Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of \textbf{con}volution-smoothed \textbf{qu}antil\textbf{e} \textbf{R}eLU neural \textbf{net}works, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.

Figure 1: Evaluation of T abEBM and other state-of-the-art tabular generative methods across six key metrics (larger area indicates better performance).

Thank reviewers for the comments. Please find our responses below, with reference indices consistent with the paper . Q3-5: Meaning of the learned divergence? We agree that BC minimizes the policy KL divergence as what we noted in Sec. 4 (line 200). It is consistent with the literature, e.g., Sec. 2 in [Y u et al. arXiv:1909.09314].

Figure 1: Evaluation of T abEBM and other state-of-the-art tabular generative methods across six key metrics (larger area indicates better performance).

Slutsky's theorem together with (S.3) and (S.5) implies the result in Theorem 1. Now we check the Lindeberg-Feller condition. 's are non-negative and E S.4 Derivation of corrected model (4) Note that π (x, 1) = 1 and π (x, 0) = π (x) . Slutsky's theorem together with (S.15) and (S.17) implies the result in Theorem 1. 's, whose distribution depends on N . From (S.27) and (S.28), Chebyshev's inequality implies that For sampled data, (5) tell us that the joint density w.r.t. the product counting measure of the responses The outline of the proof is similar to that of the proof of Theorem 2. Write Markov's inequality shows that they are both o The outline of the proof is similar to that of the proof of Theorem 4. The estimator Slutsky's theorem together with (S.38) and (S.40) implies the result in Theorem 1.

Data collection is often difficult in critical fields such as medicine, physics, and chemistry. As a result, classification methods usually perform poorly with these small datasets, leading to weak predictive performance. Increasing the training set with additional synthetic data, similar to data augmentation in images, is commonly believed to improve downstream classification performance. However, current tabular generative methods that learn either the joint distribution $ p(\mathbf{x}, y) $ or the class-conditional distribution $ p(\mathbf{x} \mid y) $ often overfit on small datasets, resulting in poor-quality synthetic data, usually worsening classification performance compared to using real data alone. To solve these challenges, we introduce TabEBM, a novel class-conditional generative method using Energy-Based Models (EBMs). Unlike existing methods that use a shared model to approximate all class-conditional densities, our key innovation is to create distinct EBM generative models for each class, each modelling its class-specific data distribution individually. This approach creates robust energy landscapes, even in ambiguous class distributions. Our experiments show that TabEBM generates synthetic data with higher quality and better statistical fidelity than existing methods. When used for data augmentation, our synthetic data consistently improves the classification performance across diverse datasets of various sizes, especially small ones. Code is available at https://github.com/andreimargeloiu/TabEBM.

Personalized medicine is expected to advance healthcare in the near future [Vicente et al., 2020]. In contrast to a one-size-fits-all approach, personalized medicine advocates for treatments tailored to individual patients based on their clinical characteristics. Responder analysis in clinical trials is a method used to evaluate the effectiveness of a treatment by identifying and analyzing the subset of participants who respond significantly to the treatment [Henschke et al., 2014]. This approach contrasts with the traditional method of evaluating average effects across all participants, which can sometimes obscure the benefits seen in a particular group of responders [Guyatt et al., 1998]. This approach is particularly important in trials with heterogeneous treatment effects, where understanding individual responses can lead to more effective therapies. Responder analysis is a common practice in clinical trials [Moore et al., 2010, Straube et al., 2010, Chuang et al., 2022].

In biomedical image analysis, data imbalance is common across several imaging modalities. Data augmentation is one of the key solutions in addressing this limitation. Generative Adversarial Networks (GANs) are increasingly being relied upon for data augmentation tasks. Biomedical image features are sensitive to evaluating the efficacy of synthetic images. These features can have a significant impact on metric scores when evaluating synthetic images across different biomedical imaging modalities. Synthetically generated images can be evaluated by comparing the diversity and quality of real images. Multi-scale Structural Similarity Index Measure and Cosine Distance are used to evaluate intra-class diversity, while Frechet Inception Distance is used to evaluate the quality of synthetic images. Assessing these metrics for biomedical and non-biomedical imaging is important to investigate an informed strategy in evaluating the diversity and quality of synthetic images. In this work, an empirical assessment of these metrics is conducted for the Deep Convolutional GAN in a biomedical and non-biomedical setting. The diversity and quality of synthetic images are evaluated using different sample sizes. This research intends to investigate the variance in diversity and quality across biomedical and non-biomedical imaging modalities. Results demonstrate that the metrics scores for diversity and quality vary significantly across biomedical-to-biomedical and biomedical-to-non-biomedical imaging modalities.