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"# GPy Introduction: Covariance Functions in GPy\n",
"## Gaussian Process Winter School, Genova, Italy\n",
"\n",
"### 20th January 2014\n",
"\n",
"### Neil D. Lawrence and Nicolas Durrande\n"
]
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"input": [
"%matplotlib inline\n",
"from IPython.display import display\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pods\n",
"import GPy"
],
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"## Covariance Functions in GPy\n",
"\n",
"In the last session we introduced Gaussian process models through constructing covariance functions in `numpy`. The `GPy` software is a BSD licensed software package for modeling with Gaussian processes in python. It is designed to make it easy for the user to construct models and interact with data. The software is BSD licensed to ensure that there are as few as possible constraints on its use. The `GPy` documentation is produced with Sphinx and is available [here](http://gpy.readthedocs.org/en/latest/).\n",
"\n",
"In the introduction to Gaussian processes we defined covariance functions (or kernels) as functions to which we passed objects in `GPy` covariance functions are objects.\n",
"\n",
"In `GPy` the covariance object is stored in `GPy.kern`. There are several covariance functions available. The exponentiated quadratic covariance is stored as `RBF` and can be created as follows."
]
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"cell_type": "code",
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"input": [
"k = GPy.kern.RBF(input_dim=1)\n",
"display(k)"
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"html": [
"\n",
"
\n",
"\n",
" rbf. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 1.0 | +ve | | |
\n",
"lengthscale | 1.0 | +ve | | |
\n",
"
"
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""
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"Here it's been given the name 'rbf' by default and some default values have been given for the lengthscale and variance, we can also name the covariance and change the initial parameters as follows,"
]
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"cell_type": "code",
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"input": [
"k = GPy.kern.RBF(input_dim=1, name='signal', variance=4.0, lengthscale=2.0)\n",
"display(k)"
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"\n",
"\n",
"\n",
" signal. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 4.0 | +ve | | |
\n",
"lengthscale | 2.0 | +ve | | |
\n",
"
"
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""
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"### Plotting the Kernel\n",
"\n",
"The covariance function expresses the covariation between two points. the `.plot()` method can be applied to the kernel to discover how the covariation changes as a function as one of the inputs with the other fixed (i.e. it plots `k(x, z)` as a function of a one dimensional `x` whilst keeping `z` fixed. By default `z` is set to `0.0`."
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"text": [
""
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here the title of the kernel is taken from the name we gave it (`signal`). \n",
"\n",
"## Changing Covariance Function Parameters\n",
"\n",
"When we constructed the covariance function we gave it particular parameters. These parameters can be changed later in a couple of different ways firstly, we can simple set the field value of the parameters. If we want to change the lengthscale of the covariance to 3.5 we do so as follows."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k.lengthscale = 3.5\n",
"display(k)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
" signal. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 4.0 | +ve | | |
\n",
"lengthscale | 3.5 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can even change the naming of the parameters, let's imagine that this covariance function was operating over time instead of space, we might prefer the name `timescale` for the `lengthscale` parameter."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k.lengthscale.name = 'timescale'\n",
"display(k)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
" signal. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 4.0 | +ve | | |
\n",
"timescale | 3.5 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can set the time scale appropriately."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k.timescale = 10.\n",
"display(k)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
" signal. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 4.0 | +ve | | |
\n",
"timescale | 10.0 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Further Covariance Functions in GPy\n",
"\n",
"There are other types of basic covariance function in `GPy`. For example the `Linear` kernel,\n",
"$$\n",
"k(\\mathbf{x}, \\mathbf{z}) = \\alpha \\mathbf{x}^\\top \\mathbf{z}\n",
"$$\n",
"and the `Bias` kernel,\n",
"$$\n",
"k(\\mathbf{x}, \\mathbf{z}) = \\alpha\n",
"$$\n",
