{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sensor Network Localization\n",
"\n",
"Data taken from Example 3 of [this article](https://amstat.tandfonline.com/doi/abs/10.1080/10618600.2017.1415911) (also available on arxiv). The paper studies how to compute posterior distributions for multimodal posteriors, a topic in Bayesian statistics. We have not covered Bayesian statistics yet. We will focus on just maximizing the likelihood.\n",
"\n",
"[Another article](http://ieeexplore.ieee.org/document/1413473/?reload=true) on self localization in sensor networks. \n",
"\n",
"Example 3 studies the problem of locating sensors in a network. In this network there are $6$ sensors in 2-dimensional space. The x,y coordinates of these sensors is given by the $X$ matrix."
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"6"
],
"text/latex": [
"6"
],
"text/markdown": [
"6"
],
"text/plain": [
"[1] 6"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"
\n",
"\n",
"\t0.57 | 0.91 |
\n",
"\t0.10 | 0.37 |
\n",
"\t0.26 | 0.14 |
\n",
"\t0.85 | 0.04 |
\n",
"\t0.50 | 0.30 |
\n",
"\t0.30 | 0.70 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{ll}\n",
"\t 0.57 & 0.91\\\\\n",
"\t 0.10 & 0.37\\\\\n",
"\t 0.26 & 0.14\\\\\n",
"\t 0.85 & 0.04\\\\\n",
"\t 0.50 & 0.30\\\\\n",
"\t 0.30 & 0.70\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| 0.57 | 0.91 | \n",
"| 0.10 | 0.37 | \n",
"| 0.26 | 0.14 | \n",
"| 0.85 | 0.04 | \n",
"| 0.50 | 0.30 | \n",
"| 0.30 | 0.70 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2]\n",
"[1,] 0.57 0.91\n",
"[2,] 0.10 0.37\n",
"[3,] 0.26 0.14\n",
"[4,] 0.85 0.04\n",
"[5,] 0.50 0.30\n",
"[6,] 0.30 0.70"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X <- cbind(c(0.57,0.10,0.26,0.85,0.50,0.30),c(0.91,0.37,0.14,0.04,0.30,0.70))\n",
"nrow(X)\n",
"X"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The article treats the location of the first 4 of these sensors as unknown and the location of the sensors 5 and 6 as known. This means that there are 8 total parameters (x,y positions of the 4 unknown parameters)."
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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WoAAMAQkhon7bp3767X68+cOdPIVKI1NTUDBgyoqKjIzs5u8gJ8fHyEEGq8MgCg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\ngg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Roughly reproduces Figure 4 in paper\n",
"options(repr.plot.width=5,repr.plot.height=4)\n",
"par(mar=c(3,3,1,1))\n",
"plot(X[,1],X[,2],xlim=c(0,1),ylim=c(0,1),pch=as.character(1:6),col=c(rep(1,4),rep(2,2)),xlab=\"\",ylab=\"\")\n",
"legend(\"topright\",c(\"Unknown Location\",\"Known Location\"),col=c(\"black\",\"red\"),pch=19)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $Y_{ij}$ entry of matrix $Y$ stores the recorded distance between sensors $i$ and $j$. If no distance is recorded between $i$ and $j$, $Y_{ij} = 0$ (missing data indicator). $Y$ is a symmetric matrix. We initially just input these distances in the upper triangle of $Y$ and then add the transpose to fill out the matrix."
