METHOD AND SYSTEM FOR DETERMINING AND USING A CLONED HIDDEN MARKOV MODEL
The system and method for determining and using a cloned hidden Markov model (CHMM) preferably including: determining an initial CHMM, learning a final CHMM, and using the final CHMM, wherein the CHMM includes a transition probability data structure and an observation probability data structure.
1 . A system comprising a processing system, the processing system comprising:
a set of potential emissions;
a hardcoded observation array, comprising:
a different set of clones for each potential emission, wherein the different sets of clones cooperatively form a plurality of clones;
a set of emission probabilities relating each clone of the plurality to each potential emission, each emission probability representing a probability of observing the potential emission from the clone; and
a transition array, comprising:
a set of transition probabilities representing a probability of transitioning from a current clone to another clone of the plurality of clones, wherein the set of transition probabilities is determined by fixing the hardcoded observation array and updating the set of transition probabilities based on a set of received observations, wherein each observation of the set of received observations is an observation of an emission from the set of potential emissions.
2 . The system of claim 1 , wherein the set of received observations is received from a sensor mounted to an agent.
3 . The system of claim 1 , wherein the observation array is sparse.
4 . The system of claim 1 , further comprising a plurality of potential actions, wherein the system is configured to determine an action from the plurality of potential actions based on a current clone of the plurality of clones.
5 . The system of claim 4 , further configured to determine a subsequent clone for a subsequent timestep based on the current clone and a received action.
6 . The system of claim 4 , wherein the transition array comprises three dimensions, wherein a first and a second dimension of the three dimensions are each associated with the plurality of clones, and wherein a third dimension is associated with the plurality of potential actions.
7 . The system of claim 4 , wherein updating the set of transition probabilities comprises updating a subarray of the transition array, wherein the subarray is determined based a set of indices associated with a set of clones corresponding to a potential emission associated with a received observation and an action of a plurality of received actions.
8 . The system of claim 1 , wherein the observation array is overcomplete.
9 . The system of claim 8 , wherein each potential emission of the set of potential emissions is associated with a number of hidden states, wherein a number of clones in a set of clones associated with a potential emission is larger than the number of hidden states associated with the potential emission.
10 . The system of claim 1 , wherein the set of received observations comprises aliased observations.
11 . The system of claim 1 , wherein an emission probability of the set of emission probabilities is determined based on sensor noise.
12 . A method comprising:
determining a set of potential emissions;
determining a hardcoded observation array, comprising:
assigning a different set of clones to each potential emission, wherein the different sets of clones cooperatively form a plurality of clones;
determining a set of emission probabilities relating each clone to a potential emission; and
determining a transition array, comprising:
determining a set of transition probabilities;
fixing the hardcoded observation array; and
updating the set of transition probabilities using the fixed hardcoded observation array based on a set of received observations, wherein each of the received observations is an observation of an emission from the set of potential emissions.
13 . The method of claim 12 , wherein the transition array represents higher-order sequences that encode temporal contexts in a first order model.
14 . The method of claim 12 , wherein received observations within the set of received observations are observed from different environments.
15 . The method of claim 12 , further comprising determining a sequence of observations and associated actions to transition from a first clone to a second clone, comprising:
clamping the first clone at a first timestep;
clamping the second clone at a subsequent timestep; and
using a backward pass of a message passing algorithm from the second clone to the first clone to determine the sequence of observations.
16 . The method of claim 15 , wherein the cloned hidden Markov model is a first order model.
17 . The method of claim 15 , wherein the set of transition probabilities is determined using an expectation-maximization (EM) algorithm.
18 . The method of claim 17 , wherein the using the expectation-maximization (EM) algorithm comprises using a Baum-Welch algorithm.
19 . The method of claim 12 , wherein the set of transition probabilities is associated with a set of potential actions, wherein the set of potential actions define a third dimension within the transition array, and wherein updating the set of transition probabilities further comprises updating the transition probabilities based on a set of received actions, wherein each received action is from the set of potential actions and is associated with a received observation.
20 . The method of claim 12 , wherein the set of emission probabilities is determined based on sensor noise.