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Indiana University-Purdue University Indianapolis

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Research library43linked papers
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Selected work

Representative Papers

A Regression-Based Framework for the ACF, PACF, Durbin-Levinson Recursion, and One-Step-Ahead Prediction

Aug 06, 2026

This study addresses the common pedagogical disconnect in time series analysis, where autocorrelation function (ACF) and partial autocorrelation function (PACF) are often taught in isolation from regression principles. The paper proposes a unified regression-based perspective, systematically interpreting ACF as the ordinary least squares (OLS) coefficient from a simple linear regression on a lagged variable, and PACF as the partial regression coefficient of an additional lag in a multivariate regression framework. It further reveals that the Durbin–Levinson recursion fundamentally embodies a sequence of partial regression steps. Through illustrative AR(1) and MA(1) examples grounded in OLS theory and stationarity assumptions, the work clarifies the regression origins of ACF’s tailing-off behavior and PACF’s cutoff property, substantially lowering conceptual barriers. Practical teaching recommendations are offered to bridge the gap between regression and time series curricula.

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Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos

Jul 23, 2026

This study addresses the challenge that multiplicative weights update algorithms in games often fail to converge to Nash equilibria and exhibit unpredictable long-term behavior due to Li-Yorke chaos. To overcome this, we introduce for the first time the natural invariant measure from ergodic theory into the analysis of game dynamics. This framework not only characterizes strategy frequencies but also precisely computes long-run time averages of economically relevant observables—such as payoffs, social cost, and regret—even in the absence of pointwise convergence. Focusing on two-strategy congestion games, we rigorously establish that the system retains statistical predictability and provide a unified description of its full dynamical spectrum, ranging from periodic attractors to coexisting chaotic regimes, thereby revealing the algorithm’s capacity to replicate canonical behaviors of one-dimensional dynamical systems.

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SLT: Robust Quantum Neural Networks for Noisy-Label Medical Image Classification via Supermartingale-based Label Transition

Jul 13, 2026

This work addresses the performance degradation of quantum neural networks in small-scale medical image classification caused by label noise. To tackle this issue, the authors propose SLT, an anchor-free loss correction framework that, for the first time, incorporates supermartingale theory into quantum learning with noisy labels. By modeling the entropy reduction of predictive distributions as a supermartingale, SLT leverages its monotonicity to dynamically refine the label transition matrix without relying on anchor points, thereby enabling robust training with guaranteed convergence stability. Experimental results demonstrate that SLT consistently outperforms existing classical methods across multiple public small-scale medical image datasets under both synthetic and real-world label noise scenarios.

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Recent publications

Latest Papers

A Regression-Based Framework for the ACF, PACF, Durbin-Levinson Recursion, and One-Step-Ahead Prediction

Aug 06, 2026

This study addresses the common pedagogical disconnect in time series analysis, where autocorrelation function (ACF) and partial autocorrelation function (PACF) are often taught in isolation from regression principles. The paper proposes a unified regression-based perspective, systematically interpreting ACF as the ordinary least squares (OLS) coefficient from a simple linear regression on a lagged variable, and PACF as the partial regression coefficient of an additional lag in a multivariate regression framework. It further reveals that the Durbin–Levinson recursion fundamentally embodies a sequence of partial regression steps. Through illustrative AR(1) and MA(1) examples grounded in OLS theory and stationarity assumptions, the work clarifies the regression origins of ACF’s tailing-off behavior and PACF’s cutoff property, substantially lowering conceptual barriers. Practical teaching recommendations are offered to bridge the gap between regression and time series curricula.

0 citationsRead paper

Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos

Jul 23, 2026

This study addresses the challenge that multiplicative weights update algorithms in games often fail to converge to Nash equilibria and exhibit unpredictable long-term behavior due to Li-Yorke chaos. To overcome this, we introduce for the first time the natural invariant measure from ergodic theory into the analysis of game dynamics. This framework not only characterizes strategy frequencies but also precisely computes long-run time averages of economically relevant observables—such as payoffs, social cost, and regret—even in the absence of pointwise convergence. Focusing on two-strategy congestion games, we rigorously establish that the system retains statistical predictability and provide a unified description of its full dynamical spectrum, ranging from periodic attractors to coexisting chaotic regimes, thereby revealing the algorithm’s capacity to replicate canonical behaviors of one-dimensional dynamical systems.

0 citationsRead paper

SLT: Robust Quantum Neural Networks for Noisy-Label Medical Image Classification via Supermartingale-based Label Transition

Jul 13, 2026

This work addresses the performance degradation of quantum neural networks in small-scale medical image classification caused by label noise. To tackle this issue, the authors propose SLT, an anchor-free loss correction framework that, for the first time, incorporates supermartingale theory into quantum learning with noisy labels. By modeling the entropy reduction of predictive distributions as a supermartingale, SLT leverages its monotonicity to dynamically refine the label transition matrix without relying on anchor points, thereby enabling robust training with guaranteed convergence stability. Experimental results demonstrate that SLT consistently outperforms existing classical methods across multiple public small-scale medical image datasets under both synthetic and real-world label noise scenarios.

0 citationsRead paper