METHODS, SYSTEMS, ARTICLES OF MANUFACTURE AND APPARATUS TO IMPROVE ISOTONIC REGRESSION

1 . An apparatus to improve isotonic regression, the apparatus comprising:

interface circuitry;

machine readable instructions; and

programmable circuitry to at least one of instantiate or execute the machine readable instructions to:

analyze a set of data points to generate a subset of data points that violate a trend rule;

average the subset of data points to establish a pooled data point value; and

adjust the pooled data point value to satisfy an upper boundary and a lower boundary corresponding to respective subset data point interval bound information to generate a minimizer.

2 . The apparatus as defined in claim 1 , wherein the subset of data points includes adjacent violators of the trend rule, and the subset of data points is complete if a non-violator data point of the trend rule is met.

3 . The apparatus as defined in claim 1 , wherein the trend rule is the set of data point values that are non-decreasing.

4 . The apparatus as defined in claim 1 , wherein the trend rule is the set of data point values that are non-increasing.

5 . The apparatus as defined in claim 1 , wherein the programmable circuitry is to generate the minimizer for the subset of data points.

6 . The apparatus as defined in claim 1 , wherein the programmable circuitry is to generate the minimizer for each data point within the subset of data points.

7 . The apparatus as defined in claim 1 , wherein the set of data points includes interval bound information including upper bound values and lower bound values.

8 . The apparatus as defined in claim 7 , wherein the lower boundary and the upper boundary are based on the interval bound information, the programmable circuitry to determine the set of data points values satisfy the lower boundary and the upper boundary.

9 . The apparatus as defined in claim 7 , wherein programmable circuitry is to:

evaluate whether ones of the lower bound values are less than respective ones of the upper bound values; and

one of (a) maintain model training when the ones of the lower bound values are less than respective ones of the upper bound values or (b) prevent model training if any lower bound value is greater than the respective upper bound value.

10 . The apparatus as defined in claim 1 , wherein the set of data points is revised with minimizers corresponding to respective ones of the pooled data points within the subset of data points.

11 . An apparatus to improve isotonic regression, the apparatus comprising:

interface circuitry to retrieve data;

computer readable instructions; and

programmable circuitry to instantiate:

interim analysis circuitry to:

analyze a set of data points to generate a subset of data points that violate a trend rule; and

average the subset of data points to establish a pooled data point value; and

minimizer circuitry to adjust the pooled data point value to satisfy an upper boundary and a lower boundary corresponding to respective subset data point interval bound information to generate a minimizer.

12 . The apparatus as defined in claim 11 , wherein the subset of data points includes adjacent violators of the trend rule, and the subset of data points is complete if a non-violator data point of the trend rule is met.

13 . The apparatus as defined in claim 11 , wherein the trend rule is the set of data point values that are non-decreasing.

14 . The apparatus as defined in claim 11 , wherein the trend rule is the set of data point values that are non-increasing.

15 . (canceled)

16 . (canceled)

17 . (canceled)

18 . (canceled)

19 . The apparatus as defined in claim 17 , further includes consistency analysis circuitry to:

evaluate whether ones of the lower bound values are less than respective ones of the upper bound values; and

one of (a) maintain model training when the ones of the lower bound values are less than respective ones of the upper bound values or (b) prevent model training if any lower bound value is greater than the respective upper bound value.

20 . A method to improve isotonic regression, the method comprising:

analyzing, by executing instructions with at least one processor, a set of data points to generate a subset of data points that violate a trend rule;

averaging, by executing instructions with at least one processor, the subset of data points to establish a pooled data point value; and

adjusting, by executing instructions with at least one processor, the pooled data point value to satisfy an upper boundary and a lower boundary corresponding to respective subset data point interval bound information to generate a minimizer.

21 . The method as defined in claim 20 , wherein the set of data points includes interval bound information including an upper bound value and a lower bound value.

22 . The method as defined in claim 21 , wherein the lower boundary and the upper boundary are based on the interval bound information wherein the set of data points values must satisfy the lower boundary and the upper boundary.

23 . The method as defined in claim 21 , further including to:

evaluating, by executing instructions with at least one processor, whether ones of the lower bound values are less than respective ones of the upper bound values; and

one of (a) maintain model training when the ones of the lower bound values are less than respective ones of the upper bound values or (b) prevent model training if any lower bound value is greater than the respective upper bound value.

24 . The method as defined in claim 20 , wherein the subset of data points includes adjacent violators of the trend rule, and the subset of data points is complete if a non-violator data point of the trend rule is met.

25 . (canceled)

26 . (canceled)

27 . (canceled)

28 . (canceled)

29 . (canceled)