Topic models with Gaussian likelihoods

Quick demonstration that you can easily use bnpy to perform mixed membership modeling of grouped data with any likelihood.

The basic idea is that we use the same Gaussian mixture model for each group of data, but the appearance probabilities are allowed to be learned in a customized way for each group.

Here, we’ll analyze motion capture data from 6 different sequences of an individual actor peforming different exercises.

Although this data is inherently sequential in nature and it is smart to use a model that accounts for time, we’ll ignore that for now and focus on the dataset’s grouped nature.

That is, we can compare the following two models:

  • Baseline: Gaussian mixture model that pools all observations from all sequences
  • Smarter alternative: Latent Dirichlet Allocation with a Gaussian likelihood

That is, we treat each sequence as a separate collection of data examples, modeled by group specific appearance probabilities but shared cluster means and covariances.

# sphinx_gallery_thumbnail_number = 1

import bnpy
import numpy as np
import os

from matplotlib import pylab
import seaborn as sns

FIG_SIZE = (5, 5)
LANDSCAPE_FIG_SIZE = (15, 5)
pylab.rcParams['figure.figsize'] = FIG_SIZE

np.set_printoptions(precision=3, suppress=1, linewidth=200)

Load dataset from file

dataset_path = os.path.join(bnpy.DATASET_PATH, 'mocap6')
dataset = bnpy.data.GroupXData.read_npz(
    os.path.join(dataset_path, 'dataset.npz'))

Setup: Function to make a simple plot of the raw data

def show_single_sequence(seq_id):
    start = dataset.doc_range[seq_id]
    stop = dataset.doc_range[seq_id + 1]
    pylab.figure(figsize=LANDSCAPE_FIG_SIZE)
    for dim in xrange(12):
        X_seq = dataset.X[start:stop]
        pylab.plot(X_seq[:, dim], '.-')
    pylab.xlabel('time')
    pylab.ylabel('angle')
    pylab.tight_layout()

Visualization of the first sequence

show_single_sequence(0)
../../_images/sphx_glr_plot-05-topic_model_gaussian_likelihood_001.png

Setup: hyperparameters

K = 10            # Number of clusters/states

alpha = 0.25      # group-level Dirichlet concentration parameter

gamma = 5.0       # top-level Dirichlet concentration parameter (used by HDP only)

sF = 1.0          # Set observation model prior so E[covariance] = identity
ECovMat = 'eye'

nLap = 200

Baseline: Mixture model with DiagGauss observation model

We’ll take the best of 3 independent inits (‘tasks’)

mix_model, mix_info_dict = bnpy.run(
    dataset, 'FiniteMixtureModel', 'DiagGauss', 'memoVB',
    output_path='/tmp/mocap6/test-model=FiniteMixtureModel+DiagGauss-ECovMat=1*eye/',
    nLap=nLap, nTask=3, nBatch=1, convergeThr=0.0001,
    gamma=1.0,
    sF=sF, ECovMat=ECovMat,
    K=K, initname='randexamples',
    )

Out:

