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- Behavioral learning machines (1)
- Convergence analysis (1)
- Fibonacci Ensembles; Recursive Ensemble Dynamics; Rao-Blackwell Optimization; Orthogonalization; Variance Reduction; Bio-inspired Learning; Second-order Update Flows; Harmonics in Machine Learning; Representational Depth (1)
- Hierarchical learning (1)
- RKHS Ensemble Theory; Spectral Shrinkage; Linear Operator Representations; Structured Weighting Laws; Bias-Variance Decomposition; Approximation Geometry; Quadratic Programming; Uniform vs. Non-uniform Ensembles; Regularized Hypothesis Spaces (1)
Articles 1 - 5 of 5
Full-Text Articles in Statistical Theory
Saturated Hierarchical Atomic Incremental Learning (Shail): A Behavioral Learning Perspective On Staged Mastery And Saturation, Ernest Fokoue
Saturated Hierarchical Atomic Incremental Learning (Shail): A Behavioral Learning Perspective On Staged Mastery And Saturation, Ernest Fokoue
Articles
We introduce Saturated Hierarchical Atomic Incremental Learning (sHAIL), a learning paradigm in which complex tasks are approached through a sequence of simpler atomic subtasks, each mastered to saturation before progression. The central mechanism is a saturation criterion that detects when learning dynamics enter a plateau region, triggering consolidation and subsequent ascent to a higher level of task complexity. We develop a theoretical framework for sHAIL and show that it naturally gives rise to \emph{staircased convergence}: alternating phases of rapid improvement and genuine plateau. Within each level, classical convergence guarantees apply under standard smoothness conditions, while the hierarchical transitions are driven …
No Intelligence Without Statistics: The Invisible Backbone Of Artificial Intelligence, Ernest Fokoue
No Intelligence Without Statistics: The Invisible Backbone Of Artificial Intelligence, Ernest Fokoue
Articles
The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars—Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification—demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the …
Decorrelation, Diversity, And Emergent Intelligence: The Isomorphism Between Social Insect Colonies And Ensemble Machine Learning, Ernest Fokoue, Gregory Babbitt, Yuval Levental
Decorrelation, Diversity, And Emergent Intelligence: The Isomorphism Between Social Insect Colonies And Ensemble Machine Learning, Ernest Fokoue, Gregory Babbitt, Yuval Levental
Articles
Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation— through stochastic response to local cues and positive feedback—map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that …
A General Weighting Theory For Ensemble Learning: Beyond Variance Reduction Via Spectral And Geometric Structure, Ernest Fokoue
A General Weighting Theory For Ensemble Learning: Beyond Variance Reduction Via Spectral And Geometric Structure, Ernest Fokoue
Articles
Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines, kernel ridge regression, Gaussian process regression, and other regularized reproducing kernel Hilbert space (RKHS) methods whose variance is already tightly controlled by regularization and spectral shrinkage. This paper develops a general weighting theory for ensemble learning that moves beyond classical variance-reduction arguments. We formalize ensembles as linear operators acting on a hypothesis space and endow the space of weighting sequences with geometric and spectral constraints. …
On Fibonacci Ensembles: An Alternative Approach To Ensemble Learning Inspired By The Timeless Architecture Of The Golden Ratio, Ernest Fokoue
On Fibonacci Ensembles: An Alternative Approach To Ensemble Learning Inspired By The Timeless Architecture Of The Golden Ratio, Ernest Fokoue
Articles
Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to the unfolding of leaves, this humble sequence reflects a universal grammar of balance. In this work, we introduce \emph{Fibonacci Ensembles}, a mathematically principled yet philosophically inspired framework for ensemble learning that complements and extends classical aggregation schemes such as bagging, boosting, and random forests \citep{Breiman1996Bagging, Breiman2001RandomForests, Friedman2001GBM, Zhou2012Ensemble, HastieTibshiraniFriedman2009ESL}. Two intertwined formulations unfold: (1) the use of normalized Fibonacci weights -- tempered through orthogonalization and Rao--Blackwell optimization -- …