{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Model selection and validation\n", "\n", "In this notebook we will study how to select the lag time of Markov state models or Hidden Markov models, and how the models can be validated in order to decide whether they can be used in order to make reliable predictions about the long-term kinetics of the molecular system studied.\n", "\n", "We start with a few general imports and settings" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "from pyemma import msm\n", "import pyemma.plots as mplt\n", "matplotlib.rcParams.update({'font.size': 14})" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# load double well data\n", "import pyemma.datasets\n", "double_well_data = pyemma.datasets.load_2well_discrete()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw double well and discretization\n", "-------\n", "We will use simulation data generated for a double-well potential. This data is part of the standard datasets in PyEMMA. In this notebook, we compare two discretizations: An excellent discretization with six states ('good discretization'), and a poor two-state discretization where the dividing surface is far away from the transition state ('bad discretization').\n", "\n", "Let's look at the double well potential and these two discretizations:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/marscher/miniconda/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == str('face'):\n" ] }, { "data": { "image/png": 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3FhsbS9u2bdmzZw8TJ06kV69eXivb3zlxrkVFRbFgwQJmz57Nhg0biI7+b6+Y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\nRKsP0BMoARy5YbeqaokkHcC9mPTy9JJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 10})\n", "fig, axis = subplots(1, 2, figsize=(10,2))\n", "P = double_well_data.transition_matrix\n", "mu = msm.markov_model(P).stationary_distribution\n", "E = -np.log(mu)\n", "# plot 1\n", "i = 0\n", "axis[i].set_title('good discretization')\n", "axis[i].plot(E-2.0, linewidth=2, color='black')\n", "axis[i].fill_between(range(len(E)), np.zeros(len(E)), E-2.0, color='lightgrey')\n", "axis[i].set_xlim(20,80); axis[i].set_xlabel('x'); axis[i].set_ylim(0,8); axis[i].set_ylabel('free energy / kT')\n", "for b in [40, 45, 50, 55, 60]:\n", " axis[i].plot([b, b], [0, 8], linewidth=2, linestyle='dashed', color='black')\n", "# plot 2\n", "i = 1\n", "axis[i].set_title('bad discretization')\n", "axis[i].plot(E-2.0, linewidth=2, color='black')\n", "axis[i].fill_between(range(len(E)), np.zeros(len(E)), E-2.0, color='lightgrey')\n", "axis[i].set_xlim(20,80); axis[i].set_xlabel('x'); axis[i].set_ylim(0,8); axis[i].set_ylabel('free energy / kT')\n", "axis[i].set_ylabel(''); axis[i].yaxis.set_ticklabels([]); \n", "axis[i].plot([40, 40], [0, 8], linewidth=2, linestyle='dashed', color='black')\n", "#\n", "savefig('figs/fig_selval_ab.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Timescales: MSM\n", "-----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we want to build Markov state models. Since the discretization is given, the only parameter that still needs to be selected is the lag time. Both the discretization and the lag time are crucial for the approximation quality of a Markov state model [1,2].\n", "\n", "One common approach to select a lagtime is to compute the relaxation timescales implied by the estimated Markov state model [3], shortly called implied timescales: \n", "\n", "$ t_i = -\\tau / \\ln | \\lambda_i (\\tau)| $\n", "\n", "where $\\lambda_i(\\tau)$ are the eigenvalues of the Markov state model estimated at lag time $\\tau$. As the relaxation timescales are physical properties of the system the implied timescales should be independent of the lag time tau. In practice, this will not be fulfilled for short lag times due to discretization errors [2]. It will neither be fulfilled for very long lag times exceeding the implied timescales as the Markov model eigenvalues are then essentially resulting from the projection on random vectors [4]." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "its_good_msm = msm.timescales_msm([double_well_data.dtraj_T100K_dt10_n6good], lags = 100)\n", "its_bad_msm = msm.timescales_msm([double_well_data.dtraj_T100K_dt10_n2bad], lags = 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting these implied timescales already show that the good discretization converges at a lag time of about 20-40 steps to a timescale somewhat about 300, while the bad discretization doesn't appear to converge. According to the variational principle of conformation dynamics [5], we know in principle that the model with longer timescales are preferable, so at this point we might select the first discretization and a lag time of 20-40 steps..." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qas/27UPBVmHp64PVq+Ev/xJOPx0+/OFoFPmkz5rsplglbcIOA74KvBjYTjRA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\nTzxmsUoAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axis = subplots(1, 2, figsize=(10,2))\n", "mplt.plot_implied_timescales(its_good_msm, ax=axis[0], ylog=False)\n", "ylim(0, 400); axis[0].set_title('good discretization')\n", "mplt.plot_implied_timescales(its_bad_msm, ax=axis[1], ylog=False)\n", "ylim(0, 400); ylabel(''); axis[1].set_title('bad discretization')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we don't know if the observations below are statistically significant. In particular, if only knew the bad discretization, it would be difficult to decide based on the plot above whether the implied timescale is sufficiently flat at any of the shown lag times. For this reason we compute the implied timescales including statistical errors. This option will use Bayesian transition matrix sampling as described in [6]. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "its_good_bmsm = msm.timescales_msm([double_well_data.dtraj_T100K_dt10_n6good], lags = 100, errors='bayes')\n", "its_bad_bmsm = msm.timescales_msm([double_well_data.dtraj_T100K_dt10_n2bad], lags = 100, errors='bayes')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we see that the uncertainties (by default two sigma's = 95% confidence are shown) are small compared to the tau-dependent changes of the timescales in the bad discretization and we can reject that discretization even without knowing about the good discretization. The good discretization has a timescale that is indistinguishable from a constant af lag times of about 30 steps or longer." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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btrTf6urc/v33obYW6utvRvX7Yek7PxwpIi8AZwfXLgY2i8jL6TFe+aKpye/6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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 10})\n", "fig, axis = subplots(1, 2, figsize=(10,2))\n", "#\n", "mplt.plot_implied_timescales(its_good_bmsm, ax=axis[0], ylog=False)\n", "axis[0].set_ylim(0, 500); \n", "axis[0].set_title('good discretization')\n", "#\n", "mplt.plot_implied_timescales(its_bad_bmsm, ax=axis[1], ylog=False)\n", "axis[1].set_ylim(0, 500); axis[1].set_ylabel(''); axis[1].yaxis.set_ticklabels([]);\n", "axis[1].set_title('bad discretization')\n", "#\n", "savefig('figs/fig_selval_cd.