Dataset Summary:
GroupXData
  total size: 6 units
  batch size: 6 units
  num. batches: 1
Allocation Model:  Finite mixture model. Dir prior param 1.00
Obs. Data  Model:  Gaussian with diagonal covariance.
Obs. Data  Prior:  independent Gauss-Wishart prior on each dimension
  Wishart params
    nu = 14  ...
  beta = [ 12  12]  ...
  Expectations
  E[  mean[k]] =
  [ 0  0] ...
  E[ covar[k]] =
  [[1. 0.]
   [0. 1.]] ...
Initialization:
  initname = randexamples
  K = 10 (number of clusters)
  seed = 1607680
  elapsed_time: 0.0 sec
Learn Alg: memoVB | task  1/3 | alg. seed: 1607680 | data order seed: 8541952
task_output_path: /tmp/mocap6/test-model=FiniteMixtureModel+DiagGauss-ECovMat=1*eye/1
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... done. converged.
Learn Alg: memoVB | task  2/3 | alg. seed: 6454144 | data order seed: 7673856
task_output_path: /tmp/mocap6/test-model=FiniteMixtureModel+DiagGauss-ECovMat=1*eye/2
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... done. converged.
Learn Alg: memoVB | task  3/3 | alg. seed: 6168832 | data order seed: 7360256
task_output_path: /tmp/mocap6/test-model=FiniteMixtureModel+DiagGauss-ECovMat=1*eye/3
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   93.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730886264e+00 | Ndiff    0.145
   94.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885689e+00 | Ndiff    0.098
   95.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885409e+00 | Ndiff    0.086
   96.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885256e+00 | Ndiff    0.074
   97.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885166e+00 | Ndiff    0.064
   98.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885111e+00 | Ndiff    0.054
   99.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885076e+00 | Ndiff    0.045
  100.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885053e+00 | Ndiff    0.038
  101.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885038e+00 | Ndiff    0.031
  102.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885028e+00 | Ndiff    0.026
  103.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885022e+00 | Ndiff    0.022
  104.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885017e+00 | Ndiff    0.018
  105.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885014e+00 | Ndiff    0.015
  106.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885012e+00 | Ndiff    0.012
  107.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885010e+00 | Ndiff    0.010
  108.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885009e+00 | Ndiff    0.008
  109.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885008e+00 | Ndiff    0.007
  110.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885007e+00 | Ndiff    0.006
  111.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885007e+00 | Ndiff    0.005
  112.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885007e+00 | Ndiff    0.004
  113.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885007e+00 | Ndiff    0.003
  114.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.003
  115.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.002
  116.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.002
  117.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.002
  118.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  119.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  120.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  121.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  122.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  123.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.001
  124.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  125.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  126.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  127.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  128.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  129.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  130.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  131.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  132.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
  133.000/200 after      1 sec. |    251.5 MiB | K   10 | loss  3.730885006e+00 | Ndiff    0.000
... done. converged.

FiniteTopicModel with DiagGauss observation model

We’ll take the best of 3 independent inits (‘tasks’)

finite_model, finite_info_dict = bnpy.run(
    dataset, 'FiniteTopicModel', 'DiagGauss', 'memoVB',
    output_path='/tmp/mocap6/test-model=FiniteTopicModel+DiagGauss-ECovMat=1*eye/',
    nLap=nLap, nTask=3, nBatch=1, convergeThr=0.0001,
    alpha=alpha,
    sF=sF, ECovMat=ECovMat,
    K=K, initname='randexamples',
    )

Out:

