Regression LLM options

Aggregate data before processing

aggregate

If selected, identical patterns are aggregated and considered as a single pattern during the training phase.

Minimize number of conditions

minimal

If selected, rules with fewer conditions, but the same covering, are privileged.

Perform a coarse-grained training

lowest

If selected, the LLM training algorithm considers the conditions with the subset of values that maximizes covering for each input attribute. Otherwise, only one value at a time is added to each condition, thus performing a more extensive search. The coarse-grained training option has the advantage of being faster than performing an extensive search.

Prevent interval conditions for ordered attributes

nointerval

If selected, interval conditions such as 1<x≤5 are avoided, and only conditions with > (greater than) ≤ (lower or equal than) are generated.

Ignore attributes not present in rules

reducenames

If selected, attributes that have not been included in rules will be flagged Ignore at the end of the training process, to reflect their redundancy in the classification problem at hand.

Hold all the generated rules

holdrules

If selected, even redundant generated rules, which are verified only by training samples that already covered by other more powerful rules, are kept.

Use median as output value

usemedian

If selected, the median is used instead of the average when computing the output of each rule.

Consider relative error instead of absolute

relerrmax

Specify whether the relative or absolute error must be considered.

The Maximum error allowed for each rule is set by considering proportions of samples belonging to different classes. Imagine a scenario where for given rule pertaining to the specific output value y_o:

• TP is the number of true positives (samples with the output value y_o that verify the conditions of the rule).

• TN is the number of true negatives (samples with output values different from y_o that do not verify the conditions of the rule).

• FP is the number of false positives (samples with output values different from y_o that do verify the conditions of the rule).

• FN is the number of false negatives (samples with the output values y_o that do not verify the conditions of the rule).

In this scenario the absolute error of that rule is FP/(TN+FP), whereas the relative error is obtained as follows: FP/Min(TP+FN,TN+FP) (samples with the output value y_o that do verify the conditions of the rule).

Maximum number of trials in bottom-up mode

nbuiter

The number of times a bottom-up procedure can be repeated, after which a top-down procedure will be adopted. 

The bottom-up procedure starts by analyzing all possible cases, defining conditions and reducing the extension of the rules. If, at the end of this procedure, the error is higher than the value entered for the Maximum error allowed for each rule (%) option, the procedure starts again, inserting an increased penalty on the error. If the maximum number of trials is reached without obtaining a satisfactory rule, the procedure is switched to a top-down approach.

Maximum desired dispersion coefficient

maxsdev

The maximum dispersion coefficient of the output points contained in the rule. The higher the dispersion the more generic the rules.

Overlap between rules (%)

maxoverlap

Set the maximum percentage of patterns, which can be shared by two rules.

Maximum nominal values

maxnomval

Set the maximum number of nominal values that can be contained in a condition. This is useful for simplifying conditions and making them more manageable, for example when an attribute has a very high number of possible nominal values. It is worth noting that overly complicated conditions also run the risk of over-fitting, where rules are too specific for the test data, and not generic enough to be accurate on new data.

Number of rules for each class (0 means 'automatic')

numrules

If set to 0 the minimum number of rules required to cover all patterns in the training set is generated. Otherwise set the desired number of rules for each class.

Initialize random generator with seed

initrandom, iseed

If selected, a seed, which defines the starting point in the sequence, is used during random generation operations. Consequently using the same seed each time will make each execution reproducible. Otherwise, each execution of the same task (with same options) may produce dissimilar results due to different random numbers being generated in some phases of the process.

Maximum error in classification sub-problems (%)

errmax

Maximum percentage of errors allowed when building rules that distinguish between the clustered and non-clustered points. A value higher than 0 could increase dispersion of rules.

Append results

append

If selected, the results of this computation are appended to the dataset, otherwise they replace the results of previous computations.

Maximum number of conditions for a rule

maxant

Set the maximum number of conditions in a rule.

Missing values verify any rule condition

missrelax

If selected, missing values will be assumed to satisfy any condition. If there is a high number of missing values, this choice can have an important impact on the outcome.

Key Attributes

keynames

Drag and drop here the key attributes. Rulex will create a different set of rules for each key attribute value.​ Instead of manually dragging and dropping attributes, they can be defined via a filtered list.

Key attributes are the attributes that must always be taken into consideration in rules, and every rule must always contain a condition for each of the key attributes.

After importing the Adult dataset with the Import from Text File task, add a Split Data task to split the data into test (30%) and training (70%) datasets.

Then add a Regression LLM task to the process, specify hours-per-week as the output attribute, and the following attributes as input attributes:

• age

• workclass

• education

• occupation

• race

• marital-status

• sex

• native-country

Then save and compute the task.

The distribution and properties of the generated rules can be viewed in the Monitor tab of the LLM task. For example, there are 2458 rules with 4 conditions.

The total number of rules, and the minimum, maximum and average of the number of conditions is reported, too.

Analogous histograms can be viewed for covering and error, by clicking on the corresponding tabs.

Clicking on the Results tab displays a great deal of information on the task, such as 

• the execution time (only for the LLM task),

• some input data properties, such as the number of patterns and attributes

• some results of the computation, such as number of rules and rule statistics, etc.

The rule spreadsheet that can be viewed by double-clicking on the Rule Manager task is initially ordered by output value.

For example, rule 2292 states that if age is 20 and occupation is in the set {Craft-repair, Farming-fishing, transport-moving} and sex is Female then hours-per-week is 36.

The forecast ability of the set of rules resulting from LLM can be viewed by adding an Apply Model task to the process, and computing it with default values.

Right-click the computed Apply Model task and select Take a look, to check the results.

The following columns have been added to the data set:

• the forecast for each pattern: pred(hours-per-week)

• the confidence relative to this forecast conf(hours-per-week) 

• the most important rule that determined the prediction: rule(hours-per-week)

• the forecast error, i.e. the difference between the real and predicted value: err(hours-per-week)

Selecting Test Set from the Displayed data drop down list shows how the rules behave on new data.

In the test set, the value of RMSE is 12.1148, slightly higher than the overall score.