Sparse higher-order Markov random field
View Patent ↗Systems and methods are provided for identifying combinatorial feature interactions, including capturing statistical dependencies between categorical variables, with the statistical dependencies being stored in a computer readable storage medium. A model is selected based on the statistical dependencies using a neighborhood estimation strategy, with the neighborhood estimation strategy including generating sets of arbitrarily high-order feature interactions using at least one rule forest and optimizing one or more likelihood functions. A damped mean-field approach is applied to the model to obtain parameters of a Markov random field (MRF); a sparse high-order semi-restricted MRF is produced by adding a hidden layer to the MRF; indirect long-range dependencies between feature groups are modeled using the sparse high-order semi-restricted MRF; and a combinatorial dependency structure between variables is output.
1. A method for identifying combinatorial feature interactions, comprising:
capturing statistical dependencies between categorical variables, with the statistical dependencies being stored in a computer readable storage medium;
selecting a model based on the statistical dependencies using a neighborhood estimation strategy, the neighborhood estimation strategy further comprising:
generating sets of arbitrarily high-order feature interactions using at least one rule forest; and
optimizing one or more likelihood functions;
applying a damped mean-field approach to the model to obtain parameters of a Markov random field (MRF), wherein the MRF is a Boltzmann machine;
producing a sparse high-order semi-restricted MRF by adding a hidden layer to the MRF;
modeling indirect long-range dependencies between feature groups using the sparse high-order semi-restricted MRF; and
outputting a combinatorial dependency structure between variables, wherein the combinatorial feature interactions are identified between transcription factors (TF).
2. The method as recited in claim 1 , wherein the selecting a model using a neighborhood estimation strategy includes employing an L1-based rule ensemble approach on any of a given transcription factor (TF).
3. The method as recited in claim 1 , wherein L1-sparsity penalized rule fitting is employed during the generating sets of arbitrarily high-order feature interactions to achieve optimal parameterization.
4. The method as recited in claim 1 , wherein the combinatorial dependency structure includes combinatorial interactions involving TF bindings in cellular systems.
5. The method as recited in claim 1 , wherein the modeling includes modeling observed feature dependencies.
6. The method as recited in claim 1 , wherein a weight associated with the arbitrarily high-order feature interactions in a final sparse high-order MRF is fine-tuned using maximum likelihood learning.
7. The method as recited in claim 1 , wherein hidden units are employed during modeling to model the indirect long-range dependencies between feature groups.
8. The method as recited in claim 1 , wherein the one or more likelihood functions are L1-penalized pseudo-likelihood functions.
9. A system for identifying combinatorial feature interactions, comprising:
a statistical dependency module configured to capture statistical dependencies between categorical variables, with the statistical dependencies being stored in a non-transitory computer readable storage medium;
a selector configured to select a model based on the statistical dependencies using a neighborhood estimation strategy, the neighborhood estimation strategy further comprising:
a generator configured to generate sets of arbitrarily high-order feature interactions using at least one rule forest; and
an optimizer configured to optimize likelihood functions;
an application module configured to apply a damped mean-field approach to the model to obtain parameters of a Markov random field (MRF), wherein the MRF is a Boltzmann machine;
a production module configured to produce a sparse high-order semi-restricted MRF by adding a hidden layer to the MRF;
a modeler configured to model, using a hardware processor, indirect long-range dependencies between feature groups using the sparse high-order semi-restricted MRF; and
an output module configured to output a combinatorial dependency structure between variables, wherein the combinatorial feature interactions are identified between transcription factors (TF).
10. The system as recited in claim 9 , wherein the selecting a model using a neighborhood estimation strategy includes employing an L1-based rule ensemble approach on any of a given transcription factor (TF).
11. The system as recited in claim 9 , wherein L1-sparsity penalized rule fitting is employed during the generating sets of arbitrarily high-order feature interactions to achieve optimal parameterization.
12. The system as recited in claim 9 , wherein the combinatorial dependency structure includes combinatorial interactions involving TF bindings in cellular systems.
13. The system as recited in claim 9 , wherein the modeler is configured to model observed feature dependencies.
14. The system as recited in claim 9 , wherein a weight associated with the arbitrarily high-order feature interactions in a final sparse high-order MRF is fine-tuned using maximum likelihood learning.
15. The system as recited in claim 9 , wherein hidden units are employed during modeling to model the indirect long-range dependencies between feature groups.
16. The system as recited in claim 9 , wherein the one or more likelihood functions are L1-penalized pseudo-likelihood functions.