Hidden Markov Model
Tags: #machine learning #nlpEquation
$$Q=\{q_{1},q_{2},...,q_{N}\}, V=\{v_{1},v_{2},...,v_{M}\} \\ I=\{i_{1},i_{2},...,i_{T}\},O=\{o_{1},o_{2},...,o_{T}\} \\ A=[a_{ij}]_{N \times N}, a_{ij}=P(i_{t+1}=q_{j}|i_{t}=q_{i}) \\ B=[b_{j}(k)]_{N \times M},b_{j}(k)=P(o_{t}=v_{k}|i_{t}=q_{j})$$Latex Code
Q=\{q_{1},q_{2},...,q_{N}\}, V=\{v_{1},v_{2},...,v_{M}\} \\
I=\{i_{1},i_{2},...,i_{T}\},O=\{o_{1},o_{2},...,o_{T}\} \\
A=[a_{ij}]_{N \times N}, a_{ij}=P(i_{t+1}=q_{j}|i_{t}=q_{i}) \\
B=[b_{j}(k)]_{N \times M},b_{j}(k)=P(o_{t}=v_{k}|i_{t}=q_{j})
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Introduction
Equation
Latex Code
Q=\{q_{1},q_{2},...,q_{N}\}, V=\{v_{1},v_{2},...,v_{M}\} \\
I=\{i_{1},i_{2},...,i_{T}\},O=\{o_{1},o_{2},...,o_{T}\} \\
A=[a_{ij}]_{N \times N}, a_{ij}=P(i_{t+1}=q_{j}|i_{t}=q_{i}) \\
B=[b_{j}(k)]_{N \times M},b_{j}(k)=P(o_{t}=v_{k}|i_{t}=q_{j})
Explanation
Q denotes the set of states and V denotes the set of obvervations. Let's assume we have state sequence I of length T, and observation sequence O of length T, Hidden Markov Model(HMM) use transition matrix A to denote the transition probability a_{ij} and matrix B to denote observation probability matrix b_jk.
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