Bayesian Neural Network (VI) for classification (under Development)

import mxfusion as mf
import mxnet as mx
import numpy as np
import mxnet.gluon.nn as nn
import mxfusion.components
import mxfusion.inference

/Users/zhenwend/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters

Generate Synthetic Data

import GPy
%matplotlib inline
from pylab import *

np.random.seed(4)
k = GPy.kern.RBF(1, lengthscale=0.1)
x = np.random.rand(200,1)
y = np.random.multivariate_normal(mean=np.zeros((200,)), cov=k.K(x), size=(1,)).T>0.
plot(x[:,0], y[:,0], '.')

[<matplotlib.lines.Line2D at 0x1a22348898>]

D = 10
net = nn.HybridSequential(prefix='nn_')
with net.name_scope():
    net.add(nn.Dense(D, activation="tanh", flatten=False, in_units=1))
    net.add(nn.Dense(D, activation="tanh", flatten=False, in_units=D))
    net.add(nn.Dense(2, flatten=False, in_units=D))
net.initialize(mx.init.Xavier(magnitude=1))

from mxfusion.components.variables.var_trans import PositiveTransformation
from mxfusion.inference import VariationalPosteriorForwardSampling

m = mf.components.Model()
m.N = mf.components.Variable()
m.f = mf.components.functions.MXFusionGluonFunction(net, nOutputs=1, broadcastable=False)
m.x = mf.components.Variable(shape=(m.N,1))
m.r = m.f(m.x)
for _,v in m.r.factor.block_variables:
    v.set_prior(mf.components.distributions.Normal(mean=mx.nd.array([0]),variance=mx.nd.array([3.])))
m.y = mf.components.distributions.Categorical.define_variable(log_prob=m.r,  shape=(m.N,1))
m.show()

Variable(45b58) ~ Normal(mean=Variable(738a7), variance=Variable(9ef9b))
Variable(d7aa2) ~ Normal(mean=Variable(b4564), variance=Variable(02ad0))
Variable(ace48) ~ Normal(mean=Variable(3989f), variance=Variable(49e6a))
Variable(35ae3) ~ Normal(mean=Variable(666b4), variance=Variable(5c0d8))
Variable(7a303) ~ Normal(mean=Variable(9d461), variance=Variable(dd20b))
Variable(28ccc) ~ Normal(mean=Variable(37c47), variance=Variable(a7de6))
r = GluonFunctionEvaluation(nn_dense0_weight=Variable(28ccc), nn_dense0_bias=Variable(7a303), nn_dense1_weight=Variable(35ae3), nn_dense1_bias=Variable(ace48), nn_dense2_weight=Variable(d7aa2), nn_dense2_bias=Variable(45b58), nn_input_0=x)
y ~ Categorical(log_prob=r)

from mxfusion.inference import BatchInferenceLoop, create_Gaussian_meanfield, GradBasedInference, StochasticVariationalInference, MAP

observed = [m.y, m.x]
q = create_Gaussian_meanfield(model=m, observed=observed)
alg = StochasticVariationalInference(num_samples=5, model=m, posterior=q, observed=observed)
# alg = MAP(model=m, observed=observed)
infr = GradBasedInference(inference_algorithm=alg, grad_loop=BatchInferenceLoop())

infr.initialize(y=mx.nd.array(y), x=mx.nd.array(x))

 /Users/zhenwend/mxfusion/src/MXFusion/mxfusion/inference/inference_parameters.py:52: UserWarning:InferenceParameters has already been initialized.  The existing one will be overwritten.

for v_name, v in m.r.factor.block_variables:
    uuid = v.uuid
    loc_uuid = infr.inference_algorithm.posterior[uuid].factor.variance.uuid
    a = infr.params.param_dict[loc_uuid].data().asnumpy()
    a[:] = 1e-8
    infr.params[infr.inference_algorithm.posterior[uuid].factor.mean] = net.collect_params()[v_name].data()
    infr.params[infr.inference_algorithm.posterior[uuid].factor.variance] = mx.nd.array(a)

infr.run(max_iter=500, learning_rate=1e-1, y=mx.nd.array(y), x=mx.nd.array(x), verbose=True)

 /Users/zhenwend/mxfusion/src/MXFusion/mxfusion/inference/inference.py:111: UserWarning:Trying to initialize the inference twice, skipping.

