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Last active April 4, 2017 13:58
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Inference of Gaussian mixture model with ADVI"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we describe how to use ADVI for inference of Gaussian mixture model. First, we will show that inference with ADVI does not need to modify the stochastic model, just call a function. Then, we will show how to use mini-batch, which is useful for large dataset. In this case, where the model should be slightly changed. \n",
"\n",
"First, create artificial data from a mixuture of two Gaussian components. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x12553ea50>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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cxfA2nU47E19R+ffr4vYlk7Zpuca1169cf/9ct/a6SvSyuSw/fWY3x7uOkU6lMRdcGMkc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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116abc6d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import pymc3 as pm\n",
"from pymc3 import Normal, Metropolis, sample, MvNormal, Dirichlet, \\\n",
" DensityDist, find_MAP, NUTS, Slice\n",
"import theano.tensor as tt\n",
"from theano.tensor.nlinalg import det\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"n_samples = 100\n",
"rng = np.random.RandomState(123)\n",
"ms = np.array([[-1, -1.5], [1, 1]])\n",
"ps = np.array([0.2, 0.8])\n",
"\n",
"zs = np.array([rng.multinomial(1, ps) for _ in range(n_samples)]).T\n",
"xs = [z[:, np.newaxis] * rng.multivariate_normal(m, np.eye(2), size=n_samples)\n",
" for z, m in zip(zs, ms)]\n",
"data = np.sum(np.dstack(xs), axis=2)\n",
"\n",
"plt.figure(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], c='g', alpha=0.5)\n",
"plt.scatter(ms[0, 0], ms[0, 1], c='r', s=100)\n",
"plt.scatter(ms[1, 0], ms[1, 1], c='b', s=100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gaussian mixture models are usually constructed with categorical random variables. However, any discrete rvs does not fit ADVI. Here, class assignment variables are marginalized out, giving weighted sum of the probability for the gaussian components. The log likelihood of the total probability is calculated using logsumexp, which is a standard technique for making this kind of calculation stable. \n",
"\n",
"In the below code, DensityDist class is used as the likelihood term. The second argument, logp_gmix(mus, pi, np.eye(2)), is a python function which recieves observations (denoted by 'value') and returns the tensor representation of the log-likelihood. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to pi and added transformed pi_stickbreaking to model.\n"
]
}
],
"source": [
"from pymc3.math import LogSumExp\n",
"\n",
"# Log likelihood of normal distribution\n",
"def logp_normal(mu, tau, value):\n",
" # log probability of individual samples\n",
" k = tau.shape[0]\n",
" delta = lambda mu: value - mu\n",
" return (-1 / 2.) * (k * tt.log(2 * np.pi) + tt.log(1./det(tau)) +\n",
" (delta(mu).dot(tau) * delta(mu)).sum(axis=1))\n",
"\n",
"# Log likelihood of Gaussian mixture distribution\n",
"def logp_gmix(mus, pi, tau):\n",
" def logp_(value): \n",
" logps = [tt.log(pi[i]) + logp_normal(mu, tau, value)\n",
" for i, mu in enumerate(mus)]\n",
" \n",
" return tt.sum(LogSumExp(tt.stacklists(logps)[:, :n_samples], axis=0))\n",
"\n",
" return logp_\n",
"\n",
"with pm.Model() as model:\n",
" mus = [MvNormal('mu_%d' % i, mu=np.zeros(2), tau=0.1 * np.eye(2), shape=(2,))\n",
" for i in range(2)]\n",
" pi = Dirichlet('pi', a=0.1 * np.ones(2), shape=(2,))\n",
" xs = DensityDist('x', logp_gmix(mus, pi, np.eye(2)), observed=data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparison with ADVI, run MCMC. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 1000 of 1000 complete in 0.5 sec"
]
}
],
"source": [
"with model:\n",
" start = find_MAP()\n",
" step = Metropolis()\n",
