Collaborative targeted maximum likelihood learning
First Claim
1. A method comprising:
- determining one or more initial distribution estimators of a true probability distribution;
determining a series of estimators of a nuisance parameter;
generating targeted candidate estimators of the probability distribution for a targeted feature using an iterative modification of the one or more initial distribution estimators based on the series of estimators and the targeted feature; and
selecting one of the candidate estimators as an estimator for the true probability distribution for the targeted feature.
2 Assignments
0 Petitions
Accused Products
Abstract
A method is provided comprising: determining one or more initial distribution estimators of a true probability distribution; determining for each series of estimators of a nuisance parameter; generating candidate targeted estimators of the probability distribution for a targeted feature using an iterative modification of the initial distribution estimator(s) designed to reduce bias in the estimate of the target feature with respect to the initial distribution estimator, based on the series of estimators and the targeted feature; selecting one of the candidate estimators as an estimator for the true probability distribution for the targeted feature; and applying a mapping to the estimator for the true probability distribution or relevant portion thereof to obtain an estimated value for the targeted feature.
4 Citations
27 Claims
-
1. A method comprising:
-
determining one or more initial distribution estimators of a true probability distribution; determining a series of estimators of a nuisance parameter; generating targeted candidate estimators of the probability distribution for a targeted feature using an iterative modification of the one or more initial distribution estimators based on the series of estimators and the targeted feature; and selecting one of the candidate estimators as an estimator for the true probability distribution for the targeted feature. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
-
-
12. A method for obtaining an estimator of a true probability distribution, and a corresponding estimator of a target feature, the method comprising:
-
selecting one or more initial estimators ({circumflex over (P)}) of a true probability distribution (PTRUE) of a dataset based on one or more candidate estimators (P), a feature map (Ψ
), and the dataset;determining one or more series of estimators (g-estimators) of a nuisance parameter (gTRUE); and employing the one or more series of estimators (g-estimators) to modify the one or more initial estimators ({circumflex over (P)}) and to provide one or more candidate targeted estimators ({circumflex over (P)}*) in response thereto. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
-
-
24. A method comprising:
-
obtaining a dataset; determining a first set of one or more candidate estimators (P) of a true probability distribution (PTRUE) of the dataset; employing a feature map, the dataset, and the one or more candidate estimators to determine a set of one or more initial distribution estimators ({circumflex over (P)}); using the feature map and the set of one or more initial distribution estimators ({circumflex over (P)}) to determine a series of estimators (g-estimators) of a nuisance parameter (gTRUE); and modifying the set of one or more initial distribution estimators ({circumflex over (P)}) via the series of estimators (g-estimators) of a nuisance parameter, yielding one or more modified estimators ({circumflex over (P)}*) in response thereto.
-
-
25. A method comprising:
-
selecting an initial estimator (ĝ
1*) of a nuisance parameter, wherein the nuisance parameter is characterized by a true distribution (gTRUE);employing the initial estimator (ĝ
1*) to construct a set of tentative candidate estimators of the nuisance parameter based on a sequence of estimators of a nuisance parameter;selecting an estimator from the set of tentative candidate estimators based on a first predetermined selection method and providing one or more selected estimators of the nuisance parameter in response thereto; and choosing a preferred candidate estimator of the nuisance parameter from the selected estimators of the nuisance parameter based on a second predetermined selection method.
-
-
26. A method comprising:
-
generating a sequence of targeted maximum likelihood estimators, wherein the sequence includes estimators with increasing likelihood, and wherein each estimator that has a higher likelihood than a previous estimator is indexed by a nuisance parameter estimator that is more nonparametric than a previous nuisance parameter estimator used to index the previous estimator; updating one or more estimators of the sequence of targeted maximum likelihood estimators and providing one or more updated estimators in response thereto, wherein updating includes adjusting one or more nuisance parameters that index targeted maximum likelihood estimators of the sequence; and selecting one or more estimators from the updated estimators and providing one or more selected estimators. - View Dependent Claims (27)
-
Specification