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\t0.0000 | 0.0000 | 0.0000 | 0.9266 | 0.6103 | 0.3631 |
\n",
"\t0.0000 | 0.0000 | 0.2970 | 0.8524 | 0.0000 | 0.0000 |
\n",
"\t0.0000 | 0.2970 | 0.0000 | 0.0000 | 0.2995 | 0.5656 |
\n",
"\t0.9266 | 0.8524 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
\n",
"\t0.6103 | 0.0000 | 0.2995 | 0.0000 | 0.0000 | 0.0000 |
\n",
"\t0.3631 | 0.0000 | 0.5656 | 0.0000 | 0.0000 | 0.0000 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllll}\n",
"\t 0.0000 & 0.0000 & 0.0000 & 0.9266 & 0.6103 & 0.3631\\\\\n",
"\t 0.0000 & 0.0000 & 0.2970 & 0.8524 & 0.0000 & 0.0000\\\\\n",
"\t 0.0000 & 0.2970 & 0.0000 & 0.0000 & 0.2995 & 0.5656\\\\\n",
"\t 0.9266 & 0.8524 & 0.0000 & 0.0000 & 0.0000 & 0.0000\\\\\n",
"\t 0.6103 & 0.0000 & 0.2995 & 0.0000 & 0.0000 & 0.0000\\\\\n",
"\t 0.3631 & 0.0000 & 0.5656 & 0.0000 & 0.0000 & 0.0000\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| 0.0000 | 0.0000 | 0.0000 | 0.9266 | 0.6103 | 0.3631 | \n",
"| 0.0000 | 0.0000 | 0.2970 | 0.8524 | 0.0000 | 0.0000 | \n",
"| 0.0000 | 0.2970 | 0.0000 | 0.0000 | 0.2995 | 0.5656 | \n",
"| 0.9266 | 0.8524 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | \n",
"| 0.6103 | 0.0000 | 0.2995 | 0.0000 | 0.0000 | 0.0000 | \n",
"| 0.3631 | 0.0000 | 0.5656 | 0.0000 | 0.0000 | 0.0000 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3] [,4] [,5] [,6] \n",
"[1,] 0.0000 0.0000 0.0000 0.9266 0.6103 0.3631\n",
"[2,] 0.0000 0.0000 0.2970 0.8524 0.0000 0.0000\n",
"[3,] 0.0000 0.2970 0.0000 0.0000 0.2995 0.5656\n",
"[4,] 0.9266 0.8524 0.0000 0.0000 0.0000 0.0000\n",
"[5,] 0.6103 0.0000 0.2995 0.0000 0.0000 0.0000\n",
"[6,] 0.3631 0.0000 0.5656 0.0000 0.0000 0.0000"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Y <- matrix(c(0,0,0,0.9266,0.6103,0.3631,\n",
" 0,0,0.2970,0.8524,0,0,\n",
" 0,0,0,0,0.2995,0.5656,\n",
" 0,0,0,0,0,0,\n",
" 0,0,0,0,0,0,\n",
" 0,0,0,0,0,0),nrow=6,byrow=TRUE)\n",
"Y <- Y + t(Y)\n",
"Y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now have all the data loaded. The plot in the paper which summarizes the data is:\n",
"\n",
"(requires internet connection to view)\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model and Likelihood Function\n",
"\n",
"We observe \"noisy\" distance estimates between pairs of sensors. Further, there is a probability that no distance measurement is made. The probability is proportional to the distance between the two sensors.\n",
"\n",
"Let $x_{i} = (x_{i1},x_{i2})$ be the Cartesian coordinates of sensor $i$. This data is stored in the rows of the matrix `X`.\n",
"\n",
"Let $W_{ij} = 1$ if a measurement is made between sensors $i$ and $j$ and $0$ if not. The article assumes\n",
"$$ W_{ij} \\sim Bernoulli(e^{-||x_i - x_j||^2/(2*.3^2)})$$.\n",
"\n",
"Given that a measurement is made, there is normal measurement error\n",
"$$ y_{ij} | w_{ij}=1 \\sim N(||x_i-x_j||,.02^2).$$\n",
"On average the measurement is correct. The standard deviation of the measurement is $0.02$.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\t0 | 0 | 0 | 1 | 1 | 1 |
\n",
"\t0 | 0 | 1 | 1 | 0 | 0 |
\n",
"\t0 | 1 | 0 | 0 | 1 | 1 |
\n",
"\t1 | 1 | 0 | 0 | 0 | 0 |
\n",
"\t1 | 0 | 1 | 0 | 0 | 0 |
\n",
"\t1 | 0 | 1 | 0 | 0 | 0 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllll}\n",
"\t 0 & 0 & 0 & 1 & 1 & 1\\\\\n",
"\t 0 & 0 & 1 & 1 & 0 & 0\\\\\n",
"\t 0 & 1 & 0 & 0 & 1 & 1\\\\\n",
"\t 1 & 1 & 0 & 0 & 0 & 0\\\\\n",
"\t 1 & 0 & 1 & 0 & 0 & 0\\\\\n",
"\t 1 & 0 & 1 & 0 & 0 & 0\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| 0 | 0 | 0 | 1 | 1 | 1 | \n",
"| 0 | 0 | 1 | 1 | 0 | 0 | \n",
"| 0 | 1 | 0 | 0 | 1 | 1 | \n",
"| 1 | 1 | 0 | 0 | 0 | 0 | \n",
"| 1 | 0 | 1 | 0 | 0 | 0 | \n",
"| 1 | 0 | 1 | 0 | 0 | 0 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3] [,4] [,5] [,6]\n",
"[1,] 0 0 0 1 1 1 \n",
"[2,] 0 0 1 1 0 0 \n",
"[3,] 0 1 0 0 1 1 \n",
"[4,] 1 1 0 0 0 0 \n",
"[5,] 1 0 1 0 0 0 \n",
"[6,] 1 0 1 0 0 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## create the W matrix\n",
"W <- 1*(Y!=0)\n",
"W"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"## create a matrix of the positions for the known sensors\n",
"Xk <- X[5:6,]"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"## this is L(x_1,x_2,x_3,x_4) above Equation 12 in paper\n",
"## note there is a typo in the paper, first exp should be\n",
"## to the W_ij power. corrected in this code\n",
"likelihood <- function(theta,Xk,Y){\n",
" thetaX <- rbind(matrix(theta,nrow=length(theta)/2,byrow=TRUE),Xk)\n",
" Xd <- as.matrix(dist(thetaX))\n",
" temp <- -Xd^2 / (2*.3^2)\n",
" out <- W*(-(Y - Xd)^2 / (2*0.02^2) + temp) + (1-W)*log(1-exp(temp))\n",
" return(sum(out[lower.tri(out)]))\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fit with BFGS, Numerically Approximated Gradient\n",
"\n",
"Run with random starting location. Check for convergence with `a$convergence` where `a` is the output from `optim`."
]
},
{
"cell_type": "code",
"execution_count": 131,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"## random initial start\n",
"init <- runif(8)\n",
"## allow for many iterations\n",
"maxit <- 1000"
]
},
{
"cell_type": "code",
"execution_count": 132,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
" Length Class Mode \n",
"par 8 -none- numeric\n",
"value 1 -none- numeric\n",
"counts 2 -none- numeric\n",
"convergence 1 -none- numeric\n",
"message 0 -none- NULL \n",
"hessian 64 -none- numeric"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"a = optim(init,likelihood,method=\"BFGS\",Xk=Xk,Y=Y,control=list(maxit=maxit,fnscale=-1),hessian=TRUE)\n",
"summary(a)"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"0"
],
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"0"
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"0"
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"a$convergence"
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Xhat <- matrix(a$par,ncol=2,byrow=TRUE)"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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GNSUiIuLlJWJoMGybffysCBtS1E0+0K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\nGkEIADC0/wcVcclpGEq5UQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=5,repr.plot.height=4)\n",
"pch_est <- c(0,1,2,5)\n",
"par(mar=c(3,3,1,1))\n",
"plot(Xhat[,1],Xhat[,2],col=1:4,xlab=\"\",ylab=\"\",\n",
" xlim=c(-.5,1.5),ylim=c(-.5,1.5),pch=pch_est)\n",
"points(X[1:4,1],X[1:4,2],col=1:4,cex=1.5,pch=as.character(1:4),font=1)\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"0"
],
"text/latex": [
"0"
],
"text/markdown": [
"0"
],
"text/plain": [
"[1] 0"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## convergence = 0 is good\n",
"## convergence = 1 indicates maximum number of iterations reached\n",
