{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 303 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Knight's Hidden Path\n", "\n", "On a chessboard, a knight may make (when unconstrained by edges) 8 different moves from his current position, or he can choose to remain where he is. We'll number the moves:\n", "\n", "1. Right 1, Forward 2\n", "2. Right 2, Forward 1\n", "3. Right 2, Backward 1\n", "4. Right 1, Backward 2\n", "5. Left 1, Backward 2\n", "6. Left 2, Backward 1\n", "7. Left 2, Forward 1\n", "8. Left 1, Forward 2\n", "\n", "and if the move is '0', remain in place\n", "\n", "We'll count positions as 0 through 7 in each direction, starting in the lower left.\n", "\n", "For this notebook, we'll assume that each move is equally likely. Later we may try to infer the likelihood of each\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Motivation\n", "In a dynamic model with unobserved state variables, if we want to infer the states, and have a good model for the system, all the known values at all the timesteps influence the probability of the unknown values at each of the timesteps.\n", "\n", "Time to learn about hidden markov models" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def move(position, move):\n", " #calculate new position\n", " if move == 0: newpos = position\n", " elif move == 1: newpos = position + [1,2]\n", " elif move == 2: newpos = position + [2,1]\n", " elif move == 3: newpos = position + [2,-1]\n", " elif move == 4: newpos = position + [1,-2]\n", " elif move == 5: newpos = position + [-1,-2]\n", " elif move == 6: newpos = position + [-2,-1]\n", " elif move == 7: newpos = position + [-2,1]\n", " elif move == 8: newpos = position + [-1,2]\n", " \n", " if newpos.max()<=7 and newpos.min()>=0: return newpos \n", " else: return position " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 231 }, { "cell_type": "code", "collapsed": false, "input": [ "positionlist = pd.DataFrame(index=range(20000), columns=['x','y'])\n", "positionlist.ix[0] = [3,5]\n", "\n", "for i in range(len(positionlist)-1):\n", " positionlist.ix[i+1] = move(positionlist.ix[i].values, np.random.randint(0,9))\n", " # I'd like to change the random selection here, as soon as I figure out what's happened to numpy choose.\n", " \n", "plt.figure(figsize(4,4))\n", "plt.plot(positionlist['x'], positionlist['y'], 'o-')\n", "plt.xlim(-.5,7.5)\n", "plt.ylim(-.5,7.5)\n", "plt.title(\"Knight's path\")\n", "print 'x values:'\n", "print positionlist['x'].values" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "x values:\n", "[3 1 3 ..., 7 7 6]\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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TFa/QpkVRvPhNk2yAa7Tn0mgAfwu2FfDZZ4Gvfz0KF08tjHNwOremi3QqLVny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\nXdXDqcNT3SRXvLgO7oPHc/C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012345678910111213141516171819
x 3 2 2 4 4 4 4 4 5 3 1 1 1 1 0 1 1 3 4 2
y 5 7 7 6 6 6 6 6 4 5 6 6 6 6 4 2 2 3 1 0
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 441, "text": [ " 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\n", "x 3 2 2 4 4 4 4 4 5 3 1 1 1 1 0 1 1 3 4 2\n", "y 5 7 7 6 6 6 6 6 4 5 6 6 6 6 4 2 2 3 1 0" ] } ], "prompt_number": 441 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given this list of x coordinates and the above rule for how the knight can move, can we infer the y coordinates, and the distriution of the random move input? How does our accuracy change with the number of samples? What if we only sample every other turn?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Scikit-learn hidden markov model package\n", "Docs: http://scikit-learn.org/stable/modules/generated/sklearn.hmm.MultinomialHMM.html" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import hmm\n", "\n", "def transprob(x1,y1, x2,y2):\n", " count = 0.