{ "cells": [ { "cell_type": "markdown", "id": "f569a665-f294-4842-9ff6-d602efc63e40", "metadata": {}, "source": [ "# Log Gaussian" ] }, { "cell_type": "markdown", "id": "6b9201df-6507-46df-96e2-a6580f9bf43b", "metadata": {}, "source": [ "`lamatrix` provides a log Gaussian to fit to data. This model has some nuances, let's take a look." ] }, { "cell_type": "markdown", "id": "bfba5521-cf4f-4b81-9733-945b3e0e2250", "metadata": {}, "source": [ "Let's look at the equation for this model" ] }, { "cell_type": "code", "execution_count": 1, "id": "47e00fe5-dd14-4dbb-ab90-4df8c172f663", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "x = np.arange(-10, 10, 0.01)\n", "\n", "\n", "from lamatrix import lnGaussian, Gaussian" ] }, { "cell_type": "code", "execution_count": 2, "id": "6d10c015-e724-465d-bbdf-c3db1b0e3581", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\\[f(\\mathbf{x}) = w_{0} x^2 + w_{1} x + w_{2} \\]
" ], "text/plain": [ "'\\\\[f(\\\\mathbf{x}) = w_{0} x^2 + w_{1} x + w_{2} \\\\]'" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lnGaussian().equation" ] }, { "cell_type": "markdown", "id": "ece54058-935f-4d69-a786-607e96c2c3cc", "metadata": {}, "source": [ "You can see here, this looks like a simple 2nd order polynomial. Let's remind ourselves of the equatino for a Gaussian\n", "\n", "\n", "$$\n", "G(x) = A\\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}\n", "$$\n", "\n", "We see that this is linear only in one of these variables: $A$. But if we look in log space\n", "$$\n", "\\ln(G(x)) = \\ln(A) -\\frac{1}{2} \\ln(2\\pi\\sigma^2) - \\frac{(x - \\mu)^2}{2\\sigma^2}\n", "$$\n", "Which expands to\n", "$$\n", "\\ln(G(x)) = \\ln(A) -\\frac{1}{2} \\ln(2\\pi\\sigma^2) - \\frac{x^2}{2\\sigma^2} + \\frac{x\\mu}{\\sigma^2} - \\frac{\\mu^2}{2\\sigma^2}\n", "$$\n", "\n", "\n", "We see that this is now a linear model where\n", "$$\n", "a = - \\frac{1}{2\\sigma^2}\n", "$$\n", "$$\n", "b = \\frac{\\mu}{\\sigma^2}\n", "$$\n", "$$\n", "c = \\ln(A) -\\frac{1}{2} \\ln(2\\pi\\sigma^2) - \\frac{\\mu^2}{2\\sigma^2}\n", "$$\n", "$$\n", "\\ln(G(x)) = a x^2 + b x + c\n", "$$\n", "\n", "This is our simple 2nd order polynomial. But you see here, there are some constraints on the weights $a$, $b$ and $c$ which relate to the properties of the Gaussian $\\mu$, $\\sigma$ and $A$.\n", "\n", "In our framework we are able to put Gaussian priors our coefficients. We specify them with `(mean, standard deviation)` (see the tutorial on setting priors). We could set priors on $a$, $b$ and $c$, which would constraint $\\mu$, $\\sigma$ and $A$. Similarly, we could specify priors in $\\mu$, $\\sigma$ and $A$, and then calculate the effective priors on $a$, $b$ and $c$. This is what the `lnGaussian` model enables you to do. However there is a nuance; priors that are Gaussian on $a$, $b$ and $c$ are not Gaussian on $\\mu$, $\\sigma$ and $A$. And priors on $\\mu$, $\\sigma$ and $A$ are not Gaussian on $a$, $b$ and $c$. Let's see an example below" ] }, { "cell_type": "code", "execution_count": 3, "id": "4fc70c7d-19bd-4ed8-99cf-869401ba870e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate normal distributed sigma, mu, and A\n", "sigma, mu, A = np.random.normal(1, 0.1, size=(10000, 3)).T\n", "\n", "# Calculate a, b, c\n", "a = lambda sigma, mu, A: -(1/(2*sigma**2))\n", "b = lambda sigma, mu, A: mu/sigma**2\n", "c = lambda sigma, mu, A: np.log(A) - 0.5*np.log(2*np.pi*sigma**2) - (mu**2/2*sigma**2)\n", "\n", "# Plot as histographs\n", "fig, ax = plt.subplots(2, 3, figsize=(8, 5), sharey=True)\n", "[a.hist(var, 100, color='black') for a, var in zip(ax.ravel(), [sigma, mu, A, a(sigma, mu, A), b(sigma, mu, A), c(sigma, mu, A)])]\n", "[a.set(title=label) for a, label in zip(ax.ravel(), ['$\\sigma$', '$\\mu$', 'A', 'a', 'b', 'c'])];\n", "\n", "[a.axvline(np.nanmedian(var), ls='--', c='r') for a, var in zip(ax[0], [sigma, mu, A])]\n", "[a.axvline(np.nanmedian(var), ls='--', c='r') for a, var in zip(ax[1], [a(sigma, mu, A), b(sigma, mu, A), c(sigma, mu, A)])]\n", "\n", "plt.subplots_adjust(hspace=0.4)" ] }, { "cell_type": "markdown", "id": "5abf8013-2115-4326-adce-4225f36b41f0", "metadata": {}, "source": [ "Here we see that normal distributed $\\mu$, $\\sigma$ and $A$ result in non-normal distributed $a$, $b$ and $c$." ] }, { "cell_type": "markdown", "id": "10b077b0-6fbf-4cbe-ac44-c3ae67444b01", "metadata": {}, "source": [ "This is important to remember. In our framework of linear algebra, we are only able to put normal priors on any value. Therefore, inside `lnGaussian`, we are implicitly approximating all of these distributions as normal. " ] }, { "cell_type": "markdown", "id": "7cc35ac1-056d-451b-baa3-24a92dea4c3e", "metadata": {}, "source": [ "Let's see this in practice" ] }, { "cell_type": "code", "execution_count": 4, "id": "da63405a-772f-4b29-b10f-f704d6c84680", "metadata": {}, "outputs": [], "source": [ "model = lnGaussian(prior_sigma=(3, 0.1), prior_mu=(2, 0.1), prior_A=(10, 1))" ] }, { "cell_type": "markdown", "id": "291eaa2f-5f37-4086-8b22-988153716c2a", "metadata": {}, "source": [ "Here I've created a `lnGaussian` model with priors on $\\mu$, $\\sigma$ and $A$. This has then generated priors on the three coefficients $a$, $b$ and $c$" ] }, { "cell_type": "code", "execution_count": 5, "id": "04d1e4a1-9494-4e3e-a766-77b6b1eb435d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DistributionContainer\n", "\t[(-0.0556, 0.0037), (0.222, 0.019), (0.06, 0.11)]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.priors" ] }, { "cell_type": "markdown", "id": "32fba8c3-842c-453c-abcc-ddfb029c719d", "metadata": {}, "source": [ "These will be treated as normal distributions, even though we know this is an approximation. Let's create some models using these priors" ] }, { "cell_type": "code", "execution_count": 6, "id": "e1fa213d-33ff-4e0f-92f5-cffca2a03ecc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "[ax.plot(x, model(x=x).dot(model.priors.sample()), c='k', alpha=0.1) for count in range(100)];\n", "ax.set(xlabel='$x$', ylabel='$y$', title='lnGaussian model sample');" ] }, { "cell_type": "markdown", "id": "2b6a62a2-563a-4899-a5fe-edaacb5420ac", "metadata": {}, "source": [ "We see here that the draws from these priors create a similar trend, not a random 2nd order polynomial. Let's look at this in linear space instead of log space" ] }, { "cell_type": "code", "execution_count": 7, "id": "c07f6945-29c7-4d7b-9a1e-df89c0510307", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "[ax.plot(x, np.exp(model(x=x).dot(model.priors.sample())), c='k', alpha=0.1) for count in range(100)];\n", "ax.set(xlabel='$x$', ylabel='$y$', title='exp(lnGaussian) model sample');" ] }, { "cell_type": "markdown", "id": "6df331af-04b5-4892-943f-98ac339e2b9e", "metadata": {}, "source": [ "Now that we take the exponent we see this has drawn many Gaussians with properties similar to our input priors. However if we take 5000 draws and plot them we see that there is a bias in our sampling" ] }, { "cell_type": "code", "execution_count": 8, "id": "a0a08cd6-2b6a-4363-ad51-0536f2b4e36d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ar = np.asarray([np.exp(model(x=x).dot(model.priors.sample())) for count in range(5000)])\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x, ar.mean(axis=0), c='k')\n", "ax.fill_between(x, ar.mean(axis=0) - 2*ar.std(axis=0), ar.mean(axis=0) + 2*ar.std(axis=0), color='k', alpha=0.4) \n", "ax.set(xlabel='$x$', ylabel='$y$', title='exp(lnGaussian) model sample');" ] }, { "cell_type": "markdown", "id": "3fd92d22-d9b7-410d-a113-16b2461ee67b", "metadata": {}, "source": [ "Here we see we are slightly biased towards drawing lower values of $\\mu$. When using this model it is important to recognize that this is not a model that is unbiased in linear space.\n", "\n", "With those understandings, let's fit some data. We'll generate some fake data using the `Gaussian` model object." ] }, { "cell_type": "code", "execution_count": 9, "id": "3bff1914-5cfd-48d6-aa9f-fd5a25d7b733", "metadata": {}, "outputs": [], "source": [ "A, mu, sigma = 10, -0.5, 1\n", "truth = Gaussian('x', sigma=sigma, mu=mu)(x=x).dot([A]) \n", "data = truth + np.random.normal(0, 0.01, size=x.shape[0])\n", "errors = np.ones_like(x) * 0.01" ] }, { "cell_type": "code", "execution_count": 10, "id": "91fa3073-6d43-4ef4-9bdb-56b73283a23d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, data, errors, ls='', c='grey')\n", "ax.plot(x, truth, c='blue')\n", "ax.set(xlabel='$x$', ylabel='$y$', title='Noisy Gaussian Data and Best Fit');" ] }, { "cell_type": "markdown", "id": "f9355366-528c-4a98-8297-b98a26907787", "metadata": {}, "source": [ "When we look at the plotted data this looks good. To fit this we will have to fit in log space, let's look at the data in log space. To use log space we will have to look at only data that is positive. We wi ll have to remove any data that goes below 0 due to noise. We will remove any points that are less than zero." ] }, { "cell_type": "code", "execution_count": 11, "id": "1643cec0-e7b4-4626-8887-da83251a5a55", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/bv/0t7fjlgx0mx3_3bdhxqzd7bmh_67k0/T/ipykernel_22770/3557338474.py:3: RuntimeWarning: invalid value encountered in log\n", " ax.errorbar(x[k], np.log(data[k]), np.abs(errors/data)[k], ls='', c='grey', lw=1, label='data')\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "k = truth > 0\n", "ax.errorbar(x[k], np.log(data[k]), np.abs(errors/data)[k], ls='', c='grey', lw=1, label='data')\n", "ax.plot(x, np.log(truth), c='blue', label='truth')\n", "ax.axhline(np.log(0.01), c='lime', ls='--', label='log of average noise')\n", "ax.legend()\n", "ax.set(ylim=(-8, 2), xlabel='$x$', ylabel='$y$', title='Noisy Gaussian Data, log space');" ] }, { "cell_type": "markdown", "id": "f0248431-9d7e-485d-875d-3fee0508a45d", "metadata": {}, "source": [ "Here we see that the noise causes a \"floor\". Anywhere where the data is close to this noise floor will impact our fit. In the case that there is a lot of noise in the wings, you may need to remove this to ensure a good fit." ] }, { "cell_type": "code", "execution_count": 12, "id": "99610ada-876c-43a7-9096-9a4235b1abd4", "metadata": {}, "outputs": [], "source": [ "model = lnGaussian('x')\n", "k = data > 0\n", "model.fit(x=x[k], data=np.log(data[k]), errors=errors[k]/data[k])" ] }, { "cell_type": "code", "execution_count": 13, "id": "029c89ef-fccf-4e86-9e89-6f23520d569e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "k = data > 0\n", "ax.errorbar(x[k], np.log(data[k]), np.abs(errors/data)[k], ls='', c='grey', lw=1, label='data')\n", "ax.plot(x, model.evaluate(x=x), c='k', label='Best