"a$convergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Compute Uncertainties"
]
},
{
"cell_type": "code",
"execution_count": 137,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\t-4.311051e+03 | -1762.7933078 | 0.0637766 | 0.1140265 | 9.452329e-02 | 0.6971049 | 2496.1513331 | 193.2050132 |
\n",
"\t-1.762793e+03 | -3223.0553369 | 0.1140265 | 0.1387508 | 6.971049e-01 | 1.2722176 | 193.2050132 | 15.8633634 |
\n",
"\t 6.377660e-02 | 0.1140265 | -2477.4215656 | -48.2601602 | 2.175986e+03 | 853.0093079 | 296.4258569 | -809.6201185 |
\n",
"\t 1.140265e-01 | 0.1387508 | -48.2601602 | -2557.2187607 | 8.530093e+02 | 339.8099662 | -809.6201185 | 2215.1375074 |
\n",
"\t 9.452329e-02 | 0.6971049 | 2175.9857658 | 853.0093079 | -3.984085e+03 | -2219.7817496 | 0.3530649 | -0.5926825 |
\n",
"\t 6.971049e-01 | 1.2722176 | 853.0093079 | 339.8099662 | -2.219782e+03 | -3561.2811772 | -0.5926825 | 0.5849765 |
\n",
"\t 2.496151e+03 | 193.2050132 | 296.4258569 | -809.6201185 | 3.530649e-01 | -0.5926825 | -2798.4115979 | 618.6219391 |
\n",
"\t 1.932050e+02 | 15.8633634 | -809.6201185 | 2215.1375074 | -5.926825e-01 | 0.5849765 | 618.6219391 | -2230.6304600 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllllll}\n",
"\t -4.311051e+03 & -1762.7933078 & 0.0637766 & 0.1140265 & 9.452329e-02 & 0.6971049 & 2496.1513331 & 193.2050132\\\\\n",
"\t -1.762793e+03 & -3223.0553369 & 0.1140265 & 0.1387508 & 6.971049e-01 & 1.2722176 & 193.2050132 & 15.8633634\\\\\n",
"\t 6.377660e-02 & 0.1140265 & -2477.4215656 & -48.2601602 & 2.175986e+03 & 853.0093079 & 296.4258569 & -809.6201185\\\\\n",
"\t 1.140265e-01 & 0.1387508 & -48.2601602 & -2557.2187607 & 8.530093e+02 & 339.8099662 & -809.6201185 & 2215.1375074\\\\\n",
"\t 9.452329e-02 & 0.6971049 & 2175.9857658 & 853.0093079 & -3.984085e+03 & -2219.7817496 & 0.3530649 & -0.5926825\\\\\n",
"\t 6.971049e-01 & 1.2722176 & 853.0093079 & 339.8099662 & -2.219782e+03 & -3561.2811772 & -0.5926825 & 0.5849765\\\\\n",
"\t 2.496151e+03 & 193.2050132 & 296.4258569 & -809.6201185 & 3.530649e-01 & -0.5926825 & -2798.4115979 & 618.6219391\\\\\n",
"\t 1.932050e+02 & 15.8633634 & -809.6201185 & 2215.1375074 & -5.926825e-01 & 0.5849765 & 618.6219391 & -2230.6304600\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| -4.311051e+03 | -1762.7933078 | 0.0637766 | 0.1140265 | 9.452329e-02 | 0.6971049 | 2496.1513331 | 193.2050132 | \n",
"| -1.762793e+03 | -3223.0553369 | 0.1140265 | 0.1387508 | 6.971049e-01 | 1.2722176 | 193.2050132 | 15.8633634 | \n",
"| 6.377660e-02 | 0.1140265 | -2477.4215656 | -48.2601602 | 2.175986e+03 | 853.0093079 | 296.4258569 | -809.6201185 | \n",
"| 1.140265e-01 | 0.1387508 | -48.2601602 | -2557.2187607 | 8.530093e+02 | 339.8099662 | -809.6201185 | 2215.1375074 | \n",
"| 9.452329e-02 | 0.6971049 | 2175.9857658 | 853.0093079 | -3.984085e+03 | -2219.7817496 | 0.3530649 | -0.5926825 | \n",
"| 6.971049e-01 | 1.2722176 | 853.0093079 | 339.8099662 | -2.219782e+03 | -3561.2811772 | -0.5926825 | 0.5849765 | \n",
"| 2.496151e+03 | 193.2050132 | 296.4258569 | -809.6201185 | 3.530649e-01 | -0.5926825 | -2798.4115979 | 618.6219391 | \n",
"| 1.932050e+02 | 15.8633634 | -809.6201185 | 2215.1375074 | -5.926825e-01 | 0.5849765 | 618.6219391 | -2230.6304600 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3] [,4] [,5] \n",
"[1,] -4.311051e+03 -1762.7933078 0.0637766 0.1140265 9.452329e-02\n",
