PINE LIBRARY
Atualizado FunctionBaumWelch
Library "FunctionBaumWelch"
Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm
to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed
feature vectors.
---
### Function List:
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs)`
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs, bool scaling)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs, array<float> c)`
> `baumwelch (array<int> observations, int nstates)`
> `baumwelch (array<int> observations, array<float> pi, matrix<float> a, matrix<float> b)`
---
### Reference:
> en.wikipedia.org/wiki/Baum–Welch_algorithm
> github.com/alexsosn/MarslandMLAlgo/blob/4277b24db88c4cb70d6b249921c5d21bc8f86eb4/Ch16/HMM.py
> en.wikipedia.org/wiki/Forward_algorithm
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/forward
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/backward
forward(pi, a, b, obs)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
Returns: - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
forward(pi, a, b, obs, scaling)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
scaling (bool): Normalize `alpha` scale.
Returns: - #### Tuple with:
> - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
> - `array<float> _c`: Array with normalization scale.
backward(a, b, obs)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
backward(a, b, obs, c)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
c (float[]): Array with Normalization scaling coefficients.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
baumwelch(observations, nstates)
**(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
nstates (int)
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
baumwelch(observations, pi, a, b)
Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
pi (float[]): Initial probaility distribution.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm
to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed
feature vectors.
---
### Function List:
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs)`
> `forward (array<float> pi, matrix<float> a, matrix<float> b, array<int> obs, bool scaling)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs)`
> `backward (matrix<float> a, matrix<float> b, array<int> obs, array<float> c)`
> `baumwelch (array<int> observations, int nstates)`
> `baumwelch (array<int> observations, array<float> pi, matrix<float> a, matrix<float> b)`
---
### Reference:
> en.wikipedia.org/wiki/Baum–Welch_algorithm
> github.com/alexsosn/MarslandMLAlgo/blob/4277b24db88c4cb70d6b249921c5d21bc8f86eb4/Ch16/HMM.py
> en.wikipedia.org/wiki/Forward_algorithm
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/forward
> rdocumentation.org/packages/HMM/versions/1.0.1/topics/backward
forward(pi, a, b, obs)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
Returns: - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
forward(pi, a, b, obs, scaling)
Computes forward probabilities for state `X` up to observation at time `k`, is defined as the
probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.
Parameters:
pi (float[]): Initial probabilities.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing
states given a state matrix is size (M x M) where M is number of states.
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. Given
state matrix is size (M x O) where M is number of states and O is number of different
possible observations.
obs (int[]): List with actual state observation data.
scaling (bool): Normalize `alpha` scale.
Returns: - #### Tuple with:
> - `matrix<float> _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first
dimension refers to the state and the second dimension to time.
> - `array<float> _c`: Array with normalization scale.
backward(a, b, obs)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
backward(a, b, obs, c)
Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.
Parameters:
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
obs (int[]): Array with actual state observation data.
c (float[]): Array with Normalization scaling coefficients.
Returns: - `matrix<float> _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time.
baumwelch(observations, nstates)
**(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
nstates (int)
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
baumwelch(observations, pi, a, b)
Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the
unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm
to compute the statistics for the expectation step.
Parameters:
observations (int[]): List of observed states.
pi (float[]): Initial probaility distribution.
a (matrix<float>): Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states
given a state matrix is size (M x M) where M is number of states
b (matrix<float>): Emissions, matrix of observation probabilities b or beta = observation probabilities. given state
matrix is size (M x O) where M is number of states and O is number of different possible observations
Returns: - #### Tuple with:
> - `array<float> _pi`: Initial probability distribution.
> - `matrix<float> _a`: Transition probability matrix.
> - `matrix<float> _b`: Emission probability matrix.
---
requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Notas de Lançamento
v2 minor update.Notas de Lançamento
Fix logger version.Notas de Lançamento
v4 - Added error checking for some errors.Notas de Lançamento
v5 - Improved calculation by merging some of the loops, where possible.Biblioteca do Pine
No verdadeiro espirito do TradingView, o autor desse código Pine o publicou como uma biblioteca de código aberto, para que outros programadores Pine da nossa comunidade possam reusa-los. Parabéns ao autor! Você pode usar essa biblioteca privadamente ou em outras publicações de código aberto, mas a reutilização desse código em publicações é regida pelas Regras da Casa.
Aviso legal
As informações e publicações não devem ser e não constituem conselhos ou recomendações financeiras, de investimento, de negociação ou de qualquer outro tipo, fornecidas ou endossadas pela TradingView. Leia mais em Termos de uso.
Biblioteca do Pine
No verdadeiro espirito do TradingView, o autor desse código Pine o publicou como uma biblioteca de código aberto, para que outros programadores Pine da nossa comunidade possam reusa-los. Parabéns ao autor! Você pode usar essa biblioteca privadamente ou em outras publicações de código aberto, mas a reutilização desse código em publicações é regida pelas Regras da Casa.
Aviso legal
As informações e publicações não devem ser e não constituem conselhos ou recomendações financeiras, de investimento, de negociação ou de qualquer outro tipo, fornecidas ou endossadas pela TradingView. Leia mais em Termos de uso.