"where everything is equally correlated to each other. `Brownian` implements Brownian motion which has a covariance function of the form,\n",
"$$\n",
"k(t, t^\\prime) = \\alpha \\text{min}(t, t^\\prime).\n",
"$$\n",
"\n",
"Broadly speaking covariances fall into two classes, *stationary* covariance functions, for which the kernel can always be written in the form\n",
"$$\n",
"k(\\mathbf{x}, \\mathbf{z}) = f(r)\n",
"$$\n",
"where $f(\\cdot)$ is a function and $r$ is the distance between the vectors $\\mathbf{x}$ and $\\mathbf{z}$, i.e.,\n",
"$$\n",
"r = ||\\mathbf{x} - \\mathbf{z}||_2 = \\sqrt{\\left(\\mathbf{x} - \\mathbf{z}\\right)^\\top \\left(\\mathbf{x} - \\mathbf{z}\\right)}.\n",
"$$\n",
"This partitioning is reflected in the object hierarchy in GPy. There is a base object `Kern` and this is inherited by `Stationary` to form the stationary covariance functions (like `RBF` and `Matern32`).\n",
"\n",
"## Computing the Covariance Function\n",
"\n",
"When using `numpy` to construct covariances we defined a function, `kern_compute` which returned a covariance matrix given the name of the covariance function. In `GPy`, the base object `Kern` implements a method `K`. That allows us to compute the associated covariance. Visualizing the structure of this covariance matrix is often informative in understanding whether we have appropriately captured the nature of the relationship between our variables in our covariance function. In `GPy` the input data is assumed to be provided in a matrix with $n$ rows and $p$ columns where $n$ is the number of data points and $p$ is the number of features we are dealing with. We can compute the entries to the covariance matrix for a given set of inputs `X` as follows."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = pods.datasets.olympic_marathon_men()\n",
"# Load in the times of the olympics\n",
"X = data['X']\n",
"K=k.K(X)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now to visualize this covariation between the time points we plot it as an image using the `imshow` command from matplotlib.\n",
"```python\n",
"imshow(K, interpolation='None')\n",
"```\n",
"Setting the interpolation to `'None'` prevents the pixels being smoothed in the image. To better visualize the structure of the covariance we've also drawn white lines at the points where the First World War and the Second World War begin. At other points the Olympics are held every four years and the covariation is given by the computing the covariance function for two points which are four years apart, appropriately scaled by the time scale."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def visualize_olympics(K):\n",
" \"\"\"Helper function for visualizing a covariance computed on the Olympics training data.\"\"\"\n",
" fig, ax = plt.subplots(figsize=(8,8))\n",
" im = ax.imshow(K, interpolation='None')\n",
"\n",
" WWI_index = np.argwhere(X==1912)[0][0]\n",
" WWII_index = np.argwhere(X==1936)[0][0]\n",
"\n",
" ax.axhline(WWI_index+0.5,color='w')\n",
" ax.axvline(WWI_index+0.5,color='w')\n",
" ax.axhline(WWII_index+0.5,color='w')\n",
" ax.axvline(WWII_index+0.5,color='w')\n",
" plt.colorbar(im)\n",
" \n",
"visualize_olympics(k.K(X))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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"text": [
""
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k.timescale"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
"\n",
" Index | \n",
" signal.timescale | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"[0] | 10.0 | +ve | | N/A |
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 11,
"text": [
"\u001b[1msignal.timescale\u001b[0;0m:\n",
"Param([ 10.])"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"of 10 is ensuring that neighbouring Olympic years are correlated, but there is only weak dependency across the period of each of the world wars. If we increase the timescale to 20 we obtain stronger dependencies between the wars."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k.timescale = 20\n",
"visualize_olympics(k.K(X))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ibomIOyLiD2abuoFQklSEiFgEfBpYSe96q5Mi4tWTmp0BbMjMw4Ax4JMRMeNp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\nMxBKkjrNQChJ6rT/DzFgfmdhn+YkAAAAAElFTkSuQmCC\n",
"text": [
""
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Covariance Matrices and Covariance Functions\n",
"\n",
"A Gaussian process specifieds that any finite set of realizations of the function will jointly have a Gaussian density. In other words, if we are interested in the joint distribution of function values at a set of particular points, realizations of those functions can be sampled according to a Gaussian density. The Gaussian process provides a prior over an infinite dimensional object: the function. For our purposes we can think of a function as being like an infinite dimensional vector. The mean of our Gaussian process is normally specified by a vector, but is now itself specified by a *mean function*. The covariance of the process, instead of being a matrix is also a *covariance function*. But to construct the infinite dimensional matrix we need to make it a function of two arguments, $k(\\mathbf{x}, \\mathbf{z})$. When we compute the covariance matrix using `k.K(X)` we are computing the values of that matrix for the different entries in $\\mathbf{X}$. `GPy` also allows us to compute the cross covariance between two input matrices, $\\mathbf{X}$ and $\\mathbf{Z}$.\n",
