{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "ADKY4re5Kx-5" }, "source": [ "##### Copyright 2018 The TensorFlow Probability Authors.\n", "\n", "Licensed under the Apache License, Version 2.0 (the \"License\");" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "cellView": "form", "id": "S2AOrHzjK0_L" }, "outputs": [], "source": [ "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "id": "56dF5DnkKx0a" }, "source": [ "# TensorFlow Probability 中的高斯过程回归\n", "\n", "\n", " \n", " \n", " \n", " \n", "
在 TensorFlow.org 上查看 在 Google Colab 中运行 在 Github 上查看源代码 下载笔记本
" ] }, { "cell_type": "markdown", "metadata": { "id": "rTFa-AE9KxFC" }, "source": [ "在此 Colab 中,我们将使用 TensorFlow 和 TensorFlow Probability 探索高斯过程回归。我们从一些已知函数中生成一些噪声观测值,并将 GP 模型拟合到这些数据。然后,我们从 GP 后验中采样,并将采样函数值绘制在其域中的网格上。\n" ] }, { "cell_type": "markdown", "metadata": { "id": "n4-qQf7qZLVI" }, "source": [ "## 背景\n", "\n", "假设 $\\mathcal{X}$ 为任意集合。*高斯过程* (GP) 是由 $\\mathcal{X}$ 索引的随机变量的集合,因此,如果 ${X_1, \\ldots, X_n} \\subset \\mathcal{X}$ 是任意有限子集,边缘密度 $p(X_1 = x_1, \\ldots, X_n = x_n)$ 为多元高斯。任何高斯分布均由其第一和第二中心矩(均值和协方差)完全指定,GP 也不例外。我们可以用它的均值函数 $\\mu : \\mathcal{X} \\to \\mathbb{R}$ 和协方差函数 $k : \\mathcal{X} \\times \\mathcal{X} \\to \\mathbb{R}$ 来完全指定 GP。GP 的大部分表达能力都体现在协方差函数的选择中。由于各种原因,协方差函数也被称为*内核函数*。仅要求其对称和正定(请参阅 [Rasmussen & Williams 所著图书的第 4 章](http://www.gaussianprocess.org/gpml/chapters/RW4.pdf))。下面我们使用 ExponentiatedQuadratic 协方差内核。它的形式为:\n", "\n", "$$ k(x, x') := \\sigma^2 \\exp \\left( \\frac{|x - x'|^2}{\\lambda^2} \\right) $$\n", "\n", "其中,$\\sigma^2$ 称为“幅值”,$\\lambda$ 称为*长度尺度*。可以通过最大似然优化程序来选择内核参数。\n", "\n", "来自 GP 的完整样本由整个空间 $\\mathcal{X}$ 上的实值函数组成,这在实践中不切实际;通常,我们会选择一组点来观察样本,并在这些点上对函数值进行抽样。这是通过从适当的(有限维)多元高斯中进行采样来实现的。\n", "\n", "请注意,根据上文的定义,任何有限维的多元高斯分布也是高斯过程。通常,当我们提到 GP 时,都隐含索引集为某个 $\\mathbb{R}^n$,我们在这里确实会做这样的假设。\n", "\n", "高斯过程在机器学习中的一个常见应用是高斯过程回归。其思想是,我们希望在给定有限数量的点 ${x_1, \\ldots x_N}$ 处函数的噪声观测值 ${y_1, \\ldots, y_N}$ 的情况下,估算出未知函数。我们想象一个生成式过程:\n", "\n", "$$ \\begin{align} f \\sim : & \\textsf{GaussianProcess}\\left( \\text{mean_fn}=\\mu(x), \\text{covariance_fn}=k(x, x')\\right) \\ y_i \\sim : & \\textsf{Normal}\\left( \\text{loc}=f(x_i), \\text{scale}=\\sigma\\right), i = 1, \\ldots, N \\end{align} $$\n", "\n", "如上所述,采样函数无法计算,因为我们需要它在无穷多个点处的值。因此,我们可以考虑从多元高斯中抽取有限样本。\n", "\n", "$$ \\begin{gather} \\begin{bmatrix} f(x_1) \\ \\vdots \\ f(x_N) \\end{bmatrix} \\sim \\textsf{MultivariateNormal} \\left( : \\text{loc}= \\begin{bmatrix} \\mu(x_1) \\ \\vdots \\ \\mu(x_N) \\end{bmatrix} :,: \\text{scale}= \\begin{bmatrix} k(x_1, x_1) & \\cdots & k(x_1, x_N) \\ \\vdots & \\ddots & \\vdots \\ k(x_N, x_1) & \\cdots & k(x_N, x_N) \\ \\end{bmatrix}^{1/2} : \\right) \\end{gather} \\ y_i \\sim \\textsf{Normal} \\left( \\text{loc}=f(x_i), \\text{scale}=\\sigma \\right) $$\n", "\n", "请注意协方差矩阵上的指数 $\\frac{1}{2}$:这表示 Cholesky 分解。必须计算 Cholesky,因为 MVN 是一个位置尺度系列分布。不幸的是,Cholesky 分解的计算开销巨大,需要花费 $O(N^3)$ 的时间和 $O(N^2)$ 的空间。许多 GP 文献都集中在处理这个看似无害的小指数上。\n", "\n", "常见的做法是将先验均值函数设为常量,通常为零。此外,某些记法约定也很方便。我们通常用 $\\mathbf{f}$ 表示采样函数值的有限向量。将 $k$ 应用于输入对时,生成的协方差矩阵使用了许多有趣的表示法。根据 [(Quiñonero-Candela, 2005)](http://www.jmlr.org/papers/volume6/quinonero-candela05a/quinonero-candela05a.pdf),我们注意到矩阵的分量是特定输入点上函数值的协方差。因此,我们可以将协方差矩阵表示为 $K_{AB}$,其中 $A$ 和 $B$ 是沿给定矩阵维度的函数值集合的一些指标。