{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "ZrwVQsM9TiUw" }, "source": [ "##### Copyright 2019 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": "CpDUTVKYTowI" }, "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": "ltPJCG6pAUoc" }, "source": [ "# TensorFlow Probability 둘러보기\n", "\n", "
![]() | \n",
" ![]() | \n",
" ![]() | \n",
" ![]() | \n",
"
Distribution
의 모음을 나타냅니다.\n",
"- **이벤트 형상**은 Distribution
에서 샘플의 형상을 나타냅니다.\n",
"\n",
"항상 배치 형상을 '왼쪽'에 배치하고 이벤트 형상을 '오른쪽'에 배치합니다."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Bt7D7EgrEdYo"
},
"source": [
"### 스칼라 변량 Distributions
의 배치\n",
"\n",
"배치는 '벡터화된' 분포와 유사합니다. 계산이 병렬로 발생하는 독립 인스턴스입니다."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "vfY1B4GqDDJo"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Batch shape: (3,)\n",
"Event shape: ()\n"
]
}
],
"source": [
"# Create a batch of 3 normals, and plot 1000 samples from each\n",
"normals = tfd.Normal([-2.5, 0., 2.5], 1.) # The scale parameter broadacasts!\n",
"print(\"Batch shape:\", normals.batch_shape)\n",
"print(\"Event shape:\", normals.event_shape)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "iNzTGgKqE5CT"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of samples: (1000, 3)\n"
]
}
],
"source": [
"# Samples' shapes go on the left!\n",
"samples = normals.sample(1000)\n",
"print(\"Shape of samples:\", samples.shape)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "hIRbVOS7OP-g"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shape of samples: (10, 10, 10, 3)\n"
]
}
],
"source": [
"# Sample shapes can themselves be more complicated\n",
"print(\"Shape of samples:\", normals.sample([10, 10, 10]).shape)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "nqXQ6DEDFsLU"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tf.Tensor([-0.9189385 -0.9189385 -0.9189385], shape=(3,), dtype=float32)\n"
]
}
],
"source": [
"# A batch of normals gives a batch of log_probs.\n",
"print(normals.log_prob([-2.5, 0., 2.5]))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "W1uSOXO8GQB4"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tf.Tensor([-4.0439386 -0.9189385 -4.0439386], shape=(3,), dtype=float32)\n"
]
}
],
"source": [
"# The computation broadcasts, so a batch of normals applied to a scalar\n",
"# also gives a batch of log_probs.\n",
"print(normals.log_prob(0.))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "nxAGVtnPGkQ4"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"TFP error: Incompatible shapes: [200] vs. [3] [Op:SquaredDifference]\n"
]
}
],
"source": [
"# Normal numpy-like broadcasting rules apply!\n",
"xs = np.linspace(-6, 6, 200)\n",
"try:\n",
" normals.log_prob(xs)\n",
"except Exception as e:\n",
" print(\"TFP error:\", e.message)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "ieF2lRhPHxgd"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Numpy error: operands could not be broadcast together with shapes (200,) (3,) \n"
]
}
],
"source": [
"# That fails for the same reason this does:\n",
"try:\n",
" np.zeros(200) + np.zeros(3)\n",
"except Exception as e:\n",
" print(\"Numpy error:\", e)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "nS9qPHdeH0gz"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Broadcast shape: (200, 3)\n"
]
}
],
"source": [
"# But this would work:\n",
"a = np.zeros([200, 1]) + np.zeros(3)\n",
"print(\"Broadcast shape:\", a.shape)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "9w64N4YQH2r5"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Broadcast log_prob shape: (200, 3)\n"
]
}
],
"source": [
"# And so will this!\n",
"xs = np.linspace(-6, 6, 200)[..., np.newaxis]\n",
"# => shape = [200, 1]\n",
"\n",
"lps = normals.log_prob(xs)\n",
"print(\"Broadcast log_prob shape:\", lps.shape)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "rfsG1F0FFAWS"
},
"outputs": [
{
"data": {
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8PAwAOHXqFK677jpotVpcccUV+PSnP40777zzkuWSyWT4/e9/j3PnzqGkpAQ7d+7EPffc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\nivKjRYGiKIry+3+bj2GrPw5GuQAAAABJRU5ErkJggg==\n",
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