The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm. For an HMM such as this one: this probability is written as . Here is the hidden state which is abbreviated as and are the observations to .
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| - Forward-Algorithmus (de)
- Forward algorithm (en)
- 前向算法 (zh)
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| - Der Forward-Algorithmus (auch Vorwärts-Algorithmus, Vorwärts-Prozedur) berechnet mit Hilfe sogenannter Forward-Variablen für ein gegebenes Hidden-Markov-Modell die Wahrscheinlichkeit einer bestimmten Beobachtung.Er verwendet die Programmiermethode der dynamischen Programmierung. (de)
- 前向算法（Forward algorithm），在隐马尔可夫模型（HMM）中，是用于计算“置信状态”的。置信状态指根据既往证据推算出的当前状态的概率分布。这个过程也被叫做“滤波”。前向算法和维特比算法紧密相关但又互不相同。 (zh)
- The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm. For an HMM such as this one: this probability is written as . Here is the hidden state which is abbreviated as and are the observations to . (en)
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| - Der Forward-Algorithmus (auch Vorwärts-Algorithmus, Vorwärts-Prozedur) berechnet mit Hilfe sogenannter Forward-Variablen für ein gegebenes Hidden-Markov-Modell die Wahrscheinlichkeit einer bestimmten Beobachtung.Er verwendet die Programmiermethode der dynamischen Programmierung. (de)
- The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm. The forward and backward algorithms should be placed within the context of probability as they appear to simply be names given to a set of standard mathematical procedures within a few fields. For example, neither "forward algorithm" nor "Viterbi" appear in the Cambridge encyclopedia of mathematics. The main observation to take away from these algorithms is how to organize Bayesian updates and inference to be efficient in the context of directed graphs of variables (see sum-product networks). For an HMM such as this one: this probability is written as . Here is the hidden state which is abbreviated as and are the observations to . The backward algorithm complements the forward algorithm by taking into account the future history if one wanted to improve the estimate for past times. This is referred to as smoothing and the forward/backward algorithm computes for . Thus, the full forward/backward algorithm takes into account all evidence. Note that a belief state can be calculated at each time step, but doing this does not, in a strict sense, produce the most likely state sequence, but rather the most likely state at each time step, given the previous history. In order to achieve the most likely sequence, the Viterbi algorithm is required. It computes the most likely state sequence given the history of observations, that is, the state sequence that maximizes . (en)
- 前向算法（Forward algorithm），在隐马尔可夫模型（HMM）中，是用于计算“置信状态”的。置信状态指根据既往证据推算出的当前状态的概率分布。这个过程也被叫做“滤波”。前向算法和维特比算法紧密相关但又互不相同。 (zh)
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