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Relationships Methodology
Relationships are the core building block of System. This section outlines how they are computed.
Criteria
The criteria for a piece of statistical evidence to become a relationship on System are:
Source
Strength
Significance
Statistical associations computed by System from a public dataset
Strong or Very Strong
Significant
Statistical associations computed by System from the test set of a machine learning model
Strong or Very Strong
Significant
Statistical associations retrieved from a (peer reviewed) scientific paper
Very Weak, Weak, Moderate, Strong, or Very Strong
Significant
What evidence System collects and computes
System programmatically collects and computes the following evidence from each source of evidence:
Source
Statistical information collected and computed
Dataset
  • For each feature in a dataset, System computes feature statistics which vary depending on the data type of the feature. For example, for numerical features, System computes summary statistics and produces a histogram of the feature’s distribution. When features are “character” or “string” types, System computes statistics based on the string length so as to mask potential sources of personally identifiable information (PII) or protected health information (PHI).
  • For the relevant features in each dataset, System also computes pairwise correlations between features also depending on their data types.
  • When pairs of features are both numerical, System calculates Pearson r correlation values and Kendall rank correlation values.
  • When pairs of features are both numerical and time series, System also calculates statistics on the data after differencing and detrending, and computes “lag” correlations between features (where one time series feature is related to lagged values of another time series feature). Appropriate lags are chosen according to the unit of the time series: {1 day: 30-unit lag, 7 days: 12-unit lag, 30 days: 6-unit lag, 365 days: 10-unit lag}
  • When pairs of features are categorical, System calculates Cramer’s V association values.
  • When one feature in a pair is numerical and the other is categorical, System calculates Kruskal Wallis h-test values.
  • For datasets retrieved with the platform’s data warehouse integrations (Redshift, BigQuery, Snowflake), System currently computes only Pearson r correlation values (for numerical and time series features) and computes the relevant relationships between time series features.
Model
  • For each feature in a dataset used for training or testing a model, System computes feature statistics which vary depending on the data type of the feature. For example, for numerical features, System computes summary statistics and produces a histogram of the feature’s distribution. When features are “character” or “string” types, System computes statistics based on the string length so as to mask potential sources of personally identifiable information (PII) or protected health information (PHI).
  • For the relevant features in each dataset, System also computes pairwise correlations between features also depending on their data types.
  • When pairs of features are both numerical, System calculates Pearson r correlation values and Kendall rank correlation values.
  • When pairs of features are both numerical and time series, System also calculates statistics on the data after differencing and detrending, and computes “lag” correlations between features (where one time series feature is related to lagged values of another time series feature, where the appropriate lags are chosen according to the unit of time).
  • When pairs of features are categorical, System calculates Cramer’s V association values.
  • When one feature in a pair is numerical and the other is categorical, System calculates Kruskal Wallis h-test values.
  • For datasets retrieved with the platform’s data warehouse integrations (Redshift, BigQuery, Snowflake), System currently computes only Pearson r correlation values (for numerical and time series features) and computes the relevant relationships between time series features. For models shared on System, the platform collects information about the model and computes performance metrics and feature importance values based on submitted “test” datasets (or “training” datasets, when also submitted).
  • For model objects, metadata about the statistical package used to train the model (e.g., scikit-learn, XGBoost, statsmodels, Tensorflow, etc.), the model specification (including any specified hyperparameters), and the names of features used to train the model are collected and presented on model pages.
  • Depending on the model type, relevant performance metrics are computed using the “test” sample provided. For classifier models, these include (but are not limited to) Accuracy, Precision, Recall, F1 score, ROC AUC, and confusion matrices. For regression models, these include R2 scores, and measures of prediction error (RMSE, etc.).
  • Additionally, feature importance scores are calculated. For each model performance metric, a “permutation score” is computed, where the contribution of each feature’s impact on the performance metric is calculated by measuring how random permutation of a feature’s value affects the performance metric. This effect is reported and features are assigned rank values based on the relative importance.
  • System also computes interpretability and explainability measures when appropriate. Model pages often include partial dependence plots (PDPs) alongside feature importance values to show the marginal impact of a feature on a model’s predicted values. Model pages will soon also include SHAP importance plots for features.
  • For models deployed “in production,” drift in both model performance and feature importance is tracked.
Paper
  • From Digital Object Identifier (DOI) ids, System retrieves metadata about the relevant objects, like author(s), titles, and publications.
  • We are working on NLP-based parsing and extraction of relationships from scientific papers. Relationship candidates are then reviewed by users.
How System determines “strength”
Strength is an algorithm-agnostic measure of the magnitude of the effect implied by an association. System's methodology differs based on the type of the association.
For correlation-style associations (such as Pearson's R, or Kendall's Tau) we use commonly accepted community guidelines to bucket those associations into one of the five following categories:
STRENGTH
PEARSON-R
KENDALL-TAU
CRAMER-V
EFFECT SIZE
Very Weak
[0, 0.1)
[0, 0.1)
[0, 0.05)
[0, 0.1)
Weak
[0.1, 0.3)
[0.1, 0.3)
[0.05, 0.1)
[0.1, 0.3)
Medium
[0.3, 0.6)
[0.3, 0.6)
[0.1, 0.15)
[0.3, 0.6)
Strong
[0.6, 0.9)
[0.6, 0.9)
[0.15, 0.25)
[0.6, 0.9)
Very Strong
[0.9, 1]
[0.9, 1]
[0.25, …)
[0.9, 1]
For associations derived from predictive models, we use the evidence already on System to bin the value of a feature’s importance into one of the above buckets. The feature importance value (e.g. permutation score) combined with the performance of the model that the association was derived from (e.g. F1 score) is compared with similar associations on System.
STRENGTH
REGRESSORS (R2 SCORE * PERMUTATION SCORE)
CLASSIFIERS (F1 SCORE * PERMUTATION SCORE)
Very Weak
[0, 0.1) of max on System
[0, 0.1) of max on System
Weak
[0.1, 0.3) of max on System
[0.1, 0.3) of max on System
Medium
[0.3, 0.6) of max on System
[0.3, 0.6) of max on System
Strong
[0.6, 0.9) of max on System
[0.6, 0.9) of max on System
Very Strong
[0.9, 1] of max on System
[0.9, 1] of max on System
Examples
Source
Source Type
Statistical Association Retrieved
Strength
Significance
Relationship on System
Dataset
PEARSON R: 0.983 between
primary_school_life_expectancy_years
and
primary_school_completion_rate_female
Very Strong
P < 0.001
Link
Dataset
Max PEARSON R (when one feature is lagged): 0.867 between
Confirmed Cases Of COVID-19
and
Deaths From COVID-19
+ 23 lag
Strong
P < 0.001
Link
Model
R2 Permutation Score: 0.225 between
Two_Week_Prior_Weekly_Deaths
and
Weekly_Deaths
Very Strong
P < 0.001
Link
Paper
Adjusted Odds Ratio: 1.94 between
Individual Is A Lifetime Cigarette Smoker
and
Individual Consumes Caffeinated Coffee
Very Strong
P = 0.003
Link
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