Regression neural networks commonly suffer from sensitivity to outliers and contaminated data, limiting their reliability in real-world applications. Abhik Ghosh and Suryasis Jana, both from the Indian Statistical Institute, Kolkata, alongside Abhik Ghosh et al., present a novel robust learning framework, termed ‘rRNet’, utilising ββ-divergences to address this critical issue. This research significantly advances the field by offering provable robustness guarantees for a broad class of regression neural networks, including those with non-smooth activation functions, something largely absent in current methods. Through rigorous theoretical characterisation of influence functions and demonstration of an optimal 50% asymptotic breakdown point, the authors establish a strong foundation for globally robust neural network learning, validated through simulations and real-data analyses.
Mitigating regression instability via beta-divergence optimisation
Researchers have developed a new robust learning framework, termed rRNet, designed to improve the reliability of regression neural networks when faced with contaminated or outlying data. Conventional training methods, typically relying on minimising mean squared prediction error, are known to be highly susceptible to even minor data imperfections.
This work addresses this vulnerability by leveraging β-divergences, also known as density power divergences, to create a learning process less affected by problematic data points. The rRNet framework is broadly applicable, functioning effectively with neural networks featuring non-smooth activation functions and accommodating various error densities.
This innovative approach recovers classical maximum likelihood learning as a specific case, offering a seamless transition for existing implementations. Implementation of rRNet involves an alternating optimisation scheme, and the study establishes convergence guarantees to stationary points under readily verifiable conditions.
Theoretical characterisation of the framework’s robustness is achieved through analysis of influence functions, demonstrating bounded behaviour for both parameter estimates and the resulting predictor, contingent on appropriate selection of the tuning parameter β and the error density. Crucially, the research proves that rRNet attains an optimal 50% asymptotic breakdown point across all values of β greater than zero, providing a strong guarantee of global robustness largely absent in current neural network learning methods.
Simulation experiments and analyses of real-world data confirm the practical advantages of rRNet over existing techniques in both function approximation and prediction tasks involving noisy observations. This advancement promises more dependable and accurate regression models, particularly in applications where data integrity is uncertain.
Î’-divergence optimisation for robust regression neural network training
Researchers developed a new robust learning framework, termed rRNet, for training regression neural networks based on the β-divergence, also known as the density power divergence. This method addresses the sensitivity of conventional training techniques, such as minimising mean squared prediction error, to outliers and data contamination.
The rRNet framework applies to a broad range of regression neural networks, accommodating models with both non-smooth activation functions and diverse error densities, and encompasses maximum likelihood learning as a specific instance. Implementation of rRNet proceeds via an alternating optimisation scheme designed to converge to stationary points under verifiable conditions.
Theoretical characterisation of the rRNet’s robustness involves analysing the influence functions of both the parameter estimates and the resulting predictor, demonstrating bounded behaviour for appropriate tuning parameter β, contingent on the error density. Crucially, the study proves that rRNet achieves an optimal 50% asymptotic breakdown point for all β values within the range of 0 to 1, inclusive, providing a significant global robustness guarantee absent in many existing neural network learning methods.
To validate these theoretical findings, the researchers conducted simulation experiments and real-data analyses. These analyses demonstrate practical advantages of rRNet over existing approaches in both function approximation problems and prediction tasks involving noisy observations. The work establishes convergence guarantees and provides a theoretical characterisation of local robustness, linking it to the influence functions and the chosen β parameter. This methodology offers a robust alternative to traditional methods, particularly in scenarios where data contamination is a concern, and provides a strong theoretical foundation for its performance.
Optimal robustness and convergence properties of a β-divergence regression network
Researchers developed a new robust learning framework, termed rRNet, for regression neural networks based on the β-divergence. This framework applies to a broad class of regression NNs, including those with non-smooth activation functions and error densities, and encompasses maximum likelihood learning as a specific case.
The study establishes convergence guarantees to stationary points via an alternating optimisation scheme under verifiable conditions. Theoretical characterisation of rRNet’s robustness reveals bounded influence functions for both parameter estimates and the resulting predictor, contingent on suitable choices for the tuning parameter β and the error density.
Importantly, rRNet attains the optimal 50% asymptotic breakdown point across all values of β within the range of 0 to 1, inclusive, providing a strong global robustness guarantee not commonly found in existing neural network learning methods. This 50% breakdown point signifies the maximum proportion of outliers the model can tolerate without complete failure.
Simulation experiments and real-data analyses demonstrate practical advantages of rRNet over existing approaches in both function approximation and prediction tasks involving noisy observations. The research proves that the influence functions are bounded, indicating stable and predictable model behaviour even with problematic data points.
Further analysis confirms that rRNet consistently achieves the theoretically predicted 50% asymptotic breakdown point, validating its robustness in practical applications. This work offers a significant advancement in training neural networks capable of handling contaminated datasets effectively.
Demonstrating fifty percent asymptotic breakdown and bounded influence functions
Researchers have developed a new robust learning framework, termed rRNet, for training regression neural networks. This framework utilizes the -divergence to minimise prediction errors, offering advantages over traditional methods that are highly susceptible to outliers and contaminated data. rRNet applies to a wide range of neural network architectures, including those with non-smooth activation functions and varying error densities, and encompasses maximum likelihood learning as a specific instance.
The method employs an alternating optimisation scheme with guaranteed convergence to stationary points under verifiable conditions. Theoretical characterisation of rRNet’s robustness is achieved through the analysis of influence functions, demonstrating bounded behaviour for appropriate parameter settings and error density.
Importantly, rRNet attains an optimal 50% asymptotic breakdown point, signifying a strong global robustness largely absent in existing neural network learning techniques. Simulation experiments and analyses of real-world data confirm rRNet’s practical benefits in both function approximation and prediction tasks involving noisy data.
The study acknowledges that the theoretical analysis of influence functions in neural networks can be complex, and interpretations require careful consideration. The current work focuses on population-level influence functions to avoid issues associated with sample-based estimations. Future research could explore the application of smoothing functions to extend the analysis to non-smooth neural network models and further refine the understanding of robustness in complex architectures. These findings establish a pathway towards more reliable and resilient regression models, particularly in scenarios where data quality is uncertain or compromised.