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`
הערות שחרור
⋅
v2 minor update.
הערות שחרור
⋅
Fix logger version.
הערות שחרור
⋅
v4 - Added error checking for some errors.
הערות שחרור
⋅
v5 - Improved calculation by merging some of the loops, where possible.
When using a new source of states (integers 1 to 8) I recently encountered a column size error. While it can be avoided by ensuring the emissions matrix (b) is also square, by changing _obsmax to also be equal to nstates, the probabilities then cease to change as the viterbi algorithm begins operating on the matrix thereafter... not sure why this is the case or what the significance of _obsmax having to be the observed maximal value instead of nstates....
edit: issue seems to be that the algo is 'hungry' 😂 ... when I increased the data feed, it sprang into action... just needs more values to function properly... seems to be some bare minimum of data that must stream in on each bar for it to function....
slowcoconut
⋅
... nvm... i forgot a 'var' .... 😩🫠
BO07
⋅
Hi Ricardo, do you know why values [pi, a, b] which I print in table returned from baumwelch(obs, ns) update (change all the time) in 5-15s intervals, given obs is a static constant array.from(1, 0, 2, 1, 0, 2, 1, 1, 0, 2, 0, 0, 1), thanks. Ok, maybe because it's random initialization. Than what's the point in not random initialization if function requires pi, a, b as inputs and returns again pi, a, b. I couldn't find anything in examples and description about it.
BO07
⋅
Ricardo, as I understood so far random init is if got no prior knowledge of [pi, a, b], and not random function is for later tuning of [pi, a, b] for currently observed states.
RicardoSantos
⋅
@BO07, yes, i think you understood correctly, the weights are returned so you can optionally overwrite the inputs
edit: issue seems to be that the algo is 'hungry' 😂 ... when I increased the data feed, it sprang into action... just needs more values to function properly... seems to be some bare minimum of data that must stream in on each bar for it to function....