example_sets.ipynb

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    "import numpy\n",
    "\n",
    "class example_sets(object):\n",
    "    \"\"\"\n",
    "    Each example contains:\n",
    "        A : transition probability matrix of size states x states (row stochastic)\n",
    "        HS : The hidden states\n",
    "        O : The observations (emissions)\n",
    "        priors : starting probabilities of the hidden states\n",
    "        B : emission probability matrix of size states x emissions (row stochastic)\n",
    "        ES : sequence of emissions (observations)\n",
    "    \"\"\"\n",
    "    \n",
    "    @staticmethod\n",
    "    def healthy_fever():\n",
    "        \"\"\"\n",
    "        A patient can be normal, cold, or dizzy.\n",
    "        Are these flu symptoms?\n",
    "        \"\"\"\n",
    "        A = numpy.array([\n",
    "            [0.7, 0.3],\n",
    "            [0.4, 0.6]\n",
    "        ])\n",
    "\n",
    "        HS = ['Healthy','Flu']\n",
    "        O = [\"normal\", \"cold\", \"dizzy\"]      \n",
    "        priors = [0.6, 0.4]\n",
    "        \n",
    "        B = numpy.array([\n",
    "            [0.5, 0.4, 0.1],\n",
    "            [0.1, 0.3, 0.6]\n",
    "        ])\n",
    "\n",
    "        ES = [\"normal\", \"cold\", \"dizzy\"]\n",
    "        \n",
    "        return [A, HS, O, priors, B, ES]\n",
    "    \n",
    "    @staticmethod\n",
    "    def dna_coding():\n",
    "        \"\"\"\n",
    "        H characterizes coding DNA while L characterizes non-coding DNA.\n",
    "        DNA can have protiens A C G T \n",
    "        \"\"\"\n",
    "\n",
    "        A = numpy.array([\n",
    "            [0.5, 0.5],\n",
    "            [0.6, 0.4]\n",
    "        ])\n",
    "\n",
    "        HS = ['H','L']\n",
    "        O = ['A', 'C', 'G', 'T']\n",
    "        priors = [0.5, 0.5]\n",
    "        \n",
    "        # states x observables (row stochastic)\n",
    "        B = numpy.array([\n",
    "            [0.2, 0.3, 0.3, 0.2],\n",
    "            [0.3, 0.2, 0.2, 0.3]\n",
    "        ])\n",
    "\n",
    "        ES = ['G', 'G', 'C', 'A', 'C', 'T', 'G', 'A', 'A']\n",
    "        \n",
    "        return [A, HS, O, priors, B, ES]\n",
    "    \n",
    "    @staticmethod\n",
    "    def happy_sad_robot():\n",
    "        \"\"\"\n",
    "        A robot is happy or sad depending on what it saw on tv\n",
    "        \"\"\"\n",
    "        A = numpy.array([\n",
    "            [0.99, 0.01],\n",
    "            [0.1, 0.9]\n",
    "        ])\n",
    "\n",
    "        HS = ['Sad','Happy']\n",
    "        O = ['GoT', 'W', 'EEnD', 'BB']\n",
    "        priors = [0.2, 0.8]\n",
    "\n",
    "        #states x observables (row stochastic)\n",
    "        B = numpy.array([\n",
    "            [0.1, 0.3, 0.5, 0.1],\n",
    "            [0.4, 0.4, 0.2, 0.0]\n",
    "        ])\n",
    "\n",
    "        ES = ['GoT','BB','EEnD']\n",
    "        \n",
    "        return [A, HS, O, priors, B, ES]\n",
    "\n",
    "    @staticmethod\n",
    "    def urn_pick():\n",
    "        \"\"\"\n",
    "        You can pick a red, green, or blue ball from three urns.\n",
    "        Which urns did you pick from?\n",
    "        \"\"\"\n",
    "        A = numpy.array([\n",
    "            [0.1, 0.4, 0.5],\n",
    "            [0.6, 0.2, 0.2],\n",
    "            [0.3, 0.4, 0.3]\n",
    "        ])\n",
    "\n",
    "        HS = ['Urn1','Urn2', 'Urn3']\n",
    "        O = ['R', 'G', 'B']\n",
    "        priors = [0.5, 0.3, 0.2]\n",
    "\n",
    "        #states x observables (row stochastic)\n",
    "        B = numpy.array([\n",
    "            [0.3, 0.5, 0.2],\n",
    "            [0.1, 0.4, 0.5],\n",
    "            [0.6, 0.1, 0.3]\n",
    "        ])\n",
    "\n",
    "        ES = ['R','R','G','G','B','R','G','R']\n",
    "        \n",
    "        return [A, HS, O, priors, B, ES]\n",
    "    \n",
    "    @staticmethod\n",
    "    def part_of_speech_tag_simple():\n",
    "        \"\"\"\n",
    "        Tags the words in a sentence with \n",
    "            Noun, Modal, Verb.\n",
    "        These words are \n",
    "            Mary, Jane, Will, Spot, Can, See, Pat.\n",
    "        \n",
    "        Notice the ambiguitity in Will, Spot, and Pat.\n",
    "        \"\"\"        \n",
    "        A = numpy.array([\n",
    "            [1/9, 1/3, 1/9],\n",
    "            [1/4, 0, 3/4],\n",
    "            [1, 0, 0]\n",
    "        ])\n",
    "\n",
    "        HS = ['Noun','Modal', 'Verb']\n",
    "        O = ['Mary', 'Jane', 'Will', 'Spot', 'Can', 'See', 'Pat']\n",
    "        priors = [3/4, 1/4, 0]\n",
    "\n",
    "        # observables x states (column stochastic)\n",
    "        B = numpy.array([\n",
    "            [4/9, 0, 0],\n",
    "            [2/9, 0, 0],\n",
    "            [1/9, 3/4, 0],\n",
    "            [2/9, 0, 1/4],\n",
    "            [0, 1/4, 0],\n",
    "            [0, 0, 1/2],\n",
    "            [0, 0, 1/4]\n",
    "        ])\n",
    "\n",
    "        B = B.T #states x observables (row stochastic)\n",
    "        ES = ['Jane','Will','Spot','Pat'] #Jane will spot Will.\n",
    "        \n",
    "        return [A, HS, O, priors, B, ES]\n",
    "\n"
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