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Timescales: HMSM\n", "------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us use a different model: a discrete Hidden Markov model (HMM) [7]. For metastable systems such as this one, discrete HMMs can be shown to be excellent approximations to PMMs, that are exact descriptions of the non-Markovian dynamics on discretized state spaces for metastable dynamics [8]. We estimate the HMM as described in [8], which involves to first estimate a coarse-grained Markov state model and then running a HMM estimation on top of it. This is a bit slower than MSM estimation:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "its_good_hmm = msm.timescales_hmsm([double_well_data.dtraj_T100K_dt10_n6good], 2, lags = 100)\n", "its_bad_hmm = msm.timescales_hmsm([double_well_data.dtraj_T100K_dt10_n2bad], 2, lags = 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the good discretization seems to converge much faster, and to a timescale that is a little bit larger than that of the MSM model. Even the bad discretization reaches similar timescales, after about 40 steps, where the MSM on the same discretization was completely hopeless." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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SKhG/3B/MbHQp2BImaXFEHCnpn0lawS6V9HjmznCkuSXMbPQZLQt4v/a18J3v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\ntW6SZgP/CuwH7AnsLulD2Z+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axis = subplots(1, 2, figsize=(10,2))\n", "mplt.plot_implied_timescales(its_good_hmm, ax=axis[0], ylog=False)\n", "ylim(0, 400); axis[0].set_title('good discretization')\n", "mplt.plot_implied_timescales(its_bad_hmm, ax=axis[1], ylog=False)\n", "ylim(0, 400); ylabel(''); axis[1].set_title('bad discretization')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But let's compute statistical errors to see if these observations are significant. We do this by using the algorithms described in [9]." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "its_good_bhmm = msm.timescales_hmsm([double_well_data.dtraj_T100K_dt10_n6good], 2, lags = 100, errors='bayes')\n", "its_bad_bhmm = msm.timescales_hmsm([double_well_data.dtraj_T100K_dt10_n2bad], 2, lags = 100, errors='bayes')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the slightly higher timescale estimate compared to the MSM is not statistically significant. However, the HMMs are useable for lag times of about 5 steps for the good and 10 steps for the bad discretization." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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30kvuPUsWH5rPRCJOZK1eDf/4h4sLbm11x6ZPd56t2bOdZ8uP5bSGkZENwuH+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\nIjXA74GLVHW7BMZJq6qKSKp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 10})\n", "fig, axis = subplots(1, 2, figsize=(10,2))\n", "#\n", "mplt.plot_implied_timescales(its_good_bhmm, ax=axis[0], ylog=False)\n", "axis[0].set_ylim(0, 500); \n", "axis[0].set_title('good discretization')\n", "#axis[0].text(-22, 540, 'g)', fontsize=16)\n", "#\n", "mplt.plot_implied_timescales(its_bad_bhmm, ax=axis[1], ylog=False)\n", "axis[1].set_ylim(0, 500); axis[1].set_ylabel(''); axis[1].yaxis.set_ticklabels([]); # axis[1].set_title('bad discretization')\n", "axis[1].set_title('bad discretization')\n", "#axis[1].text(-10, 540, 'h)', fontsize=16)\n", "#\n", "savefig('figs/fig_selval_gh.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Chapman-Kolmogorov Test\n", "-------\n", "\n", "Implied timescales can help to make the lag time decision, but they are not very strong tests of the validity of the model, because they only look at eigenvalues, while there is a lot of information in the eigenvectors. The Chapman-Kolmogorov Test as described in [1] is much stronger. In PyEMMA we have generalized the concept of the Chapman-Kolmogorov Test in order to be able to test various different models. The idea is: given a model estimated at lag time $\\tau$, let's make a prediction of a model quantity for lag time $k \\tau$, and let's compare that to an independently estimated a model at $k \\tau$. The standard cktest computes the transition probability between metastable states for different lag times. \n", "\n", "So let's do MSM estimates at a (conservative) lag time of 40 steps." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "MLMSM_good = msm.estimate_markov_model([double_well_data.dtraj_T100K_dt10_n6good], 40)\n", "ck_good_msm = MLMSM_good.cktest(2)\n", "MLMSM_bad = msm.estimate_markov_model([double_well_data.dtraj_T100K_dt10_n2bad], 40)\n", "ck_bad_msm = MLMSM_bad.cktest(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the result. This looks pretty good." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(,\n", " array([[,\n", " ],\n", " [,\n", " ]], dtype=object))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GZR9+CI8/Dj17wq23nuGuu+YxZ84UIiNn0LhxY4YPH86nn35K165dbc+iIOV2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\n/nXv9pl3obr+rekK6SHAq4SKk6GUUaEHHAIcGuc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_cktest(ck_good_msm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wherease the comparison for the bad discretization is clearly a failure:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(,\n", " array([[,\n", " ],\n", " [,\n", " ]], dtype=object))" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/nNbC/PnQtq3X1YSfqrJ58+Zgq2DhwoV89913dO3alT59+vCHP/yBXr16Ua9e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\ne88C3YB3cf54/0pEeqvqo6d5a3dgnap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Xfmd5U6ZMiZXX6XtQ4stKPendVCqVUc6KFSti\n5XX6Jkn82ydbDps3b2bWrFm88MILjB49uhcjc/o7PkLa6csMqBHSBw4coK6ujuXLl3vF4DiOUyL6\nVMvhyJEOpk//e2pqRrF06dLeDssZAHjLwenLlO2T4CRNB/4ZGAQsN7MfZ0nzL8ClwCHgK2a2NUsa\nMzNqa59iy5aT2L//gmPuD3ecUuGVg9OXKcvLSpIGAXcD04FPAXWSzumWZgYw1szGAf8A/CyX3r33\nvkx9/afYsCGVuGJoampKlN/1ylev2LGVG+V87F2v/PSSUMo+hwuAVjN7zczagTXAFd3SzARWAJjZ\nc8BwSVlv8l6woJqbbtrF5z9/euLAyv0Ldb3y0CpHyvnYu1756SWhlJXD6cAbae//P2w7XpozsomN\nH7+T2267oKgBOo7jONkpZeUQ90Jr9+thWfM9/fSkZNE4juM4sSlZh7SkCcAtZjY9vL8R6EjvlJb0\nr0CTma0J73cAk81sXzct79Fzeo2kHdLFjMVxTpRC/VvKuZWagXGSUsAe4CqgrluadcBCYE2oTN7t\nXjFAspPTcXoT967TVylZ5WBmRyQtBB4nupX1ATPbLunr4fN7zWyDpBmSWoEPgHmlisdxHMeJT58Y\nBOc4juP0MIVOytQTC9EYiR3ATuCGAjVeA7YBW4Hnw7Zq4Angd8AvgeF58v8c2Ae8nLYtZ37gxhDv\nDmBaTL1biO7U2hqWS09AbzTQCPwG+D/gW0lizKNXUIzAx4HngBbgFeCOhPHl0ktyDAeFPI8l/X77\ns39zaCU57u7dhMewpP4txLA9sYQdbgVSwOBwQM8pQGcXUN1t253Ad8P6DcCSPPkvBGq6nRBZ8xMN\n9msJ8aZC/BUx9G4GFmUpO47eqcD4sH4y8FvgnEJjzKOXJMbK8HoS8CzwhYTHMJtekvgWAQ8B65J+\nv/3Zvzm03Lu96N1S+desvB8TGmcQXVy6dwp2Db4Lr3+bK6OZPQMcjJn/CmC1mbWb2WtEB/+YwRk5\n9LLFGFdvr5m1hPX3ge1E40cKijGPXpIYD4XVIUQ/mgcLjS+PXkHxSToDmAEsT8tfcGxp9Dv/unfL\ny7tQUv+WdeUQZxBdHAxokNQs6Wth20g7elfUPiD7o7dykyv/aSHOQmL+pqSXJD0gaXgheuHOsBqi\npmviGNP0nk0So6QKSS0hjkYz+02S+HLoFRrfMuB6oCNtWzG+34HkX/duMr2C46N0/i3ryqFYPeWT\nzKyGaHK/BZIuPKaQqL1VcFkx8sfR/hnwSWA88Bbw0xPVk3Qy8B/AdWb2XtIYg96jQe/9JDGaWYeZ\njSca/X6RpClJ4suid3Eh8Um6DNhv0WSPWW85TfD9DhT/und7wbtQcv+WdeXwJlEHUyejObbWi4WZ\nvRVe/wD8F1Ezap+kUwEkjQL2n6BsrvzdYz4jbDtejPstQNQ87GzqxdKTNJjo5FppZmuTxpim9++d\nekljDBp/BNYD5yWJL4ve+QXGNxGYKWkXsBqYKmllMWLLkrZf+te922vehdL6t6w7pE8Cfk/UcTKE\nAjr0gEpgWFivAjYD04g6bG4I279Hng69kCZFZodeRn6OdvgMIfon8HvC7cLH0RuVtv4dYFVcPaJ/\nDP8GLOu2vaAY8+gVFCMwgnC3BDAUeBq4JEF8ufROLfQYhnSTOXq3R6Lvtz/7N4uWe7eXvVsK/5pZ\n+VYOYWcuJbrjoBW4sYD8nwwHo4Xo1rYbw/ZqoIF4twKuJhrh3UZ0DXlevvzA90O8O4AvxtD7ajD0\nNuAlYC3RNcO4el8gut7YwtFb4aYXGmMOvUsLjRH4G+DXQW8bcP3xvoMC9Qo+hmkn17oksfV3/2bR\ncu+WgXdL5V8fBOc4juNkUM59Do7jOE4v4ZWD4ziOk4FXDo7jOE4GXjk4juM4GXjl4DiO42TglYPj\nOI6TgVcORUTS+0XSuULSOWnvfyjpkmJoZymrQdKwPJ9/W9LQIpf5aUkPFFPTSYZ7N3aZA8a7XjkU\nl2INGrmSaDRjJGp2s5k9WSTtLiRNBX5r3eaz6cZ1RCN1i4aZbQPOkvTXxdR1EuHejcFA8q5XDiVA\n0snhX82LkrZJmpn22Q8k7ZD0jKRVkv6pW96JwOXAUkm/ljRG0i8kzQqfvybpR5K2hpk6PyPpl5Ja\nFR7BGtJdL+n5MNPjLTlC/TLw3yF9laT1klokvSxptqRvEs3k2CjpyZBumqQtYd8ekVSVFtePw/4+\nJ+mssP1LQa9F0lNpZdcDX0p0oJ2i495173ZxokP6fck73cF74XUQR+fEGQHsDOufJRrSP4ToYSS/\nI/tDPh4E/i7be6KHv3w9rN9FNOy+KpSzN2yfBtwb1iuAx4ALs5SznfAgGWAWcF/aZ8PSyqtO25en\ngKHh/Q3AD9LSdU7vcA1H53nZRpjbBjglTX8K8HBvf2e+uHfdu9mXk3BKQQVwh6LplTuA0ySNBCYB\na82sDWiT9Bg5ptrNsx1gXXh9Gagysw+ADyQdlvQXRCfYNElbQ7oqYCzwTDed08zsnbC+DfiJpCXA\n/5jZpizlTiC6ZLBFEkQ/FFvSPl8dXtcQzTMP0WRxKyQ9AvxnWtq3iCZxc8oL9657F8ArhxJxNdE/\nlc+Y2Z8UTan7caLruuknTr6TKN814MPhtYNoEjTS3nd+p3eY2X1xAzaznZJqgFrgdklPmtltWZI+\nYWZfjiMZdL8h6YKg+6Kk88JJLYp3ndspHu5d9y7gfQ6l4hSih3D8SdHDQc4kMtNm4HJJH1P0QJJa\nspvsvaBxPLKdoAY8Dnw17Zrq6ZL+KkvaPZKqQ5pRwEdm9hDwE6KnaHWP5TlgUto12SpJ49L0rkp7\n3RLSnGVmz5vZzcAfiOaQBxgF7I6xj07P4t517wLecig2nSfLQ8BjkrYBzUTXRzGzZknriJrB+4ia\n1n/MorMGuD90quXr+DKOPUE7//E8oeh2wl+FJvR7wFwig6ezieha8uNE0wkvldQBtAP/GNLcB/yv\npDfN7BJJXwFWS/pY+PwmYGdY/0tJLwEfAXVh253hJBTQYNHdHhA90OTpPPvm9CzuXffuMfiU3T2M\npCoz+0BSJVEH2dcsPBS9F2K5GLjKzL5RBK1dQGezO076JmC2mZ3oU8ycXsK925W+iQHgXb+s1PPc\nFzrbXgQe7a2TC8DMmoBxyjOQ6ETk4iaU9Gmgtb+fXP0Q9+4A8q63HBzHcZwMvOXgOI7jZOCVg+M4\njpOBVw6O4zhOBl45OI7jOBl45eA4juNk4JWD4ziOk8GfAST3uHYEHUlxAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mplt.plot_cktest(ck_bad_msm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But again, without error bars this is a bit like reading tea leaves. We didn't get errors from the cktest above, because the estimated models are just single-point models, in this case Maximum likelihood estimates. So there was no information about statistical errors available and thus could not be plotted. \n", "\n", "In order to display statistical errors we have to estimate MSMs with errors. We do this again using Bayesian MSMs [6]:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "BMSM_good = msm.bayesian_markov_model([double_well_data.dtraj_T100K_dt10_n6good], 40)\n", "ck_good_bmsm = BMSM_good.cktest(2, mlags=11)\n", "BMSM_bad = msm.bayesian_markov_model([double_well_data.dtraj_T100K_dt10_n2bad], 40)\n", "ck_bad_bmsm = BMSM_bad.cktest(2, mlags=11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Et voilà, now we see the uncertainties (for the prediction - if we want it for the estimation too, we have to ask for that in the cktest function) and we have an agreement within the error. So this MSM is acceptable and can be further analyzed." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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YdVBdDZWVPnJystm+vVaMnXW8md69+zFmzAQSEhIYPjyB4cPjGTUqgREj4hk2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\nLQZeAw4SzRB1O4EHAup2A/cD54jI2IEqf/jhXvLy/sw555xCXt4qtm8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 16})\n", "fig, axes = mplt.plot_cktest(ck_good_bmsm, figsize=(7, 5), padding_between=0.13, padding_top=0.13)\n", "axes[0,1].xaxis.set_ticks([0,100,200,300])\n", "axes[1,1].xaxis.set_ticks([0,100,200,300])\n", "#fig.text(-0.075, 0.88, 'c)', fontsize=28)\n", "#\n", "savefig('figs/fig_selval_e.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the cktest also fails within statistical error for the bad discretization. So we can't trust this MSM." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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7d+rkBDgtLX6nGkUT3zpes2YN69atY+3atWX73NxcBg4cWEmMBw0aRM+ePRNG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\nOaUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 16})\n", "fig, axes = mplt.plot_cktest(ck_bad_bmsm, figsize=(7, 5), padding_between=0.13, padding_top=0.13)\n", "axes[0,1].xaxis.set_ticks([0,100,200,300])\n", "axes[1,1].xaxis.set_ticks([0,100,200,300])\n", "#fig.text(-0.075, 0.88, 'd)', fontsize=28)\n", "#\n", "savefig('figs/fig_selval_f.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's do the same trick for the HMMs, and let's use a lag time of 5 steps which should work for the good, but not for the bad discretization. We want statistical errors, so we directly estimate a Bayesian HMM. This step is slow!" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "BHMM_good = msm.bayesian_hidden_markov_model([double_well_data.dtraj_T100K_dt10_n6good], 2, 5)\n", "ck_good_bhmm = BHMM_good.cktest(mlags=80)\n", "BHMM_bad = msm.bayesian_hidden_markov_model([double_well_data.dtraj_T100K_dt10_n2bad], 2, 5)\n", "ck_bad_bhmm = BHMM_bad.cktest(mlags=80)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed we get a nice agreement within the error for the good discretization. So we can accept this HMM:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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0HScLom7bmYpuBbCzJqRfTFi3PfCRquavu2e0RH1xmxPBCm6PufV7YJYghD5R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\nNcaGiHcL2y7AM8DdKeom5Ho9bhi8cgnIRmgzHfI3wHW/gJJWsP0z8O5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/ZihLlDJ/hDmD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\n4ziO42QJV7qO4ziOkyX+HxaxAyzmeNflAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 16})\n", "fig, axes = mplt.plot_cktest(ck_good_bhmm, figsize=(7, 5), padding_between=0.13, padding_top=0.13)\n", "axes[0,1].xaxis.set_ticks([0,100,200,300])\n", "axes[1,1].xaxis.set_ticks([0,100,200,300])\n", "#fig.text(-0.075, 0.88, 'g)', fontsize=24)\n", "#\n", "savefig('figs/fig_selval_i.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While the HMM with the bad discretization fails. Note that the implied timescales did not indicate that we could use a lag time of five steps. If we used a lag time of 10 or 20 steps, the HMM on the bad discretization would be acceptable." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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vzUhS4kLXcUoj7Xu7kHl5h2J2pFml6PIe0Er0XYppKoLFjZ5cxJjdBlg92lGY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matplotlib.rcParams.update({'font.size': 16})\n", "fig, axes = mplt.plot_cktest(ck_bad_bhmm, figsize=(7, 5), padding_between=0.13, padding_top=0.13)\n", "axes[0,1].xaxis.set_ticks([0,100,200,300])\n", "axes[1,1].xaxis.set_ticks([0,100,200,300])\n", "#fig.text(-0.075, 0.88, 'h)', fontsize=24)\n", "#\n", "savefig('figs/fig_selval_j.png', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "References\n", "---------\n", "[1] Prinz, J.-H., H. Wu, M. Sarich, B. G. Keller, M. Senne, M. Held, J. D. Chodera, Ch. Schütte and F. Noé: Markov models of molecular kinetics: Generation and Validation. J. Chem. Phys. 134, 174105 (2011)\n", "\n", "[2] Sarich, M., F. Noé, Ch. Schütte: On the Approximation Quality of Markov State Models. Multiscale Model. Simul. 8, 1154-1177 (2010)\n", "\n", "[3] Swope, W. C., J. W. Pitera and F. Suits: Describing protein folding kinetics by molecular dynamics simulations: 1. Theory, J. Phys. Chem. B. 108, 6571-6581 (2004)\n", "\n", "[4] Beauchamp, K. A., R. McGibbon, Y. S. Lin and V. S. Pande: Simple few-state models reveal hidden complexity in protein folding. Proc. Natl. Acad. Sci. USA 109, 17807-17813 (2012)\n", "\n", "[5] Noé, F. and F. Nüske: A variational approach to modeling slow processes in stochastic dynamical systems. SIAM Multiscale Model. Simul. 11. 635-655 (2013).\n", "\n", "[6] Trendelkamp-Schroer, B., H. Wu, F. Paul and F. 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Singhal Hinrichs: Bayesian hidden Markov model analysis of single-molecule force spectroscopy: Characterizing kinetics under measurement uncertainty. http://arxiv.org/abs/1108.1430." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }