Lilliefors

Assesses the normality of feature distributions in an ML model’s training dataset using the Lilliefors test.

Purpose

The purpose of this metric is to utilize the Lilliefors test, named in honor of the Swedish statistician Hubert Lilliefors, in order to assess whether the features of the machine learning model’s training dataset conform to a normal distribution. This is done because the assumption of normal distribution plays a vital role in numerous statistical procedures as well as numerous machine learning models. Should the features fail to follow a normal distribution, some model types may not operate at optimal efficiency. This can potentially lead to inaccurate predictions.

Test Mechanism

The application of this test happens across all feature columns within the training dataset. For each feature, the Lilliefors test returns a test statistic and p-value. The test statistic quantifies how far the feature’s distribution is from an ideal normal distribution, whereas the p-value aids in determining the statistical relevance of this deviation. The final results are stored within a dictionary, the keys of which correspond to the name of the feature column, and the values being another dictionary which houses the test statistic and p-value.

Signs of High Risk

• If the p-value corresponding to a specific feature sinks below a pre-established significance level, generally set at 0.05, then it can be deduced that the distribution of that feature significantly deviates from a normal distribution. This can present a high risk for models that assume normality, as these models may perform inaccurately or inefficiently in the presence of such a feature.

Strengths

• One advantage of the Lilliefors test is its utility irrespective of whether the mean and variance of the normal distribution are known in advance. This makes it a more robust option in real-world situations where these values might not be known.
• The test has the ability to screen every feature column, offering a holistic view of the dataset.

Limitations

• Despite the practical applications of the Lilliefors test in validating normality, it does come with some limitations.
• It is only capable of testing unidimensional data, thus rendering it ineffective for datasets with interactions between features or multi-dimensional phenomena.
• The test might not be as sensitive as some other tests (like the Anderson-Darling test) in detecting deviations from a normal distribution.
• Like any other statistical test, Lilliefors test may also produce false positives or negatives. Hence, banking solely on this test, without considering other characteristics of the data, may give rise to risks.