STATISTICAL MODEL FOR SYSTEMS INCORPORATING HISTORY INFORMATION

• US 20160125305A1
• Filed: 11/04/2014
• Published: 05/05/2016
• Est. Priority Date: 11/04/2014
• Status: Active Grant

• Current Assignee: Utah State University
• Original Assignee: Utah State University
• Inventors: Gunther, Jacob H., Moon, Todd K.
• Granted Patent: US 9,842,300 B2
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G06N 7/01 Probabilistic graphical models, e.g. probabilistic networks

Abstract

For calculating statistical Markov model-like state transition probabilities, a method represents state transition probabilities between a plurality of statistical Markov model-like states and output probabilities associated with a plurality of previous statistical Markov model-like states. The state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states. The output probabilities associated with each of the plurality of states depend on the sequence of previous states.

Claims

1. A method comprising:

representing, by use of a processor, state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and

calculating a state transition probability for the plurality of states.

2. The method of claim 1, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number.

3. The method of claim 1, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states.

4. The method of claim 3, wherein the state transition probability is calculated as a parametric approximation of each state transition probability.

5. The method of claim 1, wherein the output probability is calculated using a probability histogram comprising information from the sequence of previous states.

6. The method of claim 5, wherein the output probability is calculated as a parametric approximation of the output probabilities for each state.

7. The method of claim 2, wherein the state transition probability is calculated by minimizing the expression tr(Ã

_i^TD^TÃ

_iG)−

2tr(DÃ

_iP<sub>α

,i</sub>) subject to constraints that 1^TÃ

_iφ

(h)≦

0 and Ã

_iφ

(h)≧

0.

8. The method of claim 7, wherein the sequence of previous states is calculated using a branch metric with a current state, a history leading to the current state, and a next state.

9. A program product comprising a computer readable storage medium that stores code executable by a processor, the executable code comprising code to perform:

representing state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and

calculating a state transition probability for the plurality of states.

10. The program product of claim 9, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number.

11. The program product of claim 9, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states.

12. The program product of claim 11, wherein the state transition probability is calculated as a parametric approximation of each state transition probability.

13. The program product of claim 9, wherein the output probability is calculated using a probability histogram comprising information from the sequence of previous states.

14. The program product of claim 13, wherein the output probability is calculated as a parametric approximation of the output probabilities for each state.

15. The program product of claim 10, wherein the state transition probability is calculated by minimizing the expression tr(Ã

_i^TD^TÃ

_iG)−

2tr(DÃ

_iP<sub>α

,i</sub>) subject to constraints that 1^TÃ

_iφ

(h)≦

0 and Ã

_iφ

(h)≧

0.

16. The program product of claim 15, wherein the sequence of previous states is calculated using a branch metric with a current state, a history leading to the current state, and a next state.

17. An apparatus comprising:

a processor;

a memory that stores code executable by the processor, the code comprising;

code that represents state transition probabilities between a plurality of statistical Markov model-like states (plurality of states) and output probabilities associated with a plurality of previous statistical Markov model-like states (plurality of previous states), wherein the state transition probabilities between the plurality of previous states depend on a sequence of previous states of the plurality of previous states and the output probabilities associated with each of the plurality of states depend on the sequence of previous states; and

code that calculates a state transition probability for the plurality of states.

18. The apparatus of claim 17, wherein the previous states are represented by a history indicator comprising a real number created by concatenating a number representing each previous state as the most significant digit of the real number.

19. The apparatus of claim 17, wherein the state transition probability is calculated using a transition histogram comprising information from the sequence of previous states.

20. The apparatus of claim 19, wherein the state transition probability is calculated as a parametric approximation of each state transition probability.