Dataset Summary:
GroupXData
  total size: 6 units
  batch size: 6 units
  num. batches: 1
Allocation Model:  Finite LDA model with K=0 comps. alpha=0.25
Obs. Data  Model:  Gaussian with diagonal covariance.
Obs. Data  Prior:  independent Gauss-Wishart prior on each dimension
  Wishart params
    nu = 14  ...
  beta = [ 12  12]  ...
  Expectations
  E[  mean[k]] =
  [ 0  0] ...
  E[ covar[k]] =
  [[1. 0.]
   [0. 1.]] ...
Initialization:
  initname = randexamples
  K = 10 (number of clusters)
  seed = 1607680
  elapsed_time: 0.0 sec
Learn Alg: memoVB | task  1/3 | alg. seed: 1607680 | data order seed: 8541952
task_output_path: /tmp/mocap6/test-model=FiniteTopicModel+DiagGauss-ECovMat=1*eye/1
    1.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.891536742e+00 |
    2.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.786835062e+00 | Ndiff  100.168
    3.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.737768323e+00 | Ndiff   54.412
    4.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.727530929e+00 | Ndiff   36.160
    5.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.723599603e+00 | Ndiff   26.974
    6.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.720184656e+00 | Ndiff   22.499
    7.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.716998422e+00 | Ndiff   22.206
    8.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.715387533e+00 | Ndiff   16.806
    9.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.714440630e+00 | Ndiff   10.356
   10.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.713941267e+00 | Ndiff    3.672
   11.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.713490672e+00 | Ndiff    3.962
   12.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.712721251e+00 | Ndiff    8.406
   13.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.709656117e+00 | Ndiff   18.434
   14.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.707579347e+00 | Ndiff   18.312
   15.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.705009393e+00 | Ndiff   31.500
   16.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.701748620e+00 | Ndiff   35.950
   17.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.699449456e+00 | Ndiff   27.531
   18.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.698201416e+00 | Ndiff   19.346
   19.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.697699814e+00 | Ndiff   12.325
   20.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.697477890e+00 | Ndiff    7.456
   21.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.697313612e+00 | Ndiff    5.183
   22.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.696877399e+00 | Ndiff    6.362
   23.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.696505373e+00 | Ndiff    5.676
   24.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.696307102e+00 | Ndiff    6.036
   25.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.696102448e+00 | Ndiff    6.737
   26.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.695679447e+00 | Ndiff    9.203
   27.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.694597144e+00 | Ndiff   14.376
   28.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.685041402e+00 | Ndiff   30.853
   29.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.677597746e+00 | Ndiff   12.311
   30.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.677178999e+00 | Ndiff    3.866
   31.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677035862e+00 | Ndiff    3.125
   32.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676949548e+00 | Ndiff    2.439
   33.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676894316e+00 | Ndiff    1.982
   34.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676858843e+00 | Ndiff    1.695
   35.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676835687e+00 | Ndiff    1.532
   36.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676819789e+00 | Ndiff    1.462
   37.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676806623e+00 | Ndiff    1.466
   38.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676792922e+00 | Ndiff    1.542
   39.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676775557e+00 | Ndiff    1.710
   40.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676748564e+00 | Ndiff    2.025
   41.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676693004e+00 | Ndiff    2.634
   42.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676524660e+00 | Ndiff    3.860
   43.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676128557e+00 | Ndiff    4.531
   44.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675947549e+00 | Ndiff    2.672
   45.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675701308e+00 | Ndiff    4.027
   46.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.674381849e+00 | Ndiff    9.925
   47.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.672209170e+00 | Ndiff    9.991
   48.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671381562e+00 | Ndiff    5.094
   49.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671175512e+00 | Ndiff    2.531
   50.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671118852e+00 | Ndiff    1.391
   51.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671088115e+00 | Ndiff    1.059
   52.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671063566e+00 | Ndiff    0.862
   53.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671040587e+00 | Ndiff    0.964
   54.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671015918e+00 | Ndiff    1.079
   55.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.670984376e+00 | Ndiff    1.257
   56.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.670928558e+00 | Ndiff    1.644
   57.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.670576140e+00 | Ndiff    3.828
   58.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.669803526e+00 | Ndiff    3.982
   59.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.667628451e+00 | Ndiff   10.333
   60.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.662580979e+00 | Ndiff   19.256
   61.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659597910e+00 | Ndiff   12.581
   62.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659084894e+00 | Ndiff    4.864
   63.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658994520e+00 | Ndiff    3.645
   64.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658962219e+00 | Ndiff    3.068
   65.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658943558e+00 | Ndiff    2.439
   66.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658932421e+00 | Ndiff    1.960
   67.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658926018e+00 | Ndiff    1.629
   68.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658921743e+00 | Ndiff    1.393
   69.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658918574e+00 | Ndiff    1.207
   70.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658916156e+00 | Ndiff    1.053
   71.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658914300e+00 | Ndiff    0.920
   72.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658912874e+00 | Ndiff    0.805
   73.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658911779e+00 | Ndiff    0.705
   74.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658910936e+00 | Ndiff    0.618
   75.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658910286e+00 | Ndiff    0.542
   76.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658909782e+00 | Ndiff    0.475
   77.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658909391e+00 | Ndiff    0.418