"[2,] -1.762793e+03 -3223.0553369 0.1140265 0.1387508 6.971049e-01\n",
"[3,] 6.377660e-02 0.1140265 -2477.4215656 -48.2601602 2.175986e+03\n",
"[4,] 1.140265e-01 0.1387508 -48.2601602 -2557.2187607 8.530093e+02\n",
"[5,] 9.452329e-02 0.6971049 2175.9857658 853.0093079 -3.984085e+03\n",
"[6,] 6.971049e-01 1.2722176 853.0093079 339.8099662 -2.219782e+03\n",
"[7,] 2.496151e+03 193.2050132 296.4258569 -809.6201185 3.530649e-01\n",
"[8,] 1.932050e+02 15.8633634 -809.6201185 2215.1375074 -5.926825e-01\n",
" [,6] [,7] [,8] \n",
"[1,] 0.6971049 2496.1513331 193.2050132\n",
"[2,] 1.2722176 193.2050132 15.8633634\n",
"[3,] 853.0093079 296.4258569 -809.6201185\n",
"[4,] 339.8099662 -809.6201185 2215.1375074\n",
"[5,] -2219.7817496 0.3530649 -0.5926825\n",
"[6,] -3561.2811772 -0.5926825 0.5849765\n",
"[7,] -0.5926825 -2798.4115979 618.6219391\n",
"[8,] 0.5849765 618.6219391 -2230.6304600"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"a$hessian"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\t 9.516099e-04 | -4.654685e-04 | -1.234329e-04 | 3.111672e-04 | -1.437619e-06 | 1.008860e-06 | 8.621465e-04 | 0.0006720199 |
\n",
"\t-4.654685e-04 | 5.394197e-04 | 3.274443e-05 | -8.241852e-05 | 4.003402e-07 | -1.416340e-07 | -4.042024e-04 | -0.0002423089 |
\n",
"\t-1.234329e-04 | 3.274443e-05 | 2.818998e-02 | -6.848560e-02 | 9.679529e-04 | -3.994943e-04 | 5.745921e-03 | -0.0766589515 |
\n",
"\t 3.111672e-04 | -8.241852e-05 | -6.848560e-02 | 1.729261e-01 | -7.402120e-04 | 5.918137e-04 | -1.443499e-02 | 0.1926057730 |
\n",
"\t-1.437619e-06 | 4.003402e-07 | 9.679529e-04 | -7.402120e-04 | 8.144879e-04 | -3.466490e-04 | 8.027320e-05 | -0.0010645617 |
\n",
"\t 1.008860e-06 | -1.416340e-07 | -3.994943e-04 | 5.918137e-04 | -3.466490e-04 | 4.577762e-04 | -5.406376e-05 | 0.0007180069 |
\n",
"\t 8.621465e-04 | -4.042024e-04 | 5.745921e-03 | -1.443499e-02 | 8.027320e-05 | -5.406376e-05 | 2.417567e-03 | -0.0156780179 |
\n",
"\t 6.720199e-04 | -2.423089e-04 | -7.665895e-02 | 1.926058e-01 | -1.064562e-03 | 7.180069e-04 | -1.567802e-02 | 0.2152490916 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{llllllll}\n",
"\t 9.516099e-04 & -4.654685e-04 & -1.234329e-04 & 3.111672e-04 & -1.437619e-06 & 1.008860e-06 & 8.621465e-04 & 0.0006720199\\\\\n",
"\t -4.654685e-04 & 5.394197e-04 & 3.274443e-05 & -8.241852e-05 & 4.003402e-07 & -1.416340e-07 & -4.042024e-04 & -0.0002423089\\\\\n",
"\t -1.234329e-04 & 3.274443e-05 & 2.818998e-02 & -6.848560e-02 & 9.679529e-04 & -3.994943e-04 & 5.745921e-03 & -0.0766589515\\\\\n",
"\t 3.111672e-04 & -8.241852e-05 & -6.848560e-02 & 1.729261e-01 & -7.402120e-04 & 5.918137e-04 & -1.443499e-02 & 0.1926057730\\\\\n",
"\t -1.437619e-06 & 4.003402e-07 & 9.679529e-04 & -7.402120e-04 & 8.144879e-04 & -3.466490e-04 & 8.027320e-05 & -0.0010645617\\\\\n",
"\t 1.008860e-06 & -1.416340e-07 & -3.994943e-04 & 5.918137e-04 & -3.466490e-04 & 4.577762e-04 & -5.406376e-05 & 0.0007180069\\\\\n",
"\t 8.621465e-04 & -4.042024e-04 & 5.745921e-03 & -1.443499e-02 & 8.027320e-05 & -5.406376e-05 & 2.417567e-03 & -0.0156780179\\\\\n",
"\t 6.720199e-04 & -2.423089e-04 & -7.665895e-02 & 1.926058e-01 & -1.064562e-03 & 7.180069e-04 & -1.567802e-02 & 0.2152490916\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| 9.516099e-04 | -4.654685e-04 | -1.234329e-04 | 3.111672e-04 | -1.437619e-06 | 1.008860e-06 | 8.621465e-04 | 0.0006720199 | \n",
