Selected work

Representative Papers

State Algebra for Probabilistic Logic

Mar 13, 2026

This work addresses the challenge of integrating logical interpretability with probabilistic reasoning in high-stakes decision-making. It proposes a novel probabilistic state algebra that uniquely embeds logical reduction directly within purely linear algebraic operations, eliminating the need for graph traversal or circuit compilation. By mapping logical states to energy potentials and employing the Hadamard product to construct the Gibbs distribution of a Markov random field, the framework unifies symbolic rules with statistical inference. The approach supports modular rule representation using t-objects and wildcards, yielding a mathematically rigorous, auditable, and maintainable probabilistic logic system well-suited for high-risk human-AI collaboration domains such as healthcare and finance.

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Principled Frequentist Estimation of Racial Disparity in Credit Approval under Unobserved Race

Nov 18, 2025

This paper addresses the challenge of accurately identifying racial disparities in loan approval decisions under regulatory fairness requirements—despite the absence of explicit race information. We propose a frequentist identifiable estimation framework that, under weak exogeneity assumptions, constructs the first consistent estimator for the Black–White approval rate differential. Our approach innovatively integrates surnames as proxy variables with income-stratified demographic priors, thereby mitigating systematic biases inherent in conventional heuristic methods. By jointly modeling via ordinary least squares (OLS) and maximum likelihood estimation (MLE), we combine surname-based racial inference with geodemographic probability models to yield robust individual-level racial probability proxies. Empirical evaluation on Los Angeles Home Mortgage Disclosure Act (HMDA) data demonstrates that our method reduces the root-mean-square error (RMSE) of the Black–White adverse impact ratio by 79.7%, substantially outperforming existing weighted estimation approaches.

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Probabilistic Rule Models as Diagnostic Layers: Interpreting Structural Concept Drift in Post-Crisis Finance

Oct 30, 2025

Concept drift in credit risk prediction degrades model performance over time, particularly during economic crises. Method: This paper proposes an interpretable correction layer architecture based on Probabilistic Rule Models (PRMs), integrating Markov Logic Networks into the model backend to explicitly encode symbolic rules that capture systematic shifts in predicted risk scores—enabling precise diagnosis and attribution of evolving borrower risk structures. Contribution/Results: Unlike opaque adaptive methods, the architecture ensures full auditability and transparency, facilitating post-crisis identification of risk evolution mechanisms for specific demographic cohorts. Experiments on Fannie Mae mortgage data—spanning pre- and post-2008 financial crisis periods—demonstrate that the extracted rules clearly expose heterogeneous risk sensitivities across borrower groups and their structural transformations. The approach significantly enhances model interpretability, explainability, and regulatory compliance—especially in high-risk scenarios.

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State Algebra for Propositional Logic

Sep 12, 2025

Efficient algebraic modeling and computation for propositional logic remain challenging due to the tension between expressive flexibility and representational compactness. Method: This paper introduces State Algebra—a unified algebraic framework built upon a three-layer representation system: sets, coordinates, and row decomposition. It integrates set-theoretic and linear-structural principles, enabling algebraic engine–driven hierarchical representation and variable-ordered reduction. A novel non-normalized state vector reduction mechanism is proposed, restoring canonicity under a fixed variable order while preserving both flexibility and conciseness. Contribution/Results: Experimental evaluation demonstrates State Algebra’s natural expressiveness and scalability across propositional reasoning, knowledge compilation, and weighted model counting. By unifying logical state manipulation, search algorithms, and knowledge compilation within a single algebraic foundation, the framework provides a principled basis for integrating symbolic logic and probabilistic inference.

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$k$-means considered harmful: On arbitrary topological changes in Mapper complexes

Jul 08, 2025

This work identifies a critical topological distortion issue in the Mapper algorithm from Topological Data Analysis (TDA) when employing non-hierarchical clustering methods—such as k-means—as the local clustering step. Such methods can arbitrarily alter the homology groups of the resulting Mapper complex, thereby violating topological fidelity to the underlying data. Through rigorously constructed counterexamples and theoretical analysis, we establish—for the first time—that widely used clustering algorithms lack topological stability within the Mapper framework, and their induced distortions are inherently unbounded. In contrast, connectivity-preserving hierarchical methods—e.g., single-linkage clustering—are shown to be fundamentally better aligned with Mapper’s topological modeling objectives. Our findings provide a crucial theoretical caution for reliable Mapper deployment and articulate explicit topological criteria for clustering method selection. This advances robustness research in TDA by grounding algorithmic design in formal topological guarantees.