"\n",
"## Sampling from a Gaussian Process\n",
"\n",
"We cannot sample a full function from a process because it consists of infinite values, however, we can obtain a finite sample from a function as described by a Gaussian process and visualize these samples as functions. This is a useful exercise as it allows us to visualize the type of functions that fall within the support of our Gaussian process prior. Careful selection of the right covariance function can improve the performance of a Gaussian process based model in practice because the covariance function allows us to bring domain knowledge to bear on the problem. If the input domain is low dimensional, then we can at least ensure that we are encoding something reasonable in the covariance through visualizing samples from the Gaussian process. \n",
"\n",
"For a one dimensional function, if we select a vector of input values, represented by `X`, to be equally spaced, and ensure that the spacing is small relative to the lengthscale of our process, then we can visualize a sample from the function by sampling from the Gaussian (or a multivariate normal) with the `numpy` command\n",
"```python\n",
"F = np.random.multivariate_normal(mu, K, num_samps).T\n",
"```\n",
"where `mu` is the mean (which we will set to be the zero vector) and `K` is the covariance matrix computed at the points where we wish to visualize the function. The transpose at the end ensures that the the matrix `F` has `num_samps` columns and $n$ rows, where $n$ is the dimensionality of the *square* covariance matrix `K`. \n",
"\n",
"Below we build a simple helper function for sampling from a Gaussian process and visualizing the result. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sample_covariance(kern, X, num_samps=10):\n",
" \"\"\"Sample a one dimensional function as if its from a Gaussian process with the given covariance function.\"\"\"\n",
" from IPython.display import HTML\n",
" display(HTML('Samples from a Gaussian Process with ' + kern.name + ' Covariance
'))\n",
" display(k)\n",
" K = kern.K(X) \n",
"\n",
" # Generate samples paths from a Gaussian with zero mean and covariance K\n",
" F = np.random.multivariate_normal(np.zeros(X.shape[0]), K, num_samps).T\n",
"\n",
" fig, ax = plt.subplots(figsize=(8,8))\n",
" ax.plot(X,F)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now in a position to define a vector of inputs, a covariance function, and then to visualize the samples from the process."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# create an input vector\n",
"X = np.linspace(-2, 2, 200)[:, None]\n",
"\n",
"# create a covariance to visualize\n",
"k = GPy.kern.RBF(input_dim=1)\n",
"\n",
"# perform the samples.\n",
"sample_covariance(k, X)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"Samples from a Gaussian Process with rbf Covariance
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
},
{
"html": [
"\n",
"\n",
"\n",
" rbf. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 1.0 | +ve | | |
\n",
"lengthscale | 1.0 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Vr1Z7EzVIblyEEI7xySfw2mu6963BP+s61Yrjx38mJeUOYmPj8PGp3dKCbj2G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shdtBAiIkZRTs5WlYzdFpVeKaXrDtdJWtK8ZZy4WycozUKHSv+3XLAYYmNjycPDgxYuXKjS3fjq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\ne7OeNIntwt6xg72Bcy1WcLAAYf3DYPuCL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"text": [
""
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = GPy.kern.Poly(input_dim=1, order=6)\n",
"X = np.linspace(-.8, .8, 500)[:, None]\n",
"sample_covariance(k, X)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"Samples from a Gaussian Process with poly Covariance
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
},
{
"html": [
"\n",
"\n",
"\n",
" poly. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"variance | 1.0 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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hUq9JTOw5kWYOtfzvqYrUzmHwqzlyRP2DWr0aBg+GZ5+F/v11ce5HCHFlFk1j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\nWlzMiVFRXPX555z96adEPvkkXHyxfKuJZuHxFFJVtYLKyhVUVa2gqmo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UKrT2s3BhXzZv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"text": [
""
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combining Covariance Functions\n",
"\n",
"Covariance functions can be combined in various ways to make new covariance functions. \n",
"\n",
"### Adding Covariance Functions\n",
"\n",
"Perhaps simplest thing you can do to combine covariance functions is to add them. The sum of two Gaussian random variables is also Gaussian distributed, with a covariance equal to the sum of the covariances of the original variables (similarly for the mean). This implies that if we add two functions drawn from Gaussian processes together, then the result is another function drawn from a Gaussian process, and the covariance function is the sum of the two covariance functions of the original process.\n",