"| -4.654685e-04 | 5.394197e-04 | 3.274443e-05 | -8.241852e-05 | 4.003402e-07 | -1.416340e-07 | -4.042024e-04 | -0.0002423089 | \n",
"| -1.234329e-04 | 3.274443e-05 | 2.818998e-02 | -6.848560e-02 | 9.679529e-04 | -3.994943e-04 | 5.745921e-03 | -0.0766589515 | \n",
"| 3.111672e-04 | -8.241852e-05 | -6.848560e-02 | 1.729261e-01 | -7.402120e-04 | 5.918137e-04 | -1.443499e-02 | 0.1926057730 | \n",
"| -1.437619e-06 | 4.003402e-07 | 9.679529e-04 | -7.402120e-04 | 8.144879e-04 | -3.466490e-04 | 8.027320e-05 | -0.0010645617 | \n",
"| 1.008860e-06 | -1.416340e-07 | -3.994943e-04 | 5.918137e-04 | -3.466490e-04 | 4.577762e-04 | -5.406376e-05 | 0.0007180069 | \n",
"| 8.621465e-04 | -4.042024e-04 | 5.745921e-03 | -1.443499e-02 | 8.027320e-05 | -5.406376e-05 | 2.417567e-03 | -0.0156780179 | \n",
"| 6.720199e-04 | -2.423089e-04 | -7.665895e-02 | 1.926058e-01 | -1.064562e-03 | 7.180069e-04 | -1.567802e-02 | 0.2152490916 | \n",
"\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3] [,4] [,5] \n",
"[1,] 9.516099e-04 -4.654685e-04 -1.234329e-04 3.111672e-04 -1.437619e-06\n",
"[2,] -4.654685e-04 5.394197e-04 3.274443e-05 -8.241852e-05 4.003402e-07\n",
"[3,] -1.234329e-04 3.274443e-05 2.818998e-02 -6.848560e-02 9.679529e-04\n",
"[4,] 3.111672e-04 -8.241852e-05 -6.848560e-02 1.729261e-01 -7.402120e-04\n",
"[5,] -1.437619e-06 4.003402e-07 9.679529e-04 -7.402120e-04 8.144879e-04\n",
"[6,] 1.008860e-06 -1.416340e-07 -3.994943e-04 5.918137e-04 -3.466490e-04\n",
"[7,] 8.621465e-04 -4.042024e-04 5.745921e-03 -1.443499e-02 8.027320e-05\n",
"[8,] 6.720199e-04 -2.423089e-04 -7.665895e-02 1.926058e-01 -1.064562e-03\n",
" [,6] [,7] [,8] \n",
"[1,] 1.008860e-06 8.621465e-04 0.0006720199\n",
"[2,] -1.416340e-07 -4.042024e-04 -0.0002423089\n",
"[3,] -3.994943e-04 5.745921e-03 -0.0766589515\n",
"[4,] 5.918137e-04 -1.443499e-02 0.1926057730\n",
"[5,] -3.466490e-04 8.027320e-05 -0.0010645617\n",
"[6,] 4.577762e-04 -5.406376e-05 0.0007180069\n",
"[7,] -5.406376e-05 2.417567e-03 -0.0156780179\n",
"[8,] 7.180069e-04 -1.567802e-02 0.2152490916"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"avar <- solve(-a$hessian)\n",
"avar"
]
},
{
"cell_type": "code",
"execution_count": 139,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"## useful for drawing ellipses on plots\n",
"library(ellipse)"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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LRNCCG1AgWhClq0gI4O/vwTZU2NyllbIzISa9Zg61bGu2BtDR4PCQmMN0wIIbUF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\n+9HKy7nPXQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width=5,repr.plot.height=4)\n",
"pch_est <- c(0,1,2,5)\n",
"par(mar=c(3,3,1,1))\n",
"plot(Xhat[,1],Xhat[,2],col=1:4,xlab=\"\",ylab=\"\",\n",
" xlim=c(-.5,1.5),ylim=c(-.5,1.5),pch=pch_est)\n",
"points(X[1:4,1],X[1:4,2],col=1:4,cex=1.5,pch=as.character(1:4),font=1)\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)\n",
"for(jj in 1:4){\n",
" v <- avar[(2*jj-1):(2*jj),(2*jj-1):(2*jj)]\n",
" points(ellipse(centre=Xhat[jj,],v,level=0.95),type='l',col=jj)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Potential Problem / Challenge: ** The parameter values are converging to different values depending on starting point. Also the uncertainty ellipses are not capturing the true values as often as we would expect."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Explore Convergence of BFGS\n",
