algorithms.md

Federated Analysis Algorithms

The MIP federated analysis algorithms are implemented and documented in Exaflow. The algorithm-specific technical documentation is available in the Exaflow repository under documentation/algorithms.

The linked Exaflow documentation describes each algorithm's inputs, parameters, statistical or machine-learning method, federated computation, outputs, validation reference, and limitations.

Summary and Visualization

Algorithm	Description	Documentation
Descriptive Statistics	Summarizes selected numerical and nominal variables with per-dataset and combined summaries.	Documentation
Histogram	Computes counts for one numerical or categorical variable, optionally split by categorical grouping variables.	Documentation
Outlier Report	Reports outlier bounds, counts, and percentages for numerical variables using Gaussian, IQR, MAD, or quantile rules.	Documentation

Statistical Tests

Algorithm	Description	Documentation
One-way ANOVA	Tests whether a numerical outcome has the same mean across levels of one categorical grouping variable.	Documentation
Two-way ANOVA	Tests whether a numerical outcome differs across two categorical factors, including main effects and interaction.	Documentation
Chi-squared Test	Evaluates whether two categorical variables are independent using a contingency table.	Documentation
Fisher's Exact Test	Evaluates association between two binary categorical variables using exact 2 by 2 table probabilities.	Documentation
Independent t-test	Compares the mean of a numerical variable between two independent groups using the pooled-variance Student t-test.	Documentation
One-sample t-test	Compares the mean of a numerical variable with a reference mean.	Documentation
Paired t-test	Compares two related numerical measurements by testing whether the mean paired difference is zero.	Documentation
Pearson Correlation	Measures linear association between numerical variables and reports correlations, p-values, and confidence intervals.	Documentation

Regression and Survival Analysis

Algorithm	Description	Documentation
Linear Regression	Fits an ordinary least squares model for a numerical outcome using numerical and/or categorical covariates.	Documentation
Logistic Regression	Models a binary outcome as a function of numerical and/or categorical covariates.	Documentation
Cox Proportional Hazards Regression	Models time-to-event data with a partial likelihood Cox model and an unspecified baseline hazard.	Documentation
Stacked Cox Regression	Approximates time-to-event modeling by expanding survival data into risk-set rows and fitting logistic regression with time-bin indicators.	Documentation

Machine Learning

Algorithm	Description	Documentation
K-means	Partitions observations into clusters using numerical variables and squared Euclidean distance.	Documentation
Principal Component Analysis	Computes principal components using global standardization and eigendecomposition of the aggregated covariance matrix.	Documentation
PCA with Transformations	Applies selected per-variable transformations before computing principal components.	Documentation
Gaussian Naive Bayes	Classifies observations with numerical features by modeling each feature as Gaussian within each class.	Documentation
Gaussian Naive Bayes K-fold Cross-validation	Evaluates Gaussian Naive Bayes with K-fold cross-validation and returns confusion-matrix and fold-level metrics.	Documentation
Categorical Naive Bayes	Classifies observations with nominal features by estimating class-conditional category probabilities.	Documentation
Categorical Naive Bayes K-fold Cross-validation	Evaluates categorical Naive Bayes with K-fold cross-validation and returns confusion-matrix and fold-level metrics.	Documentation
Linear SVM	Fits linear support vector classifiers at each site and averages learned coefficients and intercepts.	Documentation
Federated Averaging	Combines model parameters learned separately at multiple sites by averaging each named parameter array.	Documentation

Preprocessing

Algorithm	Description	Documentation
Preprocessing Steps	Documents missing-value handling, outlier winsorization, and longitudinal transformation steps used before downstream algorithms.	Documentation
Outlier Winsorizer	Clips selected numerical variables to bounds computed from Gaussian, IQR, MAD, or quantile rules.	Documentation