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Iteration 404 logL: -145.6951446533203
Iteration 405 logL: -154.26612854003906
Iteration 406 logL: -168.78125
Iteration 407 logL: -151.6161346435547
Iteration 408 logL: -137.94374084472656
Iteration 409 logL: -162.55181884765625
Iteration 410 logL: -195.5110626220703
Iteration 411 logL: -181.4525146484375
Iteration 412 logL: -176.29464721679688
Iteration 413 logL: -161.6767578125
Iteration 414 logL: -147.3198699951172
Iteration 415 logL: -174.78868103027344
Iteration 416 logL: -241.66427612304688
Iteration 417 logL: -194.82431030273438
Iteration 418 logL: -163.0545196533203
Iteration 419 logL: -142.1942138671875
Iteration 420 logL: -161.17933654785156
Iteration 421 logL: -151.19564819335938
Iteration 422 logL: -270.526123046875
Iteration 423 logL: -174.3603973388672
Iteration 424 logL: -145.0341339111328
Iteration 425 logL: -174.63157653808594
Iteration 426 logL: -134.2644805908203
Iteration 427 logL: -198.86883544921875
Iteration 428 logL: -149.4174346923828
Iteration 429 logL: -144.0459442138672
Iteration 430 logL: -161.4966583251953
Iteration 431 logL: -134.34768676757812
Iteration 432 logL: -134.56263732910156
Iteration 433 logL: -180.6781463623047
Iteration 434 logL: -158.80487060546875
Iteration 435 logL: -159.59298706054688
Iteration 436 logL: -139.64794921875
Iteration 437 logL: -133.45777893066406
Iteration 438 logL: -152.6923370361328
Iteration 439 logL: -156.44227600097656
Iteration 440 logL: -157.8925018310547
Iteration 441 logL: -167.68077087402344
Iteration 442 logL: -161.24176025390625
Iteration 443 logL: -159.16549682617188
Iteration 444 logL: -172.21835327148438
Iteration 445 logL: -156.8822479248047
Iteration 446 logL: -133.2530975341797
Iteration 447 logL: -153.4013214111328
Iteration 448 logL: -133.96762084960938
Iteration 449 logL: -138.84234619140625
Iteration 450 logL: -183.0357666015625
Iteration 451 logL: -170.00534057617188
Iteration 452 logL: -157.46279907226562
Iteration 453 logL: -155.4312286376953
Iteration 454 logL: -178.26963806152344
Iteration 455 logL: -136.466552734375
Iteration 456 logL: -142.8925018310547
Iteration 457 logL: -159.1484832763672
Iteration 458 logL: -173.41558837890625
Iteration 459 logL: -161.4503936767578
Iteration 460 logL: -165.84906005859375
Iteration 461 logL: -173.14651489257812
Iteration 462 logL: -155.19857788085938
Iteration 463 logL: -174.43728637695312
Iteration 464 logL: -161.63243103027344
Iteration 465 logL: -140.7918701171875
Iteration 466 logL: -161.52334594726562
Iteration 467 logL: -162.0040283203125
Iteration 468 logL: -146.77978515625
Iteration 469 logL: -145.1008758544922
Iteration 470 logL: -145.02806091308594
Iteration 471 logL: -126.25932312011719
Iteration 472 logL: -134.5507049560547
Iteration 473 logL: -172.2655487060547
Iteration 474 logL: -178.7369384765625
Iteration 475 logL: -175.0013885498047
Iteration 476 logL: -155.21022033691406
Iteration 477 logL: -140.81431579589844
Iteration 478 logL: -186.590087890625
Iteration 479 logL: -147.77403259277344
Iteration 480 logL: -167.0510711669922
Iteration 481 logL: -152.2871856689453
Iteration 482 logL: -151.39828491210938
Iteration 483 logL: -129.93521118164062
Iteration 484 logL: -143.72450256347656
Iteration 485 logL: -146.91224670410156
Iteration 486 logL: -127.20298767089844
Iteration 487 logL: -144.4951934814453
Iteration 488 logL: -145.83363342285156
Iteration 489 logL: -132.7200164794922
Iteration 490 logL: -143.2606658935547
Iteration 491 logL: -144.3072509765625
Iteration 492 logL: -148.9021759033203
Iteration 493 logL: -143.65380859375
Iteration 494 logL: -141.4383544921875
Iteration 495 logL: -165.1541290283203
Iteration 496 logL: -136.8163604736328
Iteration 497 logL: -158.55410766601562
Iteration 498 logL: -138.8023681640625
Iteration 499 logL: -158.96397399902344
Iteration 500 logL: -138.33013916015625

for uuid, v in infr.inference_algorithm.posterior.variables.items():
    if uuid in infr.params.param_dict:
        print(v.name, infr.params[v])

xt = np.linspace(0,1,100)[:,None]

infr2 = VariationalPosteriorForwardSampling(10, [m.x], infr, [m.r])
res = infr2.run(x=mx.nd.array(xt))

 /Users/zhenwend/mxfusion/src/MXFusion/mxfusion/core/factor_graph.py:65: UserWarning:The value N has already been assigned in the model.
 /Users/zhenwend/mxfusion/src/MXFusion/mxfusion/core/factor_graph.py:65: UserWarning:The value y has already been assigned in the model.
 /Users/zhenwend/mxfusion/src/MXFusion/mxfusion/inference/inference_parameters.py:52: UserWarning:InferenceParameters has already been initialized.  The existing one will be overwritten.

yt = res[m.r].asnumpy()

# plot(xt[:,0],yt[:,0])
yt_mean = yt.mean(0)
yt_std = yt.std(0)
#plot(xt[:,0], yt.mean(0)[:,0])
#errorbar(xt[:,0],y=yt_mean[:,0],yerr=yt_std[:,0]*2)
for i in range(yt.shape[0]):
    plot(xt[:,0],1./(1+np.exp(-yt[i,:,0])),'k',alpha=0.2)
plot(x[:,0],y[:,0],'.')

[<matplotlib.lines.Line2D at 0x1a222e37f0>]