"\n",
"We now explore how BFGS is converging by running the algorithm $N$ times at different randomly chosen starting positions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Max 30 Iterations"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"## we run the optimizer N times from\n",
"## random starting locations\n",
"N <- 500\n",
"soln <- array(0,dim=c(N,4,2))"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"maxit <- 30\n",
"for(ii in 1:N){\n",
" init <- runif(8,min=-.5,max=1.5)\n",
" a <- optim(init,likelihood,method=\"BFGS\",Xk=Xk,Y=Y,control=list(maxit=maxit,fnscale=-1))\n",
" soln[ii,,] <- matrix(a$par,ncol=2,byrow=TRUE)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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iZIEq2teHszfz7t7Wg0fP89Hh6YmlJXR2iobkW5ceNIS0Oj4fRpPD1ZsuRyCrq5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\nHXDH8jUGQQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mar=c(3,3,1,1))\n",
"plot(0,0,xlim=c(-.5,1.5),ylim=c(-.6,1.5),col=0,xlab=\"\",ylab=\"\")\n",
"pch_est <- c(0,1,2,5)\n",
"## make colors 1:4 transparent\n",
"cols <- rgb(t(col2rgb(1:4)),alpha=70,maxColorValue=255)\n",
"for(jj in 1:4){\n",
" points(soln[,jj,1],soln[,jj,2],xlab=\"x_11\",ylab=\"x_12\",col=cols[jj],pch=pch_est[jj])\n",
" points(X[jj,1],X[jj,2],col=jj,cex=2,pch=as.character(jj),font=2)\n",
"}\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Max 100 Iterations"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"maxit <- 100\n",
"for(ii in 1:N){\n",
" init <- runif(8,min=-.5,max=1.5)\n",
" a <- optim(init,likelihood,method=\"BFGS\",Xk=Xk,Y=Y,control=list(maxit=maxit,fnscale=-1))\n",
" soln[ii,,] <- matrix(a$par,ncol=2,byrow=TRUE)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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cHBGzZsuIQDk5OTk5OT299n5cqVl1SUEN3I2rVrCwoKLL++66675Cm+6LYcFoR6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",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mar=c(3,3,1,1))\n",
"plot(0,0,xlim=c(-.5,1.5),ylim=c(-.6,1.5),col=0,xlab=\"\",ylab=\"\")\n",
"pch_est <- c(0,1,2,5)\n",
"## make colors 1:4 transparent\n",
"cols <- rgb(t(col2rgb(1:4)),alpha=70,maxColorValue=255)\n",
"for(jj in 1:4){\n",
" points(soln[,jj,1],soln[,jj,2],xlab=\"x_11\",ylab=\"x_12\",col=cols[jj],pch=pch_est[jj])\n",
" points(X[jj,1],X[jj,2],col=jj,cex=2,pch=as.character(jj),font=2)\n",
"}\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Max 1000 Iterations"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"maxit <- 1000\n",
"for(ii in 1:N){\n",
" init <- runif(8,min=-.5,max=1.5)\n",
" a <- optim(init,likelihood,method=\"BFGS\",Xk=Xk,Y=Y,control=list(maxit=maxit,fnscale=-1))\n",
" soln[ii,,] <- matrix(a$par,ncol=2,byrow=TRUE)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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iLSNAYhERFpGoOQiIg0jUFIRESaxiAkIiJNYxASEZGmMQiJiEjTGIRERKRpDEIi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\nkIiINO3/AZDHlzvhiPJWAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mar=c(3,3,1,1))\n",
"plot(0,0,xlim=c(-.5,1.5),ylim=c(-.6,1.5),col=0,xlab=\"\",ylab=\"\")\n",
"pch_est <- c(0,1,2,5)\n",
"## make colors 1:4 transparent\n",
"cols <- rgb(t(col2rgb(1:4)),alpha=70,maxColorValue=255)\n",
"for(jj in 1:4){\n",