   78.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658909085e+00 | Ndiff    0.368
   79.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908845e+00 | Ndiff    0.324
   80.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908656e+00 | Ndiff    0.287
   81.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908506e+00 | Ndiff    0.254
   82.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908388e+00 | Ndiff    0.225
   83.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908293e+00 | Ndiff    0.200
   84.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908217e+00 | Ndiff    0.178
   85.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908157e+00 | Ndiff    0.158
   86.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.658908108e+00 | Ndiff    0.141
   87.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658908069e+00 | Ndiff    0.126
   88.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658908037e+00 | Ndiff    0.113
   89.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658908011e+00 | Ndiff    0.101
   90.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907990e+00 | Ndiff    0.091
   91.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907973e+00 | Ndiff    0.081
   92.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907959e+00 | Ndiff    0.073
   93.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907948e+00 | Ndiff    0.066
   94.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907939e+00 | Ndiff    0.059
   95.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907931e+00 | Ndiff    0.053
   96.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907925e+00 | Ndiff    0.048
   97.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907920e+00 | Ndiff    0.043
   98.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907916e+00 | Ndiff    0.039
   99.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907912e+00 | Ndiff    0.035
  100.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907910e+00 | Ndiff    0.032
  101.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907907e+00 | Ndiff    0.029
  102.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907905e+00 | Ndiff    0.026
  103.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907904e+00 | Ndiff    0.023
  104.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907902e+00 | Ndiff    0.021
  105.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907901e+00 | Ndiff    0.019
  106.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907900e+00 | Ndiff    0.017
  107.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907899e+00 | Ndiff    0.016
  108.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907899e+00 | Ndiff    0.014
  109.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907898e+00 | Ndiff    0.013
  110.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907898e+00 | Ndiff    0.012
  111.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907897e+00 | Ndiff    0.011
  112.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907897e+00 | Ndiff    0.010
  113.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907897e+00 | Ndiff    0.009
  114.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907897e+00 | Ndiff    0.008
  115.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.007
  116.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.006
  117.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.006
  118.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.005
  119.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.005
  120.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.004
  121.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.004
  122.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.004
  123.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907896e+00 | Ndiff    0.003
  124.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.003
  125.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.003
  126.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  127.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  128.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  129.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  130.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  131.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.002
  132.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.001
  133.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.001
  134.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.001
  135.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.001
  136.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.001
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  158.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
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  164.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  165.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  166.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  167.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  168.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  169.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  170.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  171.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  172.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
  173.000/200 after      3 sec. |    249.8 MiB | K   10 | loss  3.658907895e+00 | Ndiff    0.000
... done. converged.
Learn Alg: memoVB | task  2/3 | alg. seed: 6454144 | data order seed: 7673856
task_output_path: /tmp/mocap6/test-model=FiniteTopicModel+DiagGauss-ECovMat=1*eye/2
    1.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.880184431e+00 |
    2.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.764859066e+00 | Ndiff  112.442
    3.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.738339717e+00 | Ndiff   72.461
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   32.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.675461158e+00 | Ndiff    2.651
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   37.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675361010e+00 | Ndiff    1.156
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   46.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675319930e+00 | Ndiff    1.782
   47.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675308859e+00 | Ndiff    2.188
   48.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675291266e+00 | Ndiff    2.801
   49.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675260893e+00 | Ndiff    3.749
   50.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675204290e+00 | Ndiff    5.243
   51.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675093495e+00 | Ndiff    7.577
   52.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.674877831e+00 | Ndiff   11.020
   53.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.674494204e+00 | Ndiff   15.319
   54.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.674002187e+00 | Ndiff   18.736
   55.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.673459444e+00 | Ndiff   20.095
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   61.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.669861634e+00 | Ndiff   10.912
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  131.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095482e+00 | Ndiff    0.000
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  133.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095482e+00 | Ndiff    0.000
  134.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095483e+00 | Ndiff    0.000
  135.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095483e+00 | Ndiff    0.000
