120 lines
4.4 KiB
Markdown
120 lines
4.4 KiB
Markdown
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Install required dependencies for matplotlib GUI frontend and all pip other packages for this project
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```bash
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sudo apt install python3-tk
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python3.9 -m pip install -r requirements.txt
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```
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CLI tool to determine most probably path of Hidden Markov Model given an observation sequence of emissions.
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Given an observation sequence of emissions, find the most probable path of traversal for a Hidden Markov Model.
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Since this is just an example of HMM, a graph can be automatically generated by specifying only the node count.
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Edges and weights connecting the nodes will be randomly assigned.
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If required, an input graph can be provided through the JSON configuration option.
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See provided examples of JSON input files for more detail on options available.
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```bash
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python3.9 markov-model.py -h
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usage: markov-model.py [-h] [--nodes [GRAPH_NODE_COUNT]] [--edges [GRAPH_EDGE_COUNT]] [--show-all] [--interactive] [--silent]
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[--file [FILE_PATH]]
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[OBSERVATION_SEQUENCE ...]
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Calculates most probable path of HMM given an observation sequence
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positional arguments:
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OBSERVATION_SEQUENCE An observation sequence to calculate the most probable path
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(default: '['A', 'B', 'D', 'C']')
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optional arguments:
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-h, --help show this help message and exit
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--nodes [GRAPH_NODE_COUNT], -n [GRAPH_NODE_COUNT]
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The total number of node states in the HMM graph
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(default: '4')
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--edges [GRAPH_EDGE_COUNT], -e [GRAPH_EDGE_COUNT]
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The total number of edges in the HMM graph
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(default: '8')
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--show-all When this flag is set, all path probabilities and their calculations will be output
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(default: 'False')
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--interactive Allow taking input to update matrices with triple (row, col, value)
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(default: 'False')
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--silent When this flag is set, final graph will not be shown
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(default: 'False')
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--file [FILE_PATH], -f [FILE_PATH]
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Optionally provide file for data to be read from. Each point must be on it's own line with format x,y
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```
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Running HMM with a graph using 4 nodes, 8 edges, and random transition / emission matrices
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Sometimes there can be a sequence with no possible path due to a constrained transition matrix
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Sometimes there can be a sequence with no possible path due to a limited emission matrix
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```bash
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python3.9 markov-model.py --nodes 4 --edges 8 --show-all A B D C G --silent
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1->3: 0.89
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1->0: 0.6
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3->3: 0.81
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3->1: 0.29
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0->2: 0.67
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0->1: 0.89
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2->0: 0.12
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2->1: 0.41
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Calculating (0, 2, 1, 0, 2): (0.98 * 0.67) * (0.74 * 0.41) * (0.22 * 0.60) * (0.22 * 0.67) * 0.36 = 0.001395
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Calculating (0, 2, 1, 3, 3): (0.98 * 0.67) * (0.74 * 0.41) * (0.22 * 0.89) * (0.11 * 0.81) * 0.52 = 0.001807
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Finding most probable path for given observation sequence: ['A', 'B', 'D', 'C', 'G']
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Total nodes in graph: 4
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Total edges in graph: 8
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Number of sequences: 5
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Interactive mode: False
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Emitting nodes: {'A': [0, 2], 'B': [1, 2], 'C': [0, 2, 3], 'D': [1, 2], 'G': [0, 2, 3]}
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Transition matrix:
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[[0. 0.89 0.67 0. ]
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[0.6 0. 0. 0.89]
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[0.12 0.41 0. 0. ]
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[0. 0.29 0. 0.81]]
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Emission matrix:
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[[ 0.98 0. 0.22 0. 0.11]
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[ 0. 0.1 -0. 0.22 0. ]
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[ 0.67 0.74 0.46 0.62 0.36]
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[-0. 0. 0.11 0. 0.52]]
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Final paths sorted by probability:
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(0, 2, 1, 3, 3) has probability: 0.001807
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(0, 2, 1, 0, 2) has probability: 0.001395
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```
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By default, a random Hidden Markov Model and visualization will be generated
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```bash
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python3.9 markov-model.py
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Finding most probable path for given observation sequence: ['A', 'B', 'D', 'C']
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Total nodes in graph: 4
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Total edges in graph: 8
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Number of sequences: 4
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Interactive mode: False
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Emitting nodes: {'A': [0, 2, 3], 'B': [1, 2, 3], 'C': [0, 3], 'D': [1, 2]}
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Transition matrix:
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[[0. 0. 0.31 0. ]
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[0.55 0.25 0. 0. ]
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[0.79 0.47 0. 0.12]
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[0.92 0. 0.81 0. ]]
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Emission matrix:
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[[0.45 0. 0.4 0. ]
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[0. 0.89 0. 0.51]
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[0.12 0.24 0. 0.78]
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[0.08 0.42 0.96 0. ]]
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(0, 2, 1, 0) has the highest probability of 0.00176553432
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```
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