" points(soln[,jj,1],soln[,jj,2],xlab=\"x_11\",ylab=\"x_12\",col=cols[jj],pch=pch_est[jj])\n",
" points(X[jj,1],X[jj,2],col=jj,cex=2,pch=as.character(jj),font=2)\n",
"}\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There appear to be:\n",
"- Sensor 1: 2 local maxima\n",
"- Sensor 2: 8 local maxima\n",
"- Sensor 3: 2 local maxima\n",
"- Sensor 4: 7 local maxima"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Which is Global Maximum?\n",
"\n",
"We can select the global maximum by evaluating the likelihood at the limit of each sequence."
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"a <- apply(soln,1,function(x) likelihood(t(x),Xk,Y))\n",
"ix <- which.max(a)"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Xhat <- soln[ix,,]"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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hg4ECdOwM6Ov6BKad067NyJM2fg4gJLS2zciAULIBAouluEkI6OkzfCVatW7d+/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"text/plain": [
"plot without title"
]
},
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}
],
"source": [
"options(repr.plot.width=5,repr.plot.height=4)\n",
"pch_est <- c(0,1,2,5)\n",
"par(mar=c(3,3,1,1))\n",
"plot(Xhat[,1],Xhat[,2],col=1:4,xlab=\"\",ylab=\"\",\n",
" xlim=c(-.5,1.5),ylim=c(-.5,1.5),pch=pch_est)\n",
"points(X[1:4,1],X[1:4,2],col=1:4,cex=1.5,pch=as.character(1:4),font=1)\n",
"legend(\"topright\",paste0(\"Sensor \",1:4),col=1:4,pch=pch_est)\n",
"for(jj in 1:4){\n",
" v <- avar[(2*jj-1):(2*jj),(2*jj-1):(2*jj)]\n",
" points(ellipse(centre=Xhat[jj,],v,level=0.95),type='l',col=jj)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Important Points\n",
"* Local maxima represent a challenge to optimizers such as BFGS. One method to address this challenge is to use many initial values. In nice examples all initial values will converge to the same location. When this does not happen (such as here), you can choose the highest local max.\n",
"* The local maxima can have interesting physical interpretations, so it may be a poor idea to simply throw out the local maximum and only report the global max.\n",
"* The inverse negative hessian matrix (inverse fisher information) approximation to the parameter variance is **not** appropriate for models which have multiple modes of comparable size or non--elliptical (banana) uncertainties. As the amount of data increases, these situations become less common. Thus the inverse Fisher information is most appropriate in large n / large sample size situations.\n",
"* Bayesian approaches are one way to address the challenge of multimodal likelihoods. Bayesian posteriors can give a more refined summary of the highly probable regions of parameter space. These more refined summaries come at the cost of having to specify a prior distribution. Often the computation for these models is more challenging as well. The article from which this data was taken discusses this model from a Bayesian perspective."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Exercise: ** Analytically compute and code gradient of likelihood and pass as `gr` argument to `optim`. Do you notice any improvement in terms of algorithm speed?\n",
"\n",
"** Exercise: ** Add some sensors to this problem and simulate from the model. Refit the model. Create a situation where one does not have these local maxima."
]
},
{
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