  136.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095483e+00 | Ndiff    0.000
  137.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095483e+00 | Ndiff    0.000
  138.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095483e+00 | Ndiff    0.000
  139.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095484e+00 | Ndiff    0.000
  140.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095484e+00 | Ndiff    0.000
  141.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095484e+00 | Ndiff    0.000
  142.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095484e+00 | Ndiff    0.000
  143.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.667095484e+00 | Ndiff    0.000
... done. converged.
Learn Alg: memoVB | task  3/3 | alg. seed: 6168832 | data order seed: 7360256
task_output_path: /tmp/mocap6/test-model=FiniteTopicModel+DiagGauss-ECovMat=1*eye/3
    1.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.960889382e+00 |
    2.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.812954811e+00 | Ndiff  106.901
    3.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.775678774e+00 | Ndiff   68.748
    4.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.760183281e+00 | Ndiff   29.861
    5.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.752879371e+00 | Ndiff   25.952
    6.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.749282461e+00 | Ndiff   24.923
    7.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.741353570e+00 | Ndiff   30.374
    8.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.734628562e+00 | Ndiff   12.783
    9.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.733089112e+00 | Ndiff    9.680
   10.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.729618996e+00 | Ndiff   11.796
   11.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.728491286e+00 | Ndiff    3.954
   12.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.728005826e+00 | Ndiff    4.496
   13.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.727627474e+00 | Ndiff    2.491
   14.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.727448628e+00 | Ndiff    1.857
   15.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.727142224e+00 | Ndiff    2.028
   16.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.726427129e+00 | Ndiff    5.899
   17.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.724227916e+00 | Ndiff    9.490
   18.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.723804571e+00 | Ndiff    3.002
   19.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.723565436e+00 | Ndiff    2.800
   20.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.723446675e+00 | Ndiff    2.095
   21.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.723273245e+00 | Ndiff    2.483
   22.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.722684880e+00 | Ndiff    3.864
   23.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721978561e+00 | Ndiff    2.712
   24.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721938966e+00 | Ndiff    0.670
   25.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721935848e+00 | Ndiff    0.248
   26.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721934654e+00 | Ndiff    0.148
   27.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721933859e+00 | Ndiff    0.112
   28.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721932594e+00 | Ndiff    0.086
   29.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721925386e+00 | Ndiff    0.125
   30.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721787282e+00 | Ndiff    0.511
   31.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721646191e+00 | Ndiff    0.232
   32.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721534458e+00 | Ndiff    0.503
   33.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721204789e+00 | Ndiff    0.529
   34.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721199428e+00 | Ndiff    0.232
   35.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721197505e+00 | Ndiff    0.160
   36.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721196629e+00 | Ndiff    0.113
   37.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721196193e+00 | Ndiff    0.092
   38.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195962e+00 | Ndiff    0.076
   39.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195834e+00 | Ndiff    0.064
   40.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195760e+00 | Ndiff    0.053
   41.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195715e+00 | Ndiff    0.045
   42.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195687e+00 | Ndiff    0.038
   43.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195668e+00 | Ndiff    0.032
   44.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195656e+00 | Ndiff    0.028
   45.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195648e+00 | Ndiff    0.026
   46.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195643e+00 | Ndiff    0.023
   47.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195639e+00 | Ndiff    0.020
   48.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195636e+00 | Ndiff    0.018
   49.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195634e+00 | Ndiff    0.016
   50.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195632e+00 | Ndiff    0.014
   51.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195631e+00 | Ndiff    0.012
   52.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195631e+00 | Ndiff    0.011
   53.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195630e+00 | Ndiff    0.009
   54.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195630e+00 | Ndiff    0.008
   55.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.007
   56.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.006
   57.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.005
   58.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.005
   59.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.004
   60.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.003
   61.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195629e+00 | Ndiff    0.003
   62.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.003
   63.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.002
   64.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.002
   65.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.002
   66.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   67.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   68.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   69.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   70.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   71.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   72.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   73.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.001
   74.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   75.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   76.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   77.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   78.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   79.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   80.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   81.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   82.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   83.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   84.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
   85.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.721195628e+00 | Ndiff    0.000
... done. converged.

