{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction to global sensitivity analysis with Emukit"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# General imports\n",
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import colors as mcolors\n",
"from matplotlib import cm\n",
"\n",
"## Figures config\n",
"colors = dict(mcolors.BASE_COLORS, **mcolors.CSS4_COLORS)\n",
"LEGEND_SIZE = 15\n",
"TITLE_SIZE = 25\n",
"AXIS_SIZE = 15"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Overview\n",
"\n",
"Sensitivity analysis is a statistical technique widely used to test the reliability of real systems. Imagine a simulator of taxis picking up customers in a city like the one showed in the Emukit playground. The profit of the taxi company depends on factors like the number of taxis on the road and the price per trip. In this example, a global sensitivity analysis of the simulator could be useful to decompose the variance of the profit in a way that can be assigned to the input variables of the simulator. \n",
"\n",
"There are different ways of doing a sensitivity analysis of the variables of a simulator. In this notebook we will start with an approach based on Monte Carlo sampling that is useful when evaluating the simulator is cheap. If evaluating the simulator is expensive, emulators can then be used to speed up computations. We will show this in the last part of the notebook. Next, we start with a few formal definitions and literature review so we can understand the basics of Sensitivity Analysis and how it can performed with Emukit."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Navigation\n",
"\n",
"1. [Global sensitivity analysis with Sobol indexes and decomposition of variance](#1.-Global-sensitivity-analysis-with-Sobol-indexes-and-decomposition-of-variance)\n",
"\n",
"2. [First order Sobol indices using Monte Carlo](#2.-First-order-Sobol-indices-using-Monte-Carlo)\n",
"\n",
"3. [Total effects using Monte Carlo](#3.-Total-Effects-using-Monte-Carlo)\n",
"\n",
"4. [Computing the sensitivity coefficients using the output of a model](#4.-Computing-the-sensitivity-coefficients-using-the-output-of-a-model)\n",
"\n",
"4. [Conclusions](#4.-Conclusions)\n",
"\n",
"5. [References](#5.-References)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Global sensitivity analysis with Sobol indexes and decomposition of variance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Any simulator can be viewed as a function \n",
"\n",
"$$y=f(\\textbf{X})$$ \n",
"\n",
"where $\\textbf{X}$ is a vector of $d$ uncertain model inputs $X_1,\\dots,X_d$, and $Y$ is some univariate model output. We assume that $f$ is a square integrable function and that the inputs are statistically independent and uniformly distributed within the hypercube $X_i \\in [0,1]$ for $i=1,2,...,d$, although the bounds can be generalized. The so-called Sobol decomposition of $f$ allows us to write it as \n",
"\n",
"$$Y = f_0 + \\sum_{i=1}^d f_i(X_i) + \\sum_{i**Note**: The previous decomposition is important because it shows how the variance in the output $Y$ can be associated to each input or interaction separately."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example: the Ishigami function\n",
"\n",
"We illustrate the exact calculation of the Sobol indexes with the three dimensional Ishigami function of [Ishigami & Homma, 1990](https://www.sciencedirect.com/science/article/pii/0951832096000026). This is a well-known example for uncertainty and sensitivity analysis methods because of its strong nonlinearity and peculiar dependence on $x_3$. More details of this function can be found in [Sobol' & Levitan (1999)](https://www.sciencedirect.com/science/article/pii/S0010465598001568).\n",
"\n",
"Mathematically, the from of the Ishigami function is\n",
"\n",
"$$f(\\textbf{x}) = \\sin(x_1) + a \\sin^2(x_2) + bx_3^4 \\sin(x_1). $$\n",
"\n",
"In this notebook we will set the parameters to be $a = 5$ and $b=0.1$ . The input variables are sampled randomly $x_i \\sim Uniform(-\\pi,\\pi)$.\n",
"\n",
"Next we create the function object and visualize its shape marginally for each one of its three inputs."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from emukit.test_functions.sensitivity import Ishigami ### change this one for the one in the library\n",
"\n",
"### --- Load the Ishigami function\n",
"ishigami = Ishigami(a=5, b=0.1)\n",
"target_simulator = ishigami.fidelity1\n",
"\n",
"### --- Define the input space in which the simulator is defined\n",
"variable_domain = (-np.pi,np.pi)\n",
"x_grid = np.linspace(*variable_domain,100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before moving to any further analysis, we first plot the non-zero components $f(\\textbf{X})$. These components are \n",
"\n",
"$$f_1(x_1) = \\sin(x_1)$$\n",
"\n",
"$$f_2(x_1) = a \\sin^2 (x_2)$$\n",
"\n",
"$$f_{13}(x_1,x_3) = bx_3^4 \\sin(x_1) $$ "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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