" trace = sample(1000, step, start=start)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Check posterior of component means and weights. We can see that the MCMC samples of the component mean for the lower-left component varied more than the upper-right due to the difference of the sample size of these clusters. "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-6, 6)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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DnNSxI8v6nUlvnP/pvr2tI3BafT/HGZfrBtyFE2odgK+B3cB0wAPc8MjjUam7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\nRFxPQScirqegExHXU9CJiOv9PxWtkpIR0WRmAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x127735250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], alpha=0.5, c='g')\n",
"mu_0, mu_1 = trace['mu_0'], trace['mu_1']\n",
"plt.scatter(mu_0[-500:, 0], mu_0[-500:, 1], c=\"r\", s=10)\n",
"plt.scatter(mu_1[-500:, 0], mu_1[-500:, 1], c=\"b\", s=10)\n",
"plt.xlim(-6, 6)\n",
"plt.ylim(-6, 6)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x127754f50>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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EOLq8EBG15va9wF3AL0XEeBfmlCStoUrI9wKnADLzNLCrZe21wOOZOZeZLwJfA+7s+JSS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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1277651d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.barplot([1, 2], np.mean(trace['pi'][-5000:], axis=0), \n",
" palette=['red', 'blue'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use the same model with ADVI as follows. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to pi and added transformed pi_stickbreaking to model.\n",
"Iteration 0 [0%]: ELBO = -412.12\n",
"Iteration 100 [10%]: ELBO = -357.93\n",
"Iteration 200 [20%]: ELBO = -328.79\n",
"Iteration 300 [30%]: ELBO = -324.32\n",
"Iteration 400 [40%]: ELBO = -321.59\n",
"Iteration 500 [50%]: ELBO = -322.9\n",
"Iteration 600 [60%]: ELBO = -324.97\n",
"Iteration 700 [70%]: ELBO = -323.26\n",
"Iteration 800 [80%]: ELBO = -322.76\n",
"Iteration 900 [90%]: ELBO = -322.89\n",
"Finished [100%]: ELBO = -324.32\n",
"CPU times: user 3.02 s, sys: 20.7 ms, total: 3.05 s\n",
"Wall time: 3.05 s\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" mus = [MvNormal('mu_%d' % i, mu=np.zeros(2), tau=0.1 * np.eye(2), shape=(2,))\n",
" for i in range(2)]\n",
" pi = Dirichlet('pi', a=0.1 * np.ones(2), shape=(2,))\n",
" xs = DensityDist('x', logp_gmix(mus, pi, np.eye(2)), observed=data)\n",
" \n",
"%time means, sds, elbos = pm.variational.advi( \\\n",
" model=model, n=1000, learning_rate=1e-1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function returns three variables. 'means' and 'sds' are the mean and standart deviations of the variational posterior. Note that these values are in the transformed space, not in the original space. For random variables in the real line, e.g., means of the Gaussian components, no transformation is applied. Then we can see the variational posterior in the original space. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-6, 6)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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iEnoKOhEJPQWdiISegk5EQk9BJyKhp6ATkdBT0IlI6CnoRCT0FHQiEnoKOhEJ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\nJPT+P2SqCmIrAAAAA0lEQVQEO2sYEbGWAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12458a090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from copy import deepcopy\n",
"\n",
"mu_0, sd_0 = means['mu_0'], sds['mu_0']\n",
"mu_1, sd_1 = means['mu_1'], sds['mu_1']\n",
"\n",
"def logp_normal_np(mu, tau, value):\n",
" # log probability of individual samples\n",
" k = tau.shape[0]\n",
" delta = lambda mu: value - mu\n",
" return (-1 / 2.) * (k * np.log(2 * np.pi) + np.log(1./np.linalg.det(tau)) +\n",
" (delta(mu).dot(tau) * delta(mu)).sum(axis=1))\n",
"\n",
"def threshold(zz): \n",
" zz_ = deepcopy(zz)\n",
" zz_[zz < np.max(zz) * 1e-2] = None\n",
" return zz_\n",
"\n",
"def plot_logp_normal(ax, mu, sd, cmap):\n",
" f = lambda value: np.exp(logp_normal_np(mu, np.diag(1 / sd**2), value))\n",
" g = lambda mu, sd: np.arange(mu - 3, mu + 3, .1)\n",
" xx, yy = np.meshgrid(g(mu[0], sd[0]), g(mu[1], sd[1]))\n",
" zz = f(np.vstack((xx.reshape(-1), yy.reshape(-1))).T).reshape(xx.shape)\n",
" ax.contourf(xx, yy, threshold(zz), cmap=cmap, alpha=0.9)\n",
" \n",
"fig, ax = plt.subplots(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], alpha=0.5, c='g')\n",
"plot_logp_normal(ax, mu_0, sd_0, cmap='Reds')\n",
"plot_logp_normal(ax, mu_1, sd_1, cmap='Blues')\n",
"plt.xlim(-6, 6)\n",
"plt.ylim(-6, 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"TODO: We need to backward-transform 'pi', which is transformed by 'stick_breaking'. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"'elbos' contains the trace of ELBO, showing stochastic convergence of the algorithm. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x124fff050>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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LPVMjsfsn78bFNCXHE0S542tDqFRAfekq13ry8ct3ev1aUhwo50dWvrML//72NL7aU4ya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\nPYMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x124e94250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(elbos)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To demonstrate that ADVI works for large dataset with mini-batch, let's create 100,000 samples from the same mixture distribution. "
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-6, 6)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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BXq3MiTvuZHVzmcHxYYCdJOBKdZvTy6dZnV/BMAyOT53gXe9491VR2bxZoIHc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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x128a18ed0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_samples = 100000\n",
"\n",
"zs = np.array([rng.multinomial(1, ps) for _ in range(n_samples)]).T\n",
"xs = [z[:, np.newaxis] * rng.multivariate_normal(m, np.eye(2), size=n_samples)\n",
" for z, m in zip(zs, ms)]\n",
"data = np.sum(np.dstack(xs), axis=2)\n",
"\n",
"plt.figure(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], c='g', alpha=0.5)\n",
"plt.scatter(ms[0, 0], ms[0, 1], c='r', s=100)\n",
"plt.scatter(ms[1, 0], ms[1, 1], c='b', s=100)\n",
"plt.xlim(-6, 6)\n",
"plt.ylim(-6, 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MCMC took 55 seconds, 20 times longer than the small dataset. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to pi and added transformed pi_stickbreaking to model.\n",
" [-----------------100%-----------------] 1000 of 1000 complete in 55.4 sec"
]
}
],
"source": [
"with pm.Model() as model:\n",
" mus = [MvNormal('mu_%d' % i, mu=np.zeros(2), tau=0.1 * np.eye(2), shape=(2,))\n",
" for i in range(2)]\n",
" pi = Dirichlet('pi', a=0.1 * np.ones(2), shape=(2,))\n",
" xs = DensityDist('x', logp_gmix(mus, pi, np.eye(2)), observed=data)\n",
" \n",
" start = find_MAP()\n",
" step = Metropolis()\n",
" trace = sample(1000, step, start=start)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Posterior samples are concentrated on the true means, so looks like single point for each component. "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-6, 6)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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III0VhD1OST3KBldH/Fp9hKo5Ksc7iCASH5hBqIjqVUSMrSFI0EcQoifn4yFI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HkRUS773+Uorz5Xs+c5ZQy3N4ULBGv+ouu50lpTRrmDC1wqYXW/ymJDFAGphc+LYwwGBQphDkNc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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13d859f10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], alpha=0.5, c='g')\n",
"mu_0, mu_1 = trace['mu_0'], trace['mu_1']\n",
"plt.scatter(mu_0[-500:, 0], mu_0[-500:, 1], c=\"r\", s=50)\n",
"plt.scatter(mu_1[-500:, 0], mu_1[-500:, 1], c=\"b\", s=50)\n",
"plt.xlim(-6, 6)\n",
"plt.ylim(-6, 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For ADVI with mini-batch, put theano tensor on the observed variable of the ObservedRV. The tensor will be replaced with mini-batches. Because of the difference of the size of mini-batch and whole samples, the log-likelihood term should be appropriately scaled. To tell the log-likelihood term, we need to give ObservedRV objects ('minibatch_RVs' below) where mini-batch is put. Also we should keep the tensor ('minibatch_tensors'). "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied stickbreaking-transform to pi and added transformed pi_stickbreaking to model.\n"
