Seokhun Park

Yongchan Choi, Seokhun Park, Chanmoo Park et al.

There are two things to be considered when we evaluate predictive models. One is prediction accuracy,and the other is interpretability. Over the recent decades, many prediction models of high performance, such as ensemble-based models and deep neural networks, have been developed. However, these models are often too complex, making it difficult to intuitively interpret their predictions. This complexity in interpretation limits their use in many real-world fields that require accountability, such as medicine, finance, and college admissions. In this study, we develop a novel method called Meta-ANOVA to provide an interpretable model for any given prediction model. The basic idea of Meta-ANOVA is to transform a given black-box prediction model to the functional ANOVA model. A novel technical contribution of Meta-ANOVA is a procedure of screening out unnecessary interaction before transforming a given black-box model to the functional ANOVA model. This screening procedure allows the inclusion of higher order interactions in the transformed functional ANOVA model without computational difficulties. We prove that the screening procedure is asymptotically consistent. Through various experiments with synthetic and real-world datasets, we empirically demonstrate the superiority of Meta-ANOVA

Seokhun Park, Choeun Kim, Kwanho Lee et al.

Activation functions play a central role in neural networks by shaping internal representations. Recently, learning binary activation representations has attracted significant attention due to their advantages in computational and memory efficiency, as well as interpretability. However, training neural networks with Heaviside activations remains challenging, as their non-differentiability obstructs standard gradient-based optimization. In this paper, we propose Heavy Tailed Activation Function (HTAF), a smooth approximation to the Heaviside function that enables stable training with gradient-based optimization. We construct HTAF as a sigmoid hyperbolic tangent composite function and theoretically show that it maintains a large gradient mass around zero inputs while exhibiting slower gradient decay in the tail regions. We show that Spiking Neural Networks, Binary Neural Networks and Deep Heaviside neural Networks can be trained stably using HTAF with gradient-based optimization. Finally, we introduce Implicit Concept Bottleneck Models (ICBMs), an interpretable image model that leverages HTAF to induce discrete feature representations. Extensive experiments across various architectures and image datasets demonstrate that ICBM enables stable discretization while achieving prediction performance comparable to or better than standard models.

Seokhun Park, Insung Kong, Yongchan Choi et al.

Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional functions (commonly referred to as components), is one of the most popular tools for interpretable AI, and recently, various neural networks have been developed for estimating each component in the functional ANOVA model. However, such neural networks are highly unstable when estimating each component since the components themselves are not uniquely defined. That is, there are multiple functional ANOVA decompositions for a given function. In this paper, we propose a novel neural network which guarantees a unique functional ANOVA decomposition and thus is able to estimate each component stably and accurately. We call our proposed neural network ANOVA Tensor Product Neural Network (ANOVA-TPNN) since it is motivated by the tensor product basis expansion. Theoretically, we prove that ANOVA-TPNN can approximate any smooth function well. Empirically, we show that ANOVA-TPNN provide much more stable estimation of each component and thus much more stable interpretation when training data and initial values of the model parameters vary than existing neural networks do.

Seokhun Park, Choeun Kim, Jihu Lee et al.

With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal the contributions of different variable groups. Recently, Tensor Product Neural Network (TPNN) has been developed and applied as basis functions in the functional ANOVA model, referred to as ANOVA-TPNN. A disadvantage of ANOVA-TPNN, however, is that the components to be estimated must be specified in advance, which makes it difficult to incorporate higher-order TPNNs into the functional ANOVA model due to computational and memory constraints. In this work, we propose Bayesian-TPNN, a Bayesian inference procedure for the functional ANOVA model with TPNN basis functions, enabling the detection of higher-order components with reduced computational cost compared to ANOVA-TPNN. We develop an efficient MCMC algorithm and demonstrate that Bayesian-TPNN performs well by analyzing multiple benchmark datasets. Theoretically, we prove that the posterior of Bayesian-TPNN is consistent.

Seokhun Park, Insung Kong, Yongdai Kim

Bayesian Additive Regression Trees (BART) is a powerful statistical model that leverages the strengths of Bayesian inference and regression trees. It has received significant attention for capturing complex non-linear relationships and interactions among predictors. However, the accuracy of BART often comes at the cost of interpretability. To address this limitation, we propose ANOVA Bayesian Additive Regression Trees (ANOVA-BART), a novel extension of BART based on the functional ANOVA decomposition, which is used to decompose the variability of a function into different interactions, each representing the contribution of a different set of covariates or factors. Our proposed ANOVA-BART enhances interpretability, preserves and extends the theoretical guarantees of BART, and achieves superior predictive performance. Specifically, we establish that the posterior concentration rate of ANOVA-BART is nearly minimax optimal, and further provides the same convergence rates for each interaction that are not available for BART. Moreover, comprehensive experiments confirm that ANOVA-BART surpasses BART in both accuracy and uncertainty quantification, while also demonstrating its effectiveness in component selection. These results suggest that ANOVA-BART offers a compelling alternative to BART by balancing predictive accuracy, interpretability, and theoretical consistency.