  | 76/100 [00:28<00:06,  3.52it/s]
    ELBO: -9231.1:  77%|#######7  | 77/100 [00:28<00:07,  3.01it/s]
    ELBO: -9215.6:  77%|#######7  | 77/100 [00:28<00:07,  3.01it/s]
    ELBO: -9215.6:  78%|#######8  | 78/100 [00:28<00:06,  3.52it/s]
    ELBO: -9332.1:  78%|#######8  | 78/100 [00:29<00:06,  3.52it/s]
    ELBO: -9332.1:  79%|#######9  | 79/100 [00:29<00:07,  2.88it/s]
    ELBO: -9314.2:  79%|#######9  | 79/100 [00:29<00:07,  2.88it/s]
    ELBO: -9314.2:  80%|########  | 80/100 [00:29<00:07,  2.64it/s]
    ELBO: -9312.4:  80%|########  | 80/100 [00:29<00:07,  2.64it/s]
    ELBO: -9312.4:  81%|########1 | 81/100 [00:29<00:05,  3.22it/s]
    ELBO: -9289.7:  81%|########1 | 81/100 [00:30<00:05,  3.22it/s]
    ELBO: -9289.7:  82%|########2 | 82/100 [00:30<00:06,  2.89it/s]
    ELBO: -9256.1:  82%|########2 | 82/100 [00:30<00:06,  2.89it/s]
    ELBO: -9256.1:  83%|########2 | 83/100 [00:30<00:04,  3.63it/s]
    ELBO: -9287.8:  83%|########2 | 83/100 [00:30<00:04,  3.63it/s]
    ELBO: -9287.8:  84%|########4 | 84/100 [00:30<00:05,  3.08it/s]
    ELBO: -9292.7:  84%|########4 | 84/100 [00:31<00:05,  3.08it/s]
    ELBO: -9292.7:  85%|########5 | 85/100 [00:31<00:05,  2.51it/s]
    ELBO: -9351.8:  85%|########5 | 85/100 [00:31<00:05,  2.51it/s]
    ELBO: -9351.8:  86%|########6 | 86/100 [00:31<00:04,  2.82it/s]
    ELBO: -9289.9:  86%|########6 | 86/100 [00:32<00:04,  2.82it/s]
    ELBO: -9289.9:  87%|########7 | 87/100 [00:32<00:04,  2.83it/s]
    ELBO: -9313.4:  87%|########7 | 87/100 [00:32<00:04,  2.83it/s]
    ELBO: -9313.4:  88%|########8 | 88/100 [00:32<00:04,  2.67it/s]
    ELBO: -9282.5:  88%|########8 | 88/100 [00:32<00:04,  2.67it/s]
    ELBO: -9282.5:  89%|########9 | 89/100 [00:32<00:03,  3.33it/s]
    ELBO: -9281.6:  89%|########9 | 89/100 [00:33<00:03,  3.33it/s]
    ELBO: -9281.6:  90%|######### | 90/100 [00:33<00:04,  2.49it/s]
    ELBO: -9307.1:  90%|######### | 90/100 [00:33<00:04,  2.49it/s]
    ELBO: -9307.1:  91%|#########1| 91/100 [00:33<00:03,  2.92it/s]
    ELBO: -9290.0:  91%|#########1| 91/100 [00:33<00:03,  2.92it/s]
    ELBO: -9290.0:  92%|#########2| 92/100 [00:33<00:02,  3.23it/s]
    ELBO: -9335.6:  92%|#########2| 92/100 [00:34<00:02,  3.23it/s]
    ELBO: -9335.6:  93%|#########3| 93/100 [00:34<00:02,  2.61it/s]
    ELBO: -9234.9:  93%|#########3| 93/100 [00:34<00:02,  2.61it/s]
    ELBO: -9234.9:  94%|#########3| 94/100 [00:34<00:01,  3.27it/s]
    ELBO: -9234.4:  94%|#########3| 94/100 [00:34<00:01,  3.27it/s]
    ELBO: -9234.4:  95%|#########5| 95/100 [00:34<00:01,  2.65it/s]
    ELBO: -9327.2:  95%|#########5| 95/100 [00:35<00:01,  2.65it/s]
    ELBO: -9327.2:  96%|#########6| 96/100 [00:35<00:01,  2.26it/s]
    ELBO: -9299.0:  96%|#########6| 96/100 [00:35<00:01,  2.26it/s]
    ELBO: -9299.0:  97%|#########7| 97/100 [00:35<00:01,  2.79it/s]
    ELBO: -9274.8:  97%|#########7| 97/100 [00:36<00:01,  2.79it/s]
    ELBO: -9274.8:  98%|#########8| 98/100 [00:36<00:00,  2.35it/s]
    ELBO: -9293.1:  98%|#########8| 98/100 [00:36<00:00,  2.35it/s]
    ELBO: -9293.1:  99%|#########9| 99/100 [00:36<00:00,  2.44it/s]
    ELBO: -9271.1:  99%|#########9| 99/100 [00:36<00:00,  2.44it/s]
    ELBO: -9271.1: 100%|##########| 100/100 [00:36<00:00,  2.84it/s]
    ELBO: -9271.1: 100%|##########| 100/100 [00:36<00:00,  2.71it/s]

    (0.0, 1000.0)





|

.. code-block:: default


    # +
    import autograd.numpy as np
    import autograd.numpy.random as npr
    npr.seed(0)

    import matplotlib.pyplot as plt
    # %matplotlib inline

    import seaborn as sns
    sns.set_style("white")
    sns.set_context("talk")

    color_names = ["windows blue",
                   "red",
                   "amber",
                   "faded green",
                   "dusty purple",
                   "orange",
                   "clay",
                   "pink",
                   "greyish",
                   "mint",
                   "light cyan",
                   "steel blue",
                   "forest green",
                   "pastel purple",
                   "salmon",
                   "dark brown"]

    colors = sns.xkcd_palette(color_names)

    import ssm
    from ssm.util import random_rotation, find_permutation
    # -

    # Set the parameters of the SLDS
    T = 1000    # number of time bins
    K = 5       # number of discrete states
    D = 2       # number of latent dimensions
    N = 10      # number of observed dimensions

    # +
    # Make an SLDS with the true parameters
    true_slds = ssm.SLDS(N, K, D, emissions="gaussian_orthog")
    for k in range(K):
        true_slds.dynamics.As[k] = .95 * random_rotation(D, theta=(k+1) * np.pi/20)
    z, x, y = true_slds.sample(T)

    # Mask off some data
    mask = npr.rand(T, N) < 0.9
    y_masked = y * mask
    # -

    # # Variational Laplace-EM
    #
    # We will fit a switching linear dynamical system (SLDS) to the observed data $y$. Our approach combines variational inference and a Laplace approximation. The objective we maximize is the evidence lower bound (ELBO)
    #
    # $$ \mathcal{L}_q(\theta) = \mathbb{E}_{q(z) q(x)}[\log p(z,x,y|\theta)] - \mathbb{E}_{q(z)}[\log q(z)] - \mathbb{E}_{q(x)}[\log q(x)] $$
    #
    # where $\theta$ are the model parameters, $z$ are the discrete latent variables, and $x$ are the continuous latent variables. We introduced an approximate posterior that factorizes over the discrete and continuous latent variables, $p(z, x \, | \, \theta, y) \approx q(z) \, q(x)$. This form of the posterior corresponds to the `variational_posterior="structured_meanfield"` argument in the `fit` method.
    #
    # The variational Laplace-EM inference method performs three updates at each iteration:
    # 1. Update $q(z)$ using the optimal coordinate ascent variational inference update
    # 2. Update $q(x)$ using a Laplace approximation at the most likely latent path (note that this step is not guaranteed to increase the ELBO)
    # 3. Update $\theta$ by optimizing the ELBO with respect to the model parameters
    #
    # You can initialize a variational posterior and fit the model by running the function
    # ```
    # # Fit the model using Laplace-EM with a structured variational posterior
    # elbos, q_lem = slds.fit(data, inputs, masks, method="laplace_em",
    #                         variational_posterior="structured_meanfield",
    #                         initialize=False, num_iters=100)
    # ```
    # The output variables are the values of the objective at each iteration `elbos` and the variational posterior object `q_lem`. If you have already initialized a variational posterior object, you can pass that object as the argument of the `variational_posterior` parameter instead. Here, the `initialize` parameter was set to `False`, which assumes we have already initialized the model. Additionally, note that in `fit` you can also pass in keyword arguments for initialization of the variational posterior. 

    # ### Hyperparameters
    # There are a number of hyperparameters that can be used when fitting with `laplace_em`. These include generic hyperparameters:
    # - `num_iters` - the number of iterations to run (default = 100)
    # - `learning` - optimize the model parameters when True (default = True)
    #     
    # Discrete state hyperparameters:
    # - `num_samples` - number of Monte Carlo samples (default = 1) used for evaluating expectations with respect to $q(x)$ in the update for $q(z)$
    #
    # Continuous state hyperparameters:
    # - `continuous_optimizer`, `continuous_tolerance`, `continuous_maxiter` specify parameters of the optimization for finding the most likely latent path in the continuous latent update. We recommend using the default optimizer Newton's method (`newton`) to compute the most likely latent path. However, Hessian-free optimization is supported with `lbfgs`. The tolerance and maxiter parameters can be adjusted for the user's requirements. 
    #
    # Model parameter update hyperparameters:
    # - `alpha` - parameter in $[0,1)$ with default $0.5$ that determines how greedy we are in updating the model parameters at each iteration. This is only used in conjunction with `parameters_update="mstep"`. 
    # - `parameters_update` - the model parameter updates are implemented via an m-step given a single sample from $q(x)$ (default, `"mstep"`) or whether using SGD with samples from $q(x)$ (`"sgd"`).
    # - `emission_optimizer` - the optimizer used to update parameters in the m-step. This defaults to the `adam` optimizer when using the `"sgd"` parameter updates. 
    # - `emission_optimizer_maxiter` - the maximum number of iterations for the inner loop of optimizing the emissions parameters. 

    # ### Exploring the effect of the `alpha` hyperparameter
    #
    # In the `"mstep"` parameters update, we optimize the joint log-likelihood conditioned on a single sample from $q(x)$ to get a point estimate of the parameters $\theta^\star$. The new parameters at iteration $t$ are then given by
    #
    # $$ \theta^{(t)} = (1 - \alpha) \, \theta^\star + \alpha \, \theta^{(t-1)}. $$
    #
    # If `alpha=0.0` we set the parameters to $\theta^\star$, whereas for nonzero `alpha` the parameters are partially updated towards $\theta^\star$. The default is `alpha=0.5`. We have found that performance varies for different values of `alpha` and that the performance can depend on the specific problem. We will demonstrate below how `alpha` can affect inference by sweeping over five different values of `alpha` in model fits below.

    alphas = [0.0, 0.25, 0.5, 0.75, 0.9]
    results = {}
    for alpha in alphas:
        print("Fitting SLDS with Laplace-EM, alpha = {}".format(alpha))

        # Create the model and initialize its parameters
        slds = ssm.SLDS(N, K, D, emissions="gaussian_orthog")
        slds.initialize(y_masked, masks=mask)

        # Fit the model using Laplace-EM with a structured variational posterior
        q_lem_elbos, q_lem = slds.fit(y_masked, masks=mask, method="laplace_em",
                                   variational_posterior="structured_meanfield",
                                   initialize=False, num_iters=100, alpha=alpha)

        # Get the posterior mean of the continuous states
        q_lem_x = q_lem.mean_continuous_states[0]

        # Find the permutation that matches the true and inferred states
        slds.permute(find_permutation(z, slds.most_likely_states(q_lem_x, y)))
        q_lem_z = slds.most_likely_states(q_lem_x, y)

        # Smooth the data under the variational posterior
        q_lem_y = slds.smooth(q_lem_x, y)

        results[(alpha)] = (slds, q_lem, q_lem_elbos, q_lem_x, q_lem_z, q_lem_y)

    # Plot the ELBOs
    q_elbos = []
    for alpha in alphas:
        _,_,q_lem_elbos,_,_,_ = results[(alpha)]
        q_elbos += [q_lem_elbos]
        plt.plot(q_lem_elbos[1:], label="alpha = {}".format(alpha), alpha=0.8)
    plt.xlabel("Iteration")
    plt.ylabel("ELBO")
    q_max = np.array(q_elbos).max()
    plt.ylim([q_max-0.1*np.abs(q_max),q_max+0.01*np.abs(q_max)])
    plt.legend()

    # +
    # Plot the true and inferred states
    xlim = (0, 1000)

    zs = []
    for alpha in alphas:
        (_, _, _, _, q_lem_z, _) = results[(alpha)]
        zs += [q_lem_z]
    
    plt.figure(figsize=(16,4))
    plt.imshow(np.row_stack((z, zs)), aspect="auto", interpolation="none")
    plt.plot(xlim, [0.5, 0.5], '-k', lw=2)
    plt.yticks([0,1,2,3,4,5],["$z_{\\mathrm{true}}$", *alphas])
    plt.ylabel("alpha")
    plt.xlim(xlim)
    # -

    plt.figure(figsize=(8,4))
    for d in range(D):
        plt.plot(x[:,d] + 4 * d, '-', color='k', label="True" if d==0 else None)
        for i, alpha in enumerate(alphas):
            _,_,_,q_lem_x,_,_ = results[(alpha)]
            plt.plot(q_lem_x[:,d] + 4 * d, '-',  color=colors[i+1], label=alpha if d == 0 else None, alpha=0.75)
    plt.ylabel("$x$")
    plt.xlim(xlim)
    plt.legend()

    # Plot the smoothed observations
    plt.figure(figsize=(12,8))
    for n in range(N):
        plt.plot(y[:, n] + 6 * n, '-', color='k', label="True" if n == 0 else None)
        for i, alpha in enumerate(alphas):
            _,_,_,_,_,q_lem_y = results[(alpha)]
            plt.plot(q_lem_y[:,n] + 6 * n, '-',  color=colors[i+1], label=alpha if n == 0 else None, alpha=0.75)
    plt.legend()
    plt.xlabel("time")
    plt.xlim(xlim)




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 3 minutes  1.824 seconds)


.. _sphx_glr_download_auto_examples_7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py <7-Variatonal-Laplace-EM-for-SLDS-Tutorial.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 7-Variatonal-Laplace-EM-for-SLDS-Tutorial.ipynb <7-Variatonal-Laplace-EM-for-SLDS-Tutorial.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_