HDP-HMM with DiagGauss observation model

We’ll take the best of 3 independent inits (‘tasks’)

hdp_topic_model, hdp_info_dict = bnpy.run(
    dataset, 'HDPTopicModel', 'DiagGauss', 'memoVB',
    output_path='/tmp/mocap6/test-model=HDPTopicModel+DiagGauss-ECovMat=1*eye/',
    nLap=nLap, nTask=3, nBatch=1, convergeThr=0.0001,
    gamma=gamma, alpha=alpha,
    sF=sF, ECovMat=ECovMat,
    K=K, initname='randexamples',
    moves='shuffle',
    )

Out:

Dataset Summary:
GroupXData
  total size: 6 units
  batch size: 6 units
  num. batches: 1
Allocation Model:  HDP model with K=0 active comps. gamma=5.00. alpha=0.25
Obs. Data  Model:  Gaussian with diagonal covariance.
Obs. Data  Prior:  independent Gauss-Wishart prior on each dimension
  Wishart params
    nu = 14  ...
  beta = [ 12  12]  ...
  Expectations
  E[  mean[k]] =
  [ 0  0] ...
  E[ covar[k]] =
  [[1. 0.]
   [0. 1.]] ...
Initialization:
  initname = randexamples
  K = 10 (number of clusters)
  seed = 1607680
  elapsed_time: 0.0 sec
Learn Alg: memoVB | task  1/3 | alg. seed: 1607680 | data order seed: 8541952
task_output_path: /tmp/mocap6/test-model=HDPTopicModel+DiagGauss-ECovMat=1*eye/1
    1.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.892295970e+00 |
    2.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.787474069e+00 | Ndiff  167.893
    3.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.738420912e+00 | Ndiff  108.155
    4.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.728232794e+00 | Ndiff   36.020
    5.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.724249654e+00 | Ndiff   78.033
    6.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.721009176e+00 | Ndiff   87.093
    7.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.717815642e+00 | Ndiff  110.105
    8.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.716133498e+00 | Ndiff   17.207
    9.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.715152039e+00 | Ndiff  108.292
   10.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.714666091e+00 | Ndiff    3.784
   11.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.714242891e+00 | Ndiff    3.528
   12.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.713537978e+00 | Ndiff    8.000
   13.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.710603627e+00 | Ndiff   35.132
   14.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.708700954e+00 | Ndiff   16.257
   15.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.706776744e+00 | Ndiff   75.015
   16.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.703666205e+00 | Ndiff   42.738
   17.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.700832620e+00 | Ndiff   27.477
   18.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.699218948e+00 | Ndiff   23.414
   19.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.698514238e+00 | Ndiff   52.198
   20.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.698213092e+00 | Ndiff    9.303
   21.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.698031745e+00 | Ndiff    6.076
   22.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.697593507e+00 | Ndiff    6.353
   23.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.697312701e+00 | Ndiff    5.777
   24.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.697000999e+00 | Ndiff    5.781
   25.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.696799733e+00 | Ndiff    6.540
   26.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.696450679e+00 | Ndiff    8.455
   27.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.695590334e+00 | Ndiff   12.813
   28.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.690354289e+00 | Ndiff   25.794
   29.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.678496849e+00 | Ndiff   20.770
   30.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677870894e+00 | Ndiff    4.266
   31.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677699846e+00 | Ndiff    3.254
   32.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677604942e+00 | Ndiff    2.568
   33.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677544330e+00 | Ndiff    2.070
   34.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677505748e+00 | Ndiff    1.750
   35.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677480640e+00 | Ndiff    1.561
   36.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677463781e+00 | Ndiff    1.472
   37.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677450456e+00 | Ndiff    1.459
   38.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677437218e+00 | Ndiff    1.516
   39.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677421149e+00 | Ndiff    1.659
   40.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677397455e+00 | Ndiff    1.929
   41.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677352400e+00 | Ndiff    2.442
   42.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.677228102e+00 | Ndiff    3.488
   43.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676860040e+00 | Ndiff   44.712
   44.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676621743e+00 | Ndiff    2.927
   45.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.676434834e+00 | Ndiff    3.269
   46.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.675565207e+00 | Ndiff    8.094
   47.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.673280429e+00 | Ndiff   11.293