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Latest Papers

State Algebra for Probabilistic Logic

Mar 13, 2026

This work addresses the challenge of integrating logical interpretability with probabilistic reasoning in high-stakes decision-making. It proposes a novel probabilistic state algebra that uniquely embeds logical reduction directly within purely linear algebraic operations, eliminating the need for graph traversal or circuit compilation. By mapping logical states to energy potentials and employing the Hadamard product to construct the Gibbs distribution of a Markov random field, the framework unifies symbolic rules with statistical inference. The approach supports modular rule representation using t-objects and wildcards, yielding a mathematically rigorous, auditable, and maintainable probabilistic logic system well-suited for high-risk human-AI collaboration domains such as healthcare and finance.

0 citationsRead paper

Principled Frequentist Estimation of Racial Disparity in Credit Approval under Unobserved Race

Nov 18, 2025

This paper addresses the challenge of accurately identifying racial disparities in loan approval decisions under regulatory fairness requirements—despite the absence of explicit race information. We propose a frequentist identifiable estimation framework that, under weak exogeneity assumptions, constructs the first consistent estimator for the Black–White approval rate differential. Our approach innovatively integrates surnames as proxy variables with income-stratified demographic priors, thereby mitigating systematic biases inherent in conventional heuristic methods. By jointly modeling via ordinary least squares (OLS) and maximum likelihood estimation (MLE), we combine surname-based racial inference with geodemographic probability models to yield robust individual-level racial probability proxies. Empirical evaluation on Los Angeles Home Mortgage Disclosure Act (HMDA) data demonstrates that our method reduces the root-mean-square error (RMSE) of the Black–White adverse impact ratio by 79.7%, substantially outperforming existing weighted estimation approaches.

0 citationsRead paper

Probabilistic Rule Models as Diagnostic Layers: Interpreting Structural Concept Drift in Post-Crisis Finance

Oct 30, 2025

Concept drift in credit risk prediction degrades model performance over time, particularly during economic crises. Method: This paper proposes an interpretable correction layer architecture based on Probabilistic Rule Models (PRMs), integrating Markov Logic Networks into the model backend to explicitly encode symbolic rules that capture systematic shifts in predicted risk scores—enabling precise diagnosis and attribution of evolving borrower risk structures. Contribution/Results: Unlike opaque adaptive methods, the architecture ensures full auditability and transparency, facilitating post-crisis identification of risk evolution mechanisms for specific demographic cohorts. Experiments on Fannie Mae mortgage data—spanning pre- and post-2008 financial crisis periods—demonstrate that the extracted rules clearly expose heterogeneous risk sensitivities across borrower groups and their structural transformations. The approach significantly enhances model interpretability, explainability, and regulatory compliance—especially in high-risk scenarios.

0 citationsRead paper

State Algebra for Propositional Logic

Sep 12, 2025

Efficient algebraic modeling and computation for propositional logic remain challenging due to the tension between expressive flexibility and representational compactness. Method: This paper introduces State Algebra—a unified algebraic framework built upon a three-layer representation system: sets, coordinates, and row decomposition. It integrates set-theoretic and linear-structural principles, enabling algebraic engine–driven hierarchical representation and variable-ordered reduction. A novel non-normalized state vector reduction mechanism is proposed, restoring canonicity under a fixed variable order while preserving both flexibility and conciseness. Contribution/Results: Experimental evaluation demonstrates State Algebra’s natural expressiveness and scalability across propositional reasoning, knowledge compilation, and weighted model counting. By unifying logical state manipulation, search algorithms, and knowledge compilation within a single algebraic foundation, the framework provides a principled basis for integrating symbolic logic and probabilistic inference.

0 citationsRead paper

$k$-means considered harmful: On arbitrary topological changes in Mapper complexes

Jul 08, 2025

This work identifies a critical topological distortion issue in the Mapper algorithm from Topological Data Analysis (TDA) when employing non-hierarchical clustering methods—such as k-means—as the local clustering step. Such methods can arbitrarily alter the homology groups of the resulting Mapper complex, thereby violating topological fidelity to the underlying data. Through rigorously constructed counterexamples and theoretical analysis, we establish—for the first time—that widely used clustering algorithms lack topological stability within the Mapper framework, and their induced distortions are inherently unbounded. In contrast, connectivity-preserving hierarchical methods—e.g., single-linkage clustering—are shown to be fundamentally better aligned with Mapper’s topological modeling objectives. Our findings provide a crucial theoretical caution for reliable Mapper deployment and articulate explicit topological criteria for clustering method selection. This advances robustness research in TDA by grounding algorithmic design in formal topological guarantees.

0 citationsRead paper