\n", "\n", "例如,在给定观测数据 $(\\mathbf{x}, \\mathbf{y})$ 和隐函数值 $\\mathbf{f}$ 的情况下,我们可以编写为:\n", "\n", "$$ K_{\\mathbf{f},\\mathbf{f}} = \\begin{bmatrix} k(x_1, x_1) & \\cdots & k(x_1, x_N) \\ \\vdots & \\ddots & \\vdots \\ k(x_N, x_1) & \\cdots & k(x_N, x_N) \\ \\end{bmatrix} $$\n", "\n", "同样,我们可以混合多组输入,例如:\n", "\n", "$$ K_{\\mathbf{f},} = \\begin{bmatrix} k(x_1, x^_1) & \\cdots & k(x_1, x^_T) \\ \\vdots & \\ddots & \\vdots \\ k(x_N, x^_1) & \\cdots & k(x_N, x^*_T) \\ \\end{bmatrix} $$\n", "\n", "其中,我们假设有 $N$ 个训练输入和 $T$ 个测试输入。因此,可以将上面的生成式过程紧凑地编写为:\n", "\n", "$$ \\begin{align} \\mathbf{f} \\sim : & \\textsf{MultivariateNormal} \\left( \\text{loc}=\\mathbf{0}, \\text{scale}=K_{\\mathbf{f},\\mathbf{f}}^{1/2} \\right) \\ y_i \\sim : & \\textsf{Normal} \\left( \\text{loc}=f_i, \\text{scale}=\\sigma \\right), i = 1, \\ldots, N \\end{align} $$\n", "\n", "第一行中的采样运算会从多元高斯生成一组有限的 $N$ 函数值,*而不是上面 GP 抽样表示法中的整个函数*。第二行描述了从*一元*高斯抽样的 $N$ 的集合,它们以各种函数值为中心,具有固定的观测噪声 $\\sigma^2$。\n", "\n", "借助上述生成式模型,我们就可以继续考虑后验推断问题。这将以上述过程中观测的噪声数据为条件,产生函数值在一组新的测试点上的后验分布。\n", "\n", "借助上面的表示法,我们就可以根据相应的输入和训练数据,紧凑地编写未来(噪声)观测值的后验预测分布,如下所示(有关详情,请参阅 [Rasmussen & Williams](http://www.gaussianprocess.org/gpml/) 所著图书的第 2.2 节)。\n", "\n", "$$ \\mathbf{y}^* \\mid \\mathbf{x}^, \\mathbf{x}, \\mathbf{y} \\sim \\textsf{Normal} \\left( \\text{loc}=\\mathbf{\\mu}^, \\text{scale}=(\\Sigma^*)^{1/2} \\right), $$\n", "\n", "其中\n", "\n", "$$ \\mathbf{\\mu}^* = K_{*,\\mathbf{f}}\\left(K_{\\mathbf{f},\\mathbf{f}} + \\sigma^2 I \\right)^{-1} \\mathbf{y} $$\n", "\n", "且\n", "\n", "$$ \\Sigma^* = K_{,} - K_{,\\mathbf{f}} \\left(K_{\\mathbf{f},\\mathbf{f}} + \\sigma^2 I \\right)^{-1} K_{\\mathbf{f},} $$" ] }, { "cell_type": "markdown", "metadata": { "id": "QF_BW8m_c3_d" }, "source": [ "## 导入" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "cellView": "code", "id": "jw-_1yC50xaM" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "import time\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import tensorflow.compat.v2 as tf\n", "import tensorflow_probability as tfp\n", "tfb = tfp.bijectors\n", "tfd = tfp.distributions\n", "tfk = tfp.math.psd_kernels\n", "tf.enable_v2_behavior()\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "%pylab inline\n", "# Configure plot defaults\n", "plt.rcParams['axes.facecolor'] = 'white'\n", "plt.rcParams['grid.color'] = '#666666'\n", "%config InlineBackend.figure_format = 'png'" ] }, { "cell_type": "markdown", "metadata": { "id": "cu9S6c7uuvC1" }, "source": [ "## 示例:噪声正弦数据上的精确 GP 回归\n", "\n", "在这里,我们从存在噪声的正弦曲线中生成训练数据,然后从 GP 回归模型的后验中采样一组曲线。我们使用 [Adam](https://arxiv.org/abs/1412.6980) 来优化内核超参数(将先验下数据的负对数似然最小化)。我们绘制训练曲线,然后是真实函数和后验样本。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Qrys68xzZE-c" }, "outputs": [], "source": [ "def sinusoid(x):\n", " return np.sin(3 * np.pi * x[..., 0])\n", "\n", "def generate_1d_data(num_training_points, observation_noise_variance):\n", " \"\"\"Generate noisy sinusoidal observations at a random set of points.\n", "\n", " Returns:\n", " observation_index_points, observations\n", " \"\"\"\n", " index_points_ = np.random.uniform(-1., 1., (num_training_points, 1))\n", " index_points_ = index_points_.astype(np.float64)\n", " # y = f(x) + noise\n", " observations_ = (sinusoid(index_points_) +\n", " np.random.normal(loc=0,\n", " scale=np.sqrt(observation_noise_variance),\n", " size=(num_training_points)))\n", " return index_points_, observations_" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Tem9p8rUlqQR" }, "outputs": [], "source": [ "# Generate training data with a known noise level (we'll later try to recover\n", "# this value from the data).\n", "NUM_TRAINING_POINTS = 100\n", "observation_index_points_, observations_ = generate_1d_data(\n", " num_training_points=NUM_TRAINING_POINTS,\n", " observation_noise_variance=.1)" ] }, { "cell_type": "markdown", "metadata": { "id": "JiJukqfWuXUq" }, "source": [ "我们会将先验放在内核超参数上,然后使用 `tfd.JointDistributionNamed` 编写超参数和观测数据的联合分布。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "i63dMy4FbnTd" }, "outputs": [], "source": [ "def build_gp(amplitude, length_scale, observation_noise_variance):\n", " \"\"\"Defines the conditional dist. of GP outputs, given kernel parameters.\"\"\"\n", "\n", " # Create the covariance kernel, which will be shared between the prior (which we\n", " # use for maximum likelihood training) and the posterior (which we use for\n", " # posterior predictive sampling)\n", " kernel = tfk.ExponentiatedQuadratic(amplitude, length_scale)\n", "\n", " # Create the GP prior distribution, which we will use to train the model\n", " # parameters.\n", " return tfd.GaussianProcess(\n", " kernel=kernel,\n", " index_points=observation_index_points_,\n", " observation_noise_variance=observation_noise_variance)\n", "\n", "gp_joint_model = tfd.JointDistributionNamed({\n", " 'amplitude': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n", " 'length_scale': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n", " 'observation_noise_variance': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n", " 'observations': build_gp,\n", "})" ] }, { "cell_type": "markdown", "metadata": { "id": "sNprcU_0umhK" }, "source": [ "我们可以通过验证是否能够从先验中进行采样,以及是否能够计算样本的对数密度,对我们的实现进行健全性检查。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "HK1Pyen7ci_A" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampled {'observation_noise_variance': , 'length_scale': , 'amplitude': , 'observations': }\n", "log_prob of sample: -194.96442183797524\n" ] } ], "source": [ "x = gp_joint_model.sample()\n", "lp = gp_joint_model.log_prob(x)\n", "\n", "print(\"sampled {}\".format(x))\n", "print(\"log_prob of sample: {}\".format(lp))" ] }, { "cell_type": "markdown", "metadata": { "id": "Cw50WxSmu3Ge" }, "source": [ "现在,我们来进行优化,以找到具有最高后验概率的参数值。我们将为每个参数定义一个变量,并将它们的值约束为正值。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "ByXndE3pkA4x" }, "outputs": [], "source": [ "# Create the trainable model parameters, which we'll subsequently optimize.\n", "# Note that we constrain them to be strictly positive.\n", "\n", "constrain_positive = tfb.Shift(np.finfo(np.float64).tiny)(tfb.Exp())\n", "\n", "amplitude_var = tfp.util.TransformedVariable(\n", " initial_value=1.,\n", " bijector=constrain_positive,\n", " name='amplitude',\n", " dtype=np.float64)\n", "\n", "length_scale_var = tfp.util.TransformedVariable(\n", " initial_value=1.,\n", " bijector=constrain_positive,\n", " name='length_scale',\n", " dtype=np.float64)\n", "\n", "observation_noise_variance_var = tfp.util.TransformedVariable(\n", " initial_value=1.,\n", " bijector=constrain_positive,\n", " name='observation_noise_variance_var',\n", " dtype=np.float64)\n", "\n", "trainable_variables = [v.trainable_variables[0] for v in \n", " [amplitude_var,\n", " length_scale_var,\n", " observation_noise_variance_var]]" ] }, { "cell_type": "markdown", "metadata": { "id": "2Ji95UUYvE-K" }, "source": [ "为了使模型符合我们的观测数据,我们将定义一个 `target_log_prob` 函数,该函数采用(仍待推断)内核超参数。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "yjO8TWIXvFr5" }, "outputs": [], "source": [ "def target_log_prob(amplitude, length_scale, observation_noise_variance):\n", " return gp_joint_model.log_prob({\n", " 'amplitude': amplitude,\n", " 'length_scale': length_scale,\n", " 'observation_noise_variance': observation_noise_variance,\n", " 'observations': observations_\n", " })" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "4swUVjI0DZY4" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Trained parameters:\n", "amplitude: 0.9176153445125278\n", "length_scale: 0.18444082442910079\n", "observation_noise_variance: 0.0880273312850989\n" ] } ], "source": [ "# Now we optimize the model parameters.\n", "num_iters = 1000\n", "optimizer = tf.optimizers.Adam(learning_rate=.01)\n", "\n", "# Use `tf.function` to trace the loss for more efficient evaluation.\n", "@tf.function(autograph=False, jit_compile=False)\n", "def train_model():\n", " with tf.GradientTape() as tape:\n", " loss = -target_log_prob(amplitude_var, length_scale_var,\n", " observation_noise_variance_var)\n", " grads = tape.gradient(loss, trainable_variables)\n", " optimizer.apply_gradients(zip(grads, trainable_variables))\n", " return loss\n", "\n", "# Store the likelihood values during training, so we can plot the progress\n", "lls_ = np.zeros(num_iters, np.float64)\n", "for i in range(num_iters):\n", " loss = train_model()\n", " lls_[i] = loss\n", "\n", "print('Trained parameters:')\n", "print('amplitude: {}'.format(amplitude_var._value().numpy()))\n", "print('length_scale: {}'.format(length_scale_var._value().numpy()))\n", "print('observation_noise_variance: {}'.format(observation_noise_variance_var._value().numpy()))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "QKS1ZvcEuHZs" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the loss evolution\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(lls_)\n", "plt.xlabel(\"Training iteration\")\n", "plt.ylabel(\"Log marginal likelihood\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "1DOkwqQEsXVs" }, "outputs": [], "source": [ "# Having trained the model, we'd like to sample from the posterior conditioned\n", "# on observations. We'd like the samples to be at points other than the training\n", "# inputs.\n", "predictive_index_points_ = np.linspace(-1.2, 1.2, 200, dtype=np.float64)\n", "# Reshape to [200, 1] -- 1 is the dimensionality of the feature space.\n", "predictive_index_points_ = predictive_index_points_[..., np.newaxis]\n", "\n", "optimized_kernel = tfk.ExponentiatedQuadratic(amplitude_var, length_scale_var)\n", "gprm = tfd.GaussianProcessRegressionModel(\n", " kernel=optimized_kernel,\n", " index_points=predictive_index_points_,\n", " observation_index_points=observation_index_points_,\n", " observations=observations_,\n", " observation_noise_variance=observation_noise_variance_var,\n", " predictive_noise_variance=0.)\n", "\n", "# Create op to draw 50 independent samples, each of which is a *joint* draw\n", "# from the posterior at the predictive_index_points_. Since we have 200 input\n", "# locations as defined above, this posterior distribution over corresponding\n", "# function values is a 200-dimensional multivariate Gaussian distribution!\n", "num_samples = 50\n", "samples = gprm.sample(num_samples)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "1XgqrfsSub15" }, "outputs": [ { "data": { "image/png": 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8RxUAFgpCIFTTiWIRtm9noGBhKFKixldLwuVFDyX5zQtZyjev4KpFnVJ3MjJi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\ngQX00BAFNg4dMkEWbpLFnvncEdayjDd/IGA8/t1uPH1sGlu37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Ep5yOcpahyJmNSKUIgE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\nIAiCUCf/PzSiudQoznsgAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the true function, observations, and posterior samples.\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(predictive_index_points_, sinusoid(predictive_index_points_),\n", " label='True fn')\n", "plt.scatter(observation_index_points_[:, 0], observations_,\n", " label='Observations')\n", "for i in range(num_samples):\n", " plt.plot(predictive_index_points_, samples[i, :], c='r', alpha=.1,\n", " label='Posterior Sample' if i == 0 else None)\n", "leg = plt.legend(loc='upper right')\n", "for lh in leg.legendHandles: \n", " lh.set_alpha(1)\n", "plt.xlabel(r\"Index points ($\\mathbb{R}^1$)\")\n", "plt.ylabel(\"Observation space\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "aZe4H-7jy0hR" }, "source": [ "*注:如果您多次运行上面的代码,有时效果会很好,有时效果会很糟!参数的最大似然训练非常敏感,并且有时会收敛到较差的模型。最好的方式是使用 MCMC 来边缘化模型超参数。*" ] }, { "cell_type": "markdown", "metadata": { "id": "NThOGRM1oxuW" }, "source": [ "## 使用 HMC 边缘化超参数" ] }, { "cell_type": "markdown", "metadata": { "id": "RdCdMag7ymYp" }, "source": [ "与其优化超参数,不如尝试用汉密尔顿蒙特卡洛对它们积分。我们首先定义并运行一个采样器,在给定观测值的情况下,从内核超参数的后验分布中进行抽样。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "t1sZUooao1D0" }, "outputs": [], "source": [ "num_results = 100\n", "num_burnin_steps = 50\n", "\n", "sampler = tfp.mcmc.TransformedTransitionKernel(\n", " tfp.mcmc.NoUTurnSampler(\n", " target_log_prob_fn=target_log_prob,\n", " step_size=tf.cast(0.1, tf.float64)),\n", " bijector=[constrain_positive, constrain_positive, constrain_positive])\n", "\n", "adaptive_sampler = tfp.mcmc.DualAveragingStepSizeAdaptation(\n", " inner_kernel=sampler,\n", " num_adaptation_steps=int(0.8 * num_burnin_steps),\n", " target_accept_prob=tf.cast(0.75, tf.float64))\n", "\n", "initial_state = [tf.cast(x, tf.float64) for x in [1., 1., 1.]]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "MyOYZ0LEpnjQ" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Inference ran in 9.00s.\n" ] } ], "source": [ "# Speed up sampling by tracing with `tf.function`.\n", "@tf.function(autograph=False, jit_compile=False)\n", "def do_sampling():\n", " return tfp.mcmc.sample_chain(\n", " kernel=adaptive_sampler,\n", " current_state=initial_state,\n", " num_results=num_results,\n", " num_burnin_steps=num_burnin_steps,\n", " trace_fn=lambda current_state, kernel_results: kernel_results)\n", "\n", "t0 = time.time()\n", "samples, kernel_results = do_sampling()\n", "t1 = time.time()\n", "print(\"Inference ran in {:.2f}s.\".format(t1-t0))" ] }, { "cell_type": "markdown", "metadata": { "id": "zAySwdGWy8Jm" }, "source": [ "我们通过检查超参数轨迹来对采样器进行健全性检查。 " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "_5GA7jzwwPT9" }, "outputs": [ { "data": { "image/png": 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IFgrbzV2PMtnkcAzO8ckMfrlv6dYqXXbGJP+SvYL7J+bNza43GUF3IuJwc8/l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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(amplitude_samples,\n", " length_scale_samples,\n", " observation_noise_variance_samples) = samples\n", "\n", "f = plt.figure(figsize=[15, 3])\n", "for i, s in enumerate(samples):\n", " ax = f.add_subplot(1, len(samples) + 1, i + 1)\n", " ax.plot(s)" ] }, { "cell_type": "markdown", "metadata": { "id": "BQoBYHsAzJr3" }, "source": [ "现在,我们不是使用优化的超参数来构造单个 GP,而是将*后验预测分布*构造为一个 GP 的混合,每个 GP 均由超参数的后验分布中的样本定义。这种方式通过蒙特卡洛采样对后验参数进行近似积分,以计算未观测位置的边缘预测分布。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "XzZmJc7yrNGJ" }, "outputs": [], "source": [ "# The sampled hyperparams have a leading batch dimension, `[num_results, ...]`,\n", "# so they construct a *batch* of kernels.\n", "batch_of_posterior_kernels = tfk.ExponentiatedQuadratic(\n", " amplitude_samples, length_scale_samples)\n", "\n", "# The batch of kernels creates a batch of GP predictive models, one for each\n", "# posterior sample.\n", "batch_gprm = tfd.GaussianProcessRegressionModel(\n", " kernel=batch_of_posterior_kernels,\n", " index_points=predictive_index_points_,\n", " observation_index_points=observation_index_points_,\n", " observations=observations_,\n", " observation_noise_variance=observation_noise_variance_samples,\n", " predictive_noise_variance=0.)\n", "\n", "# To construct the marginal predictive distribution, we average with uniform\n", "# weight over the posterior samples.\n", "predictive_gprm = tfd.MixtureSameFamily(\n", " mixture_distribution=tfd.Categorical(logits=tf.zeros([num_results])),\n", " components_distribution=batch_gprm)\n", "\n", "num_samples = 50\n", "samples = predictive_gprm.sample(num_samples)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "QwfcWtDfyayd" }, "outputs": [ { "data": { "image/png": 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VVGxay7WrW1jVEMBt02YKWmeWcAGK1bC0jRWxGL6d3Tz6xKvUxKdJ21yEXF5G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\nfnk55TJVpVosNLGUqs84BEEQBEEQziQsoG020jrpdL1HNCP1y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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the true function, observations, and posterior samples.\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(predictive_index_points_, sinusoid(predictive_index_points_),\n", " label='True fn')\n", "plt.scatter(observation_index_points_[:, 0], observations_,\n", " label='Observations')\n", "for i in range(num_samples):\n", " plt.plot(predictive_index_points_, samples[i, :], c='r', alpha=.1,\n", " label='Posterior Sample' if i == 0 else None)\n", "leg = plt.legend(loc='upper right')\n", "for lh in leg.legendHandles: \n", " lh.set_alpha(1)\n", "plt.xlabel(r\"Index points ($\\mathbb{R}^1$)\")\n", "plt.ylabel(\"Observation space\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "bzCP7uFlzpq5" }, "source": [ "尽管在这种情况下差异很细微,但总的来说,比起上面仅使用最有可能的参数的做法,我们希望后验预测分布能够更好地泛化(为保留的数据提供更高的可能性)。" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Gaussian_Process_Regression_In_TFP.ipynb", "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 0 }