   48.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.672136550e+00 | Ndiff    6.062
   49.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671844779e+00 | Ndiff    3.071
   50.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671769618e+00 | Ndiff    1.512
   51.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671735696e+00 | Ndiff    1.142
   52.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671710158e+00 | Ndiff    0.876
   53.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671687061e+00 | Ndiff    0.939
   54.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671663107e+00 | Ndiff    1.047
   55.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671633942e+00 | Ndiff    1.205
   56.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671587402e+00 | Ndiff    1.514
   57.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.671425597e+00 | Ndiff   64.143
   58.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.670559079e+00 | Ndiff    4.216
   59.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.669226819e+00 | Ndiff    8.370
   60.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.664809723e+00 | Ndiff  127.493
   61.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.660628433e+00 | Ndiff   74.491
   62.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659730940e+00 | Ndiff    5.971
   63.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659588723e+00 | Ndiff    3.721
   64.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659548008e+00 | Ndiff    3.247
   65.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659526731e+00 | Ndiff    2.593
   66.000/200 after      1 sec. |    249.8 MiB | K   10 | loss  3.659513884e+00 | Ndiff    2.070
   67.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659506608e+00 | Ndiff    1.704
   68.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659501945e+00 | Ndiff    1.447
   69.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659498546e+00 | Ndiff    1.251
   70.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659495962e+00 | Ndiff    1.089
   71.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659493979e+00 | Ndiff    0.951
   72.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659492457e+00 | Ndiff    0.832
   73.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659491287e+00 | Ndiff    0.728
   74.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659490387e+00 | Ndiff    0.638
   75.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659489693e+00 | Ndiff    0.560
   76.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659489156e+00 | Ndiff    0.491
   77.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659488739e+00 | Ndiff    0.431
   78.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659488414e+00 | Ndiff    0.380
   79.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659488159e+00 | Ndiff    0.335
   80.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487958e+00 | Ndiff    0.295
   81.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487800e+00 | Ndiff    0.261
   82.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487674e+00 | Ndiff    0.232
   83.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487574e+00 | Ndiff    0.206
   84.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487493e+00 | Ndiff    0.183
   85.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487429e+00 | Ndiff    0.163
   86.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487378e+00 | Ndiff    0.145
   87.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487336e+00 | Ndiff    0.130
   88.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487303e+00 | Ndiff    0.116
   89.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487275e+00 | Ndiff    0.104
   90.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487253e+00 | Ndiff    0.093
   91.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487235e+00 | Ndiff    0.083
   92.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487221e+00 | Ndiff    0.075
   93.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487209e+00 | Ndiff    0.067
   94.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487199e+00 | Ndiff    0.061
   95.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487191e+00 | Ndiff    0.054
   96.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.659487185e+00 | Ndiff    0.049
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... done. converged.
Learn Alg: memoVB | task  2/3 | alg. seed: 6454144 | data order seed: 7673856
task_output_path: /tmp/mocap6/test-model=HDPTopicModel+DiagGauss-ECovMat=1*eye/2
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  137.000/200 after      4 sec. |    249.8 MiB | K   10 | loss  3.667644331e+00 | Ndiff    0.000
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  140.000/200 after      4 sec. |    249.8 MiB | K   10 | loss  3.667644331e+00 | Ndiff    0.000
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  144.000/200 after      4 sec. |    249.8 MiB | K   10 | loss  3.667644331e+00 | Ndiff    0.000
... done. converged.
Learn Alg: memoVB | task  3/3 | alg. seed: 6168832 | data order seed: 7360256
task_output_path: /tmp/mocap6/test-model=HDPTopicModel+DiagGauss-ECovMat=1*eye/3
    1.000/200 after      0 sec. |    249.8 MiB | K   10 | loss  3.961512682e+00 |
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   85.000/200 after      2 sec. |    249.8 MiB | K   10 | loss  3.721733214e+00 | Ndiff    0.000
... done. converged.