Fit')\n", "ax.legend()\n", "ax.set(ylim=(-8, 2), xlabel='$x$', ylabel='$y$', title='Noisy Gaussian Data, log space');" ] }, { "cell_type": "markdown", "id": "230f9cf3-aba2-4cae-babe-a420f24901e1", "metadata": {}, "source": [ "We see here that the model doesn't fit well at the wings. This is because the noise is more significant of a contribution in the wings and it's impacting our fit. We can remove those wings by removing any data that is within 3x the error of zero." ] }, { "cell_type": "code", "execution_count": 14, "id": "523513a1-8dd2-4485-acfe-55739eb10f36", "metadata": {}, "outputs": [], "source": [ "model = lnGaussian('x')\n", "k = data > 3*errors\n", "model.fit(x=x[k], data=np.log(data[k]), errors=errors[k]/data[k])" ] }, { "cell_type": "code", "execution_count": 15, "id": "f70877c0-df5a-463b-a369-35ad782e231f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "k = data > 0\n", "ax.errorbar(x[k], np.log(data[k]), np.abs(errors/data)[k], ls='', c='grey', lw=1, label='data')\n", "ax.plot(x, model.evaluate(x=x), c='k', label='Best Fit')\n", "ax.legend()\n", "ax.set(ylim=(-8, 2), xlabel='$x$', ylabel='$y$', title='Noisy Gaussian Data, log space');" ] }, { "cell_type": "markdown", "id": "e10f6db7-d7fd-4e69-9ffc-49d5eb9a6fd8", "metadata": {}, "source": [ "Let's look in linear space" ] }, { "cell_type": "code", "execution_count": 16, "id": "ef5c90db-28ad-416d-82bb-50aff5162f0e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, data, errors, ls='', c='grey', label='data')\n", "ax.plot(x, np.exp(model.evaluate(x=x)), c='k', label='best fit')\n", "ax.set(xlabel='$x$', ylabel='$y$', title='Noisy Gaussian Data');\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "49c20120-9655-43ae-97ea-2e50a31d8945", "metadata": {}, "source": [ "We can take a look at the results of our fit by looking at the posteriors" ] }, { "cell_type": "code", "execution_count": 17, "id": "9c761ddb-6239-4f50-b3e2-52e6c51fa2f2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DistributionContainer\n", "\t[(-0.49863, 0.00027), (-0.49828, 0.00038), (1.25817, 0.00024)]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.posteriors" ] }, { "cell_type": "markdown", "id": "467c788a-0594-44e6-b74d-0e5b719637df", "metadata": {}, "source": [ "These are the posteriors on our coefficients. We can convert these to posteriors on the Gaussian parameters, under the assumption that the distributions are all normal (which we tolerate is an approximation)" ] }, { "cell_type": "code", "execution_count": 18, "id": "65af3558-8e05-4cc5-b95f-99fdf34cbf78", "metadata": {}, "outputs": [], "source": [ "A, mu, sigma = model.coefficients_to_gaussian_parameters(model.posteriors)" ] }, { "cell_type": "code", "execution_count": 19, "id": "1e03aeb6-92b1-4e4f-9926-a5e5666aeb6a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((10.0038, 0.0047), (-0.49965, 0.00046), (1.00137, 0.00027))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A, mu, sigma" ] }, { "cell_type": "markdown", "id": "a2473425-4e95-46f3-81d8-d9da5b132658", "metadata": {}, "source": [ "Here we see these are the same as our inputs! We note that the reported errors are an approximation, and may be an underestimate.\n", "\n", "This model is a special case of a 2nd order polynomial to enable estimates of Gaussian parameters when using data in log space. It should be used with full understanding of the caveats discussed here, but can be powerful to fit Gaussian data." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }