Statistical Convergence Rates of Optimal Transport Map Estimation between General Distributions

This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity assumptions that are very restrictive in practice and much stricter than those in Brenier's Theorem, including the compactness and convexity of the probability support and the bi-Lipschitz property of the OT maps. We aim to broaden the scope of OT map estimation and fill this gap between theory and practice. Given the strong convexity assumption on Brenier's potential, we first establish the non-asymptotic convergence rates for the original plug-in estimator without requiring restrictive assumptions on probability measures. Additionally, we introduce a sieve plug-in estimator and establish its convergence rates without the strong convexity assumption on Brenier's potential, enabling the widely used cases such as the rank functions of normal or t-distributions. We also establish new Poincar\'e-type inequalities, which are proved given sufficient conditions on the local boundedness of the probability density and mild topological conditions of the support, and these new inequalities enable us to achieve faster convergence rates for the Donsker function class. Moreover, we develop scalable algorithms to efficiently solve the OT map estimation using neural networks and present numerical experiments to demonstrate the effectiveness and robustness.

The Effect of Personalization in FedProx: A Fine-grained Analysis on Statistical Accuracy and Communication Efficiency

FedProx is a simple yet effective federated learning method that enables model personalization via regularization. Despite remarkable success in practice, a rigorous analysis of how such a regularization provably improves the statistical accuracy of each client's local model hasn't been fully established. Setting the regularization strength heuristically presents a risk, as an inappropriate choice may even degrade accuracy. This work fills in the gap by analyzing the effect of regularization on statistical accuracy, thereby providing a theoretical guideline for setting the regularization strength for achieving personalization. We prove that by adaptively choosing the regularization strength under different statistical heterogeneity, FedProx can consistently outperform pure local training and achieve a nearly minimax-optimal statistical rate. In addition, to shed light on resource allocation, we design an algorithm, provably showing that stronger personalization reduces communication complexity without increasing the computation cost overhead. Finally, our theory is validated on both synthetic and real-world datasets and its generalizability is verified in a non-convex setting.

Time-aware Heterogeneous Graph Transformer with Adaptive Attention Merging for Health Event Prediction

The widespread application of Electronic Health Records (EHR) data in the medical field has led to early successes in disease risk prediction using deep learning methods. These methods typically require extensive data for training due to their large parameter sets. However, existing works do not exploit the full potential of EHR data. A significant challenge arises from the infrequent occurrence of many medical codes within EHR data, limiting their clinical applicability. Current research often lacks in critical areas: 1) incorporating disease domain knowledge; 2) heterogeneously learning disease representations with rich meanings; 3) capturing the temporal dynamics of disease progression. To overcome these limitations, we introduce a novel heterogeneous graph learning model designed to assimilate disease domain knowledge and elucidate the intricate relationships between drugs and diseases. This model innovatively incorporates temporal data into visit-level embeddings and leverages a time-aware transformer alongside an adaptive attention mechanism to produce patient representations. When evaluated on two healthcare datasets, our approach demonstrated notable enhancements in both prediction accuracy and interpretability over existing methodologies, signifying a substantial advancement towards personalized and proactive healthcare management.

TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this work, we tackle model shifts in the presence of covariate shifts in the high-dimensional regression setting. Specifically, we propose a two-step method with a novel fused-regularizer that effectively leverages samples from source tasks to improve the learning performance on a target task with limited samples. Nonasymptotic bound is provided for the estimation error of the target model, showing the robustness of the proposed method to covariate shifts. We further establish conditions under which the estimator is minimax-optimal. Additionally, we extend the method to a distributed setting, allowing for a pretraining-finetuning strategy, requiring just one round of communication while retaining the estimation rate of the centralized version. Numerical tests validate our theory, highlighting the method's robustness to covariate shifts.

AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression

We consider the transfer learning problem in the high dimensional setting, where the feature dimension is larger than the sample size. To learn transferable information, which may vary across features or the source samples, we propose an adaptive transfer learning method that can detect and aggregate the feature-wise (F-AdaTrans) or sample-wise (S-AdaTrans) transferable structures. We achieve this by employing a novel fused-penalty, coupled with weights that can adapt according to the transferable structure. To choose the weight, we propose a theoretically informed, data-driven procedure, enabling F-AdaTrans to selectively fuse the transferable signals with the target while filtering out non-transferable signals, and S-AdaTrans to obtain the optimal combination of information transferred from each source sample. The non-asymptotic rates are established, which recover existing near-minimax optimal rates in special cases. The effectiveness of the proposed method is validated using both synthetic and real data.

Enhancing Robustness of Gradient-Boosted Decision Trees through One-Hot Encoding and Regularization

Gradient-boosted decision trees (GBDT) are widely used and highly effective machine learning approach for tabular data modeling. However, their complex structure may lead to low robustness against small covariate perturbation in unseen data. In this study, we apply one-hot encoding to convert a GBDT model into a linear framework, through encoding of each tree leaf to one dummy variable. This allows for the use of linear regression techniques, plus a novel risk decomposition for assessing the robustness of a GBDT model against covariate perturbations. We propose to enhance the robustness of GBDT models by refitting their linear regression forms with $L_1$ or $L_2$ regularization. Theoretical results are obtained about the effect of regularization on the model performance and robustness. It is demonstrated through numerical experiments that the proposed regularization approach can enhance the robustness of the one-hot-encoded GBDT models.

Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series

In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution theory comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where the proposed test has power, and results in stable power performance when breaks are sparse in the alternative hypothesis. Furthermore, we impose a latent group structure on the subjects with heterogeneous break points and introduce an easy-to-implement clustering algorithm with an information criterion to consistently estimate the unknown group number and membership. The estimated group structure can subsequently improve the convergence property of the post-clustering break point estimate. Monte-Carlo simulation studies and empirical applications show that the proposed estimation and testing techniques have satisfactory performance in finite samples.

RECLIP: Resource-efficient CLIP by Training with Small Images

We present RECLIP (Resource-efficient CLIP), a simple method that minimizes computational resource footprint for CLIP (Contrastive Language Image Pretraining). Inspired by the notion of coarse-to-fine in computer vision, we leverage small images to learn from large-scale language supervision efficiently, and finetune the model with high-resolution data in the end. Since the complexity of the vision transformer heavily depends on input image size, our approach significantly reduces the training resource requirements both in theory and in practice. Using the same batch size and training epoch, RECLIP achieves highly competitive zero-shot classification and image text retrieval accuracy with 6 to 8$\times$ less computational resources and 7 to 9$\times$ fewer FLOPs than the baseline. Compared to the state-of-the-art contrastive learning methods, RECLIP demonstrates 5 to 59$\times$ training resource savings while maintaining highly competitive zero-shot classification and retrieval performance. We hope this work will pave the path for the broader research community to explore language supervised pretraining in more resource-friendly settings.

MonoIndoor++:Towards Better Practice of Self-Supervised Monocular Depth Estimation for Indoor Environments

Self-supervised monocular depth estimation has seen significant progress in recent years, especially in outdoor environments. However, depth prediction results are not satisfying in indoor scenes where most of the existing data are captured with hand-held devices. As compared to outdoor environments, estimating depth of monocular videos for indoor environments, using self-supervised methods, results in two additional challenges: (i) the depth range of indoor video sequences varies a lot across different frames, making it difficult for the depth network to induce consistent depth cues for training; (ii) the indoor sequences recorded with handheld devices often contain much more rotational motions, which cause difficulties for the pose network to predict accurate relative camera poses. In this work, we propose a novel framework-MonoIndoor++ by giving special considerations to those challenges and consolidating a set of good practices for improving the performance of self-supervised monocular depth estimation for indoor environments. First, a depth factorization module with transformer-based scale