Compare loss function traces for all methods

We’ll notice that the simple mixture performs noticeably worse than the more flexible models that allow group-specific cluster weights

pylab.figure()
pylab.plot(
    mix_info_dict['lap_history'],
    mix_info_dict['loss_history'], 'k--',
    label='mix + diag gauss')
pylab.plot(
    finite_info_dict['lap_history'],
    finite_info_dict['loss_history'], 'm.-',
    label='LDA + diag gauss')
pylab.plot(
    hdp_info_dict['lap_history'],
    hdp_info_dict['loss_history'], 'r.-',
    label='HDP + diag gauss')
pylab.legend(loc='upper right')
pylab.xlabel('num. laps')
pylab.ylabel('loss')
pylab.xlim([0, 200]) # avoid early iterations
pylab.ylim([3.5, 3.7]) # handpicked
pylab.draw()
pylab.tight_layout()
../../_images/sphx_glr_plot-05-topic_model_gaussian_likelihood_002.png

Show the baseline per-sequence appearances

np.set_printoptions(precision=3, suppress=1, linewidth=200)

## Compute approx. posterior parameter 'resp' for each example
# resp : 2D array, n_examples x n_clusters
# resp[n] defines Discrete probability of using clusters to explain each example
LP = mix_model.calc_local_params(dataset)
resp_NK = LP['resp']

## Compute the per-sequence average usage.
avg_resp_DK = np.zeros((dataset.nDoc, K))
for d in range(dataset.nDoc):
    start = dataset.doc_range[d]
    stop = dataset.doc_range[d+1]
    avg_resp_DK[d] = np.mean(resp_NK[start:stop], axis=0)

print("Baseline mixture model: per-sequence average cluster usage")
print(avg_resp_DK)

nnz = np.sum(avg_resp_DK < 0.001)
print("Sparsity level: %d/%d entries close-to-zero" % (
    nnz, avg_resp_DK.size))
print("")

Out:

Baseline mixture model: per-sequence average cluster usage
[[0.045 0.14  0.193 0.086 0.097 0.088 0.085 0.057 0.14  0.07 ]
 [0.014 0.245 0.081 0.114 0.098 0.169 0.    0.035 0.166 0.077]
 [0.085 0.125 0.232 0.071 0.    0.143 0.037 0.056 0.149 0.103]
 [0.065 0.053 0.045 0.085 0.051 0.102 0.123 0.109 0.316 0.052]
 [0.097 0.001 0.283 0.094 0.07  0.125 0.088 0.049 0.133 0.06 ]
 [0.211 0.004 0.216 0.069 0.    0.068 0.034 0.048 0.234 0.115]]
Sparsity level: 4/60 entries close-to-zero

Show the learned group-specific mixture weights

# Compute approx. posterior parameter 'theta' for each document
LP = finite_model.calc_local_params(dataset)
resp_NK = LP['resp']

avg_resp_DK = np.zeros((dataset.nDoc, K))
for d in range(dataset.nDoc):
    start = dataset.doc_range[d]
    stop = dataset.doc_range[d+1]
    avg_resp_DK[d] = np.mean(resp_NK[start:stop], axis=0)

print("LDA mixed membership model: per-sequence average cluster usage")
print(avg_resp_DK)
nnz = np.sum(avg_resp_DK < 0.001)
print("Sparsity level: %d/%d entries close-to-zero" % (
    nnz, avg_resp_DK.size))
print("")

# theta : 2D array, n_docs x n_clusters
# theta[d] defines Dirichlet parameters for d-th document
theta_DK = LP['theta']

# Compute expected probabilities
E_pi_DK = theta_DK / np.sum(theta_DK, axis=1)[:,np.newaxis]


print("LDA mixed membership model: per-sequence cluster probabilities")
print(E_pi_DK)

Out:

LDA mixed membership model: per-sequence average cluster usage
[[0.126 0.168 0.181 0.085 0.106 0.083 0.05  0.048 0.    0.154]
 [0.063 0.296 0.057 0.111 0.117 0.158 0.    0.024 0.    0.174]
 [0.161 0.144 0.224 0.063 0.008 0.123 0.    0.036 0.    0.241]
 [0.    0.043 0.027 0.081 0.058 0.101 0.068 0.043 0.502 0.078]
 [0.    0.    0.283 0.091 0.077 0.124 0.077 0.045 0.201 0.103]
 [0.175 0.    0.206 0.067 0.    0.067 0.    0.041 0.22  0.223]]
Sparsity level: 11/60 entries close-to-zero

LDA mixed membership model: per-sequence cluster probabilities
[[0.126 0.168 0.181 0.085 0.106 0.083 0.05  0.048 0.    0.154]
 [0.063 0.296 0.057 0.111 0.117 0.158 0.    0.024 0.    0.174]
 [0.161 0.144 0.224 0.063 0.008 0.123 0.    0.036 0.    0.241]
 [0.    0.043 0.027 0.081 0.058 0.101 0.068 0.043 0.502 0.078]
 [0.    0.    0.282 0.091 0.077 0.124 0.077 0.045 0.201 0.103]
 [0.175 0.    0.206 0.067 0.    0.067 0.    0.041 0.22  0.223]]

Total running time of the script: ( 0 minutes 21.194 seconds)

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