"$$\n",
"k(\\mathbf{x}, \\mathbf{z}) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(\\mathbf{x}, \\mathbf{z}).\n",
"$$\n",
"Here the domains of the two processes don't even need to be the same, so one of the covariance functions could perhaps depend on time and the other on space,\n",
"$$\n",
"k\\left(\\left[\\mathbf{x}\\quad t\\right], \\left[\\mathbf{z}\\quad t^\\prime\\right]\\right) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(t, t^\\prime).\n",
"$$\n",
"\n",
"In `GPy` the addition operator is overloaded so that it is easy to construct new covariance functions by adding other covariance functions together."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k1 = GPy.kern.RBF(1, variance=4.0, lengthscale=10., name='long term trend')\n",
"k2 = GPy.kern.RBF(1, variance=1.0, lengthscale=2., name='short term trend')\n",
"k = k1 + k2\n",
"k.name = 'signal'\n",
"k.long_term_trend.lengthscale.name = 'timescale'\n",
"k.short_term_trend.lengthscale.name = 'timescale'\n",
"display(k)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
" signal. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"long term trend.variance | 4.0 | +ve | | |
\n",
"long term trend.timescale | 10.0 | +ve | | |
\n",
"short term trend.variance | 1.0 | +ve | | |
\n",
"short term trend.timescale | 2.0 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Multiplying Covariance Functions\n",
"\n",
"An alternative is to multiply covariance functions together. This also leads to a valid covariance function (i.e. the kernel is within the space of Mercer kernels), although the interpretation isn't as straightforward as the additive covariance. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k1 = GPy.kern.Linear(1)\n",
"k2 = GPy.kern.RBF(1)\n",
"k = k1*k2\n",
"display(k)\n",
"visualize_olympics(k.K(X))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n",
"\n",
" mul. | \n",
" Value | \n",
" Constraint | \n",
" Prior | \n",
" Tied to | \n",
"
\n",
"linear.variances | 1.0 | +ve | | |
\n",
"rbf.variance | 1.0 | +ve | | |
\n",
"rbf.lengthscale | 1.0 | +ve | | |
\n",
"
"
],
"metadata": {},
"output_type": "display_data",
"text": [
""
]
},
{
"ename": "IndexError",
"evalue": "index 0 is out of bounds for axis 0 with size 0",
"output_type": "pyerr",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mk1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mk2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mvisualize_olympics\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m\u001b[0m in \u001b[0;36mvisualize_olympics\u001b[0;34m(K)\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0max\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterpolation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'None'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mWWI_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1912\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0mWWII_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margwhere\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1936\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mIndexError\u001b[0m: index 0 is out of bounds for axis 0 with size 0"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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U+OCwbcP+ZfC6fO1VxlypvI6FwqeMURM4eKIun0X9es63rfS9KWor4XJEzfVr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\nt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iCibyCiTxLRs0T0HBG9ty/359wYRHTa58v46/7en3FDzJOTZItFM5gR0SmAP8R2//UD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\n",
"text": [
""
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our choice of `X` means that the points are close enough together to look like functions. We can see the structure of the covariance matrix we are plotting from if we visualize C."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.matshow(C)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 253,
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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U3GS354wlv3O2P4EoiUnqyKATc5Pu1RsSk/JkbhIqrLnJVfVnyKm5KVoe/Zog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\nRK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 253
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now try a range of different covariance functions and values and plot the corresponding sample paths for each using the same approach given above."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Try plotting sample paths here"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 254
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise 3\n",
"\n",
"Can you tell the covariance structures that have been used for generating the\n",
"sample paths shown in the figure below?\n",
"
\n",
"\n",
" \n",
"\n",
" \n",
"\n",
" \n",
"\n",
"\n"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"# Exercise 3 answer"
]
}
],
"metadata": {}
}
]
}