]
}
],
"source": [
"data_t = tt.matrix()\n",
"data_t.tag.test_value = np.zeros((1, 2)).astype(float)\n",
"\n",
"with pm.Model() as model:\n",
" mus = [MvNormal('mu_%d' % i, mu=np.zeros(2), tau=0.1 * np.eye(2), shape=(2,))\n",
" for i in range(2)]\n",
" pi = Dirichlet('pi', a=0.1 * np.ones(2), shape=(2,))\n",
" xs = DensityDist('x', logp_gmix(mus, pi, np.eye(2)), observed=data_t)\n",
" \n",
"minibatch_tensors = [data_t]\n",
"minibatch_RVs = [xs]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make a generator for mini-batches of size 200. Here, we take random sampling strategy to make mini-batches. "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def create_minibatch(data):\n",
" rng = np.random.RandomState(0)\n",
" \n",
" while True:\n",
" ixs = rng.randint(len(data), size=200)\n",
" yield data[ixs]\n",
"\n",
"minibatches = [create_minibatch(data)]\n",
"total_size = len(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Run ADVI. It's much faster than MCMC, though the problem here is simple and it's not a fair comparison. "
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration 0 [0%]: ELBO = -424201.48\n",
"Iteration 100 [10%]: ELBO = -350008.63\n",
"Iteration 200 [20%]: ELBO = -317598.75\n",
"Iteration 300 [30%]: ELBO = -314518.88\n",
"Iteration 400 [40%]: ELBO = -328082.93\n",
"Iteration 500 [50%]: ELBO = -320686.56\n",
"Iteration 600 [60%]: ELBO = -314541.02\n",
"Iteration 700 [70%]: ELBO = -341864.92\n",
"Iteration 800 [80%]: ELBO = -320904.08\n",
"Iteration 900 [90%]: ELBO = -322863.3\n",
"Finished [100%]: ELBO = -313688.76\n",
"CPU times: user 2.7 s, sys: 34.4 ms, total: 2.74 s\n",
"Wall time: 2.72 s\n"
]
}
],
"source": [
"# Used only to write the function call in single line for using %time\n",
"# is there more smart way?\n",
"def f():\n",
" return pm.variational.advi_minibatch(\n",
" model=model, n=1000, minibatch_tensors=minibatch_tensors, \n",
" minibatch_RVs=minibatch_RVs, minibatches=minibatches,\n",
" total_size=total_size, learning_rate=1e-1)\n",
"\n",
"%time means, sds, elbos = f()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The result is almost the same. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(-6, 6)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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III0VhD1OST3KBldH/Fp9hKo5Ksc7iCASH5hBqIjqVUSMrSFI0EcQoifn4yFI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\noXSIS5XIDQmYWJgGeyEfSzQq8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Rz6nKQAMYJZvq9gOipEN08quR2w6zZ21sazPSzfJhfl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\neITQCQSCDc//B0TldTDepYghAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x128560890>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from copy import deepcopy\n",
"\n",
"mu_0, sd_0 = means['mu_0'], sds['mu_0']\n",
"mu_1, sd_1 = means['mu_1'], sds['mu_1']\n",
"\n",
"fig, ax = plt.subplots(figsize=(5, 5))\n",
"plt.scatter(data[:, 0], data[:, 1], alpha=0.5, c='g')\n",
"plt.scatter(mu_0[0], mu_0[1], c=\"r\", s=50)\n",
"plt.scatter(mu_1[0], mu_1[1], c=\"b\", s=50)\n",
"plt.xlim(-6, 6)\n",
"plt.ylim(-6, 6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The variance of the trace of ELBO is larger than without mini-batch because of the subsampling from the whole samples. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x125263210>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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LPVMjsfsn78bFNCXHE0S542tDqFRAfekq13ry8ct3ev1aUhwo50dWvrML//72NL7aU4ya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\nPYMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x124e951d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(elbos)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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