For what purpose was the dataset created?

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the

We thank all the reviewers for the helpful comments. Here, we address the main concerns raised by the reviewers. While the traditional method (e.g., Lasso) can find important individual The motivations and application are discussed in [1.1.] When the sparse assumption doesn't hold] Theoretically, the sparsity assumption is commonly Motivations] The motivations and one real application where sparsity holds are discussed in [1.1.]

While practitioners often employ variable importance methods that rely on this impurity-based information, these methods remain poorly characterized from a theoretical perspective.

Biological data sets are often high-dimensional, noisy, and governed by complex interactions among sparse signals. This poses major challenges for interpretability and reliable feature selection. Tasks such as identifying motif interactions in genomics exemplify these difficulties, as only a small subset of biologically relevant features (e.g., motifs) are typically active, and their effects are often non-linear and context-dependent. While statistical approaches often result in more interpretable models, deep learning models have proven effective in modeling complex interactions and prediction accuracy, yet their black-box nature limits interpretability. We introduce BaGGLS, a flexible and interpretable probabilistic binary regression model designed for high-dimensional biological inference involving feature interactions. BaGGLS incorporates a Bayesian group global-local shrinkage prior, aligned with the group structure introduced by interaction terms. This prior encourages sparsity while retaining interpretability, helping to isolate meaningful signals and suppress noise. To enable scalable inference, we employ a partially factorized variational approximation that captures posterior skewness and supports efficient learning even in large feature spaces. In extensive simulations, we can show that BaGGLS outperforms the other methods with regard to interaction detection and is many times faster than MCMC sampling under the horseshoe prior. We also demonstrate the usefulness of BaGGLS in the context of interaction discovery from motif scanner outputs and noisy attribution scores from deep learning models. This shows that BaGGLS is a promising approach for uncovering biologically relevant interaction patterns, with potential applicability across a range of high-dimensional tasks in computational biology.

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schrödinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schrödinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy. Code is available at: https://github.com/zhenyiizhang/CytoBridge-NeurIPS.

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the

Interpretability is one of the considerations when applying machine learning to high-stakes fields such as healthcare that involve matters of life safety. Generalized Additive Models (GAMs) enhance interpretability by visualizing shape functions. Nevertheless, to preserve interpretability, GAMs omit higher-order interaction effects (beyond pairwise interactions), which imposes significant constraints on their predictive performance. We observe that Curve Ergodic Set Regression (CESR), a multiplicative model, naturally enables the visualization of its shape functions and simultaneously incorporates both interactions among all features and individual feature effects. Nevertheless, CESR fails to demonstrate superior performance compared to GAMs. We introduce Multiplicative-Additive Constrained Models (MACMs), which augment CESR with an additive part to disentangle the intertwined coefficients of its interactive and independent terms, thus effectively broadening the hypothesis space. The model is composed of a multiplicative part and an additive part, whose shape functions can both be naturally visualized, thereby assisting users in interpreting how features participate in the decision-making process. Consequently, MACMs constitute an improvement over both CESR and GAMs. The experimental results indicate that neural network-based MACMs significantly outperform both CESR and the current state-of-the-art GAMs in terms of predictive performance.