\n", " for potmove in range(9):\n", " [nx, ny] = move(np.array([x1,y1]), potmove)\n", " if(nx == x2 and ny == y2): count+=1\n", " return count/9\n", "\n", "transmat = np.zeros((64,64)) #reshape the original state matrix to (1,1), (1,2) ...\n", "for S1 in range(64):\n", " for(S2) in range(64):\n", " transmat[S1, S2] = transprob(S1/8, S1%8, S2/8, S2%8)\n", "\n", "plt.figure(figsize(8,7)) \n", "plt.matshow(transmat)\n", "plt.xlabel('State at time t')\n", "plt.ylabel('State at time t+1')\n", "plt.title('Probabilities of transitioning from \\none state to the next')\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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F4uLioNVqMXnyZAQFBSE5ORkAMH36dAQGBmLQoEHo1q0b7OzsMHXqVAQHB9co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\nEFqtVjz++OPihx9+qHEeJyen2m8YUR0ACOCMRIt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"text": [ "" ] } ], "prompt_number": 563 }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "emissionprob = np.zeros((64,8))\n", "for State in range(64):\n", " for Emission in range(8):\n", " if State/8 == Emission: emissionprob[State, Emission] = 1\n", " \n", "plt.matshow(emissionprob.T, origin='lower')\n", "plt.colorbar(orientation='horizontal');\n", "plt.ylabel('Observation')\n", "plt.xlabel('State')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 564, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 564 }, { "cell_type": "code", "collapsed": false, "input": [ "startprob = np.ones(64)/64\n", "\n", "model = hmm.MultinomialHMM(n_components=64, transmat=transmat, startprob=startprob)\n", "model.n_symbols_ = 8\n", "model.emissionprob_ = emissionprob\n", "\n", "#model.fit([positionlist['x'].tolist()])\n", "predictions = model.predict(positionlist['x'].tolist())\n", "proba = model.predict_proba(positionlist['x'].tolist())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 565 }, { "cell_type": "code", "collapsed": false, "input": [ "step=15\n", "plt.matshow(np.reshape(proba[step,:], (8,8), order='F'))\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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FakdArfS52hGIItzu2/qkwZIkCdgS2j7wv6WQc4SCM14iEs9Uv3KNiIjCizNe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\n", "text": [ "" ] } ], "prompt_number": 457 }, { "cell_type": "code", "collapsed": false, "input": [ "y_estimate = pd.DataFrame(data = 1./8, columns=range(0,8), index=positionlist.index);\n", "for step in y_estimate.index[:-1]:\n", " x = positionlist['x'].ix[step]\n", " y_estimate.ix[step] = proba[step,x*8:(x+1)*8]\n", "\n", "plt.figure(figsize(20,6)) \n", "plt.subplot(211)\n", "plt.imshow(y_estimate.T, origin='lower',interpolation='nearest')\n", "plt.plot(positionlist['y'], 'wo')\n", "plt.plot(predictions%8, 'r+')\n", "plt.xlim(-.5, 49.5)\n", "plt.ylim(-.5, 7.5)\n", "plt.ylabel('Y position of knight');\n", "plt.colorbar(); \n", "\n", "plt.subplot(212)\n", "plt.imshow(y_estimate.T, origin='lower',interpolation='nearest')\n", "plt.plot(positionlist['y'], 'wo')\n", "plt.plot(predictions%8, 'r+')\n", "plt.xlim(49.5,99.5)\n", "plt.ylim(-.5, 7.5)\n", "plt.ylabel('Y position of knight');\n", "plt.xlabel('Timestep');\n", "plt.colorbar(); " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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G7N27F0uXLsXDDz9se02SJOj1euzevdtloQ94cGbfbDZj8ODBtuc33ngjzF6e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"text": [ "" ] } ], "prompt_number": 458 }, { "cell_type": "code", "collapsed": false, "input": [ "startprob = np.zeros(64)\n", "startprob[positionlist['x'].ix[0]*8+positionlist['y'].ix[0]] = 1\n", " \n", "model = hmm.MultinomialHMM(n_components=64, transmat=transmat, startprob=startprob)\n", "model.n_symbols_ = 8\n", "model.emissionprob_ = emissionprob\n", "\n", "#model.fit([positionlist['x'].tolist()])\n", "predictions = model.predict(positionlist['x'].tolist())\n", "proba = model.predict_proba(positionlist['x'].tolist())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 572 }, { "cell_type": "code", "collapsed": false, "input": [ "y_estimate = pd.DataFrame(data = 1./8, columns=range(0,8), index=positionlist.index);\n", "for step in y_estimate.index[:-1]:\n", " x = positionlist['x'].ix[step]\n", " y_estimate.ix[step] = proba[step,x*8:(x+1)*8]\n", "\n", "plt.figure(figsize(20,6)) \n", "plt.subplot(211)\n", "plt.imshow(y_estimate.T, origin='lower',interpolation='nearest', label='likelihood')\n", "plt.plot(positionlist['y'], 'wo', label='Predictions')\n", "plt.plot(predictions%8, 'r+', label='True Value')\n", "plt.xlim(-.5, 49.5)\n", "plt.ylim(-.5, 7.5)\n", "plt.ylabel('Y position of knight');\n", "plt.colorbar(); \n", "plt.legend(loc=(.37,1.05), ncol=2, frameon=False)\n", "\n", "plt.subplot(212)\n", "plt.imshow(y_estimate.T, origin='lower',interpolation='nearest')\n", "plt.plot(positionlist['y'], 'wo')\n", "plt.plot(predictions%8, 'r+')\n", "plt.xlim(49.5,99.5)\n", "plt.ylim(-.5, 7.5)\n", "plt.ylabel('Y position of knight');\n", "plt.xlabel('Timestep');\n", "plt.colorbar(); " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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BNe0+UfIhx8Tv1XhlHCIiIiJv0KyOrSaTyYRp06YhNzcXBw8eRHZ2Ng4dOmTVZ/78+ejR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"text": [ "" ] } ], "prompt_number": 574 }, { "cell_type": "markdown", "metadata": {}, "source": [ "So it looks like we won't ever get perfect prediction, because of the symmetry of the problem, and because it is inherently random - the most likely path isn't likely to be the one we take! The next problem arises because once you get off track, you aren't likely to get back on. So, can we periodically sample the y value to see if we're off track and get back on? Is there an optimal strategy for sampling y such that we minimize the cost while still meeting some performance target?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "truthmatrix = pd.DataFrame(data=0, index=y_estimate.index, columns=y_estimate.columns.values)\n", "for timestep, y in zip(positionlist.index, positionlist['y']): \n", " truthmatrix[y].ix[timestep] = 1\n", " \n", " \n", "delta = .02\n", "accuracy = pd.Series(data=0., index=np.arange(0,1.01, delta))\n", "numpredictions = pd.Series(data=0., index=np.arange(0,1.01, delta))\n", "for val in accuracy.index:\n", " numpredictions[val] = ((y_estimate > val-delta/2) & (y_estimate <= val+delta/2)).sum().sum()\n", " numhits = truthmatrix[((y_estimate > val-delta/2) & (y_estimate <= val+delta/2))].sum().sum()\n", " accuracy[val] = 1.*numhits/numpredictions[val]\n", "\n", "plt.figure(figsize=(6,4))\n", "plt.plot(accuracy.index, accuracy.values, 'bo')\n", "plt.plot([0,1],[0,1],'r')\n", "plt.title('Prediction Calibration')\n", "plt.xlabel('Confidence / Expected accuracy')\n", "plt.ylabel('Measured Accuracy')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 577, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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4YmLetmAjhSiZ0l47TZbEOHXqFH379qVDhw4AHD16lHfeKfyfQgi7VIoaRyWq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\n6CKNqjzOa7lL9JVQ89c2Skg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"text": [ "" ] } ], "prompt_number": 577 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(6,4))\n", "plt.semilogy(numpredictions.index, numpredictions.values, 'bo');\n", "plt.title('Prediction Usefulness')\n", "plt.ylabel('Number of Predictions')\n", "plt.xlabel('Confidence / Expected accuracy')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 583, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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YKIiIDGe2YvbDM7/aCtYoiIj0Y/YaRXl5OdauXYu0tDQoFAoEBwdj5syZaNmypdEHbSje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\n2NhYVFdX480338TAgQPh7++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