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})
Have Fun
Let's Vote for the Most Difficult Equation!
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.
Discussion
Comment to Make Wishes Come True
Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true

Dylan GriffithsPlease universe, let me pass this exam.Jennifer Williams reply to Dylan GriffithsYou can make it...20230610 00:00:00.0 
Jeremy SnyderI just want to get through this exam.Willie Fox reply to Jeremy SnyderYou can make it...20230310 00:00:00.0 
Lillian TuckerHere's to passing this test, let's make it happen!Olivia Evans reply to Lillian TuckerYou can make it...20230217 00:00:00.0
Reply