Methods and systems for induction and use of probabilistic patterns to support decisions under uncertainty
Methods and systems are provided for the induction and use of probabilistic patterns in data to support decisions under uncertainty. In an aspect, the proposed approach both suggests a decision and justifies the suggestion in a convenient form for an end-user (e.g., a physician). At least one probabilistic pattern of the form B(x)→C may be generated based on data for cases with known classification. Pattern-coded data may be generated for the known cases and for another case (e.g., a test case or a new case), by evaluating the data for the known cases and other case with the at least one probabilistic pattern. A classification decision may be made for the test case by subjecting the pattern-coded data to, for example, an ordering and ranking procedure or a voting procedure. Because the probabilistic patterns are readily interpretable, the end-user can verify the validity of both the patterns and the decision.
1 . A method for the induction and use of probabilistic patterns to support a decision under uncertainty, the method comprising:
generating at least one probabilistic pattern of the form B(x)→C based on data for cases with known classification, where B(x) comprises at least one condition on a variable and C comprises an outcome;
generating pattern-coded data for the cases with known classification and for another case, by evaluating the data for the cases with known classification and data for the other case with the at least one probabilistic pattern; and
using the pattern-coded data to classify the other case.
2 . The method of claim 1 , wherein said generating at least one probabilistic pattern comprises identifying in the data for the cases with known classification rules of the form B(x)→C that satisfy criteria for statistical significance and generality.
3 . The method of claim 2 , wherein said statistical significance is determined by a z-test criterion.
4 . The method of claim 2 , wherein said statistical significance is determined by a chi-squared criterion.
5 . The method of claim 1 , wherein said generating the at least one probabilistic pattern comprises:
identifying one or more rules B(X)→C from the data for the cases with known classification that satisfy the following a criteria for statistical significance:
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determining, for each identified rule, whether that rule is the most general rule amongst other rules comparable by generality.
6 . The method of claim 5 , wherein said generating further comprises identifying rules with no more than k non-trivial conditions on the variable(s).
7 . The method of claim 1 , wherein said using the pattern-coded data to classify the other case comprises subjecting the pattern-coded data to a multi-dimensional partial ordering and ranking procedure in order to classify the test case.
8 . The method of claim 1 , wherein said using the pattern-coded data to classify a test case comprises:
determining a score, for each case of the known cases and the test case;
determining a threshold value based on the scores for the known cases; and
comparing the score for the test case to the threshold.
9 . A method for using probabilistic patterns to support a decision under uncertainty, the method comprising:
generating pattern-coded data for a case by evaluating if feature data for the case satisfies the premise B(x) of at least one probabilistic pattern of the form B(x)→C, wherein C comprises an outcome; and
classifying the case according to the pattern-coded dataset.
10 . The method of claim 9 , wherein said classifying the case according to the pattern-coded dataset comprises:
determining a score for the case based on the pattern-coded dataset by subtracting a number of patterns associated with a first class that the case exhibits from a number of patterns associated with a second class that the case exhibits; and
comparing the score to a threshold.
11 . The method of claim 9 , wherein evaluating feature data comprises evaluating data for one or more clinical features, one or more molecular features, and one or more computer-generated morphometric features.
12 . A system for the induction and use of probabilistic patterns to support a decision under uncertainty, the system comprising processing circuitry configured to:
generate at least one probabilistic pattern of the form B(x)→C based on data for cases with known classification, where B(x) comprises at least one condition on a variable and C comprises an outcome;
generate pattern-coded data for the cases with known classification and for another case, by evaluating the data for the cases with known classification and data for the other case with the at least one probabilistic pattern; and
use the pattern-coded data to classify the other case.
13 . The system of claim 12 , wherein said processing circuitry configured to generate at least one probabilistic pattern comprises processing circuitry configured to identify in the data for the cases with known classification rules of the form B(x)→C that satisfy criteria for statistical significance and generality.
14 . The system of claim 13 , wherein said statistical significance is determined by a z-test criteria.
15 . The system of claim 13 , wherein said statistical significance is determined by a chi-squared criteria.
16 . The system of claim 12 , wherein said processing circuitry configured to generate the at least one probabilistic pattern comprises processing circuitry configured to:
identify one or more rules B(X)→C from the data for the cases with known classification that satisfy the following a criteria for statistical significance:
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where h and g are constants; and
determine, for each identified rule, whether that dependency is the most general rule amongst other rules comparable by generality.
17 . The system of claim 16 , wherein said processing circuitry configured to generate the at least one probabilistic pattern is further configured to identify rules with no more than k non-trivial conditions on the variable(s).
18 . The system of claim 12 , wherein said processing circuitry configured to use the pattern-coded data to classify a test case is configured to subject the pattern-coded data to a multi-dimensional partial ordering and ranking procedure in order to classify the test case.
19 . The system of claim 12 , wherein said processing circuitry configured to use the pattern-coded data to classify a test case is configured to:
determine a score, for each case of the known cases and the test case;
determine a threshold value based on the scores for the known cases; and
compare the score for the test case to the threshold.
20 . A system for predicting an outcome for a case, the system comprising processing circuitry configured to:
generate pattern-coded data for a case by evaluating if feature data for the case satisfies the premise B(x) of at least one probabilistic pattern of the form B(x)→C, wherein C comprises an outcome; and
classifying the case according to the pattern-coded dataset.
21 . The system of claim 20 , wherein said processing circuitry configured to classify the case is configured to:
determine a score for the case based on the pattern-coded dataset by subtracting a number of patterns associated with a first class that the case exhibits from a number of patterns associated with a second class that the case exhibits; and
comparing the score to a threshold.
22 . The system of claim 20 , wherein said feature data comprises one or more clinical features, one or more molecular features, and one or more computer-generated morphometric features.
23 . Computer-readable medium encoded with computer program instructions for performing the method comprising:
generating at least one probabilistic pattern of the form B(x)→C based on data for cases with known classification, where B(x) comprises at least one condition on a variable and C comprises an outcome;
generating pattern-coded data for the cases with known classification and for another case, by evaluating the data for the cases with known classification and data for the other case with the at least one probabilistic pattern; and
using the pattern-coded data to classify the other case.
24 . The computer-readable medium of claim 23 , wherein said generating at least one probabilistic pattern comprises identifying in the data for the cases with known classification rules of the form B(x)→C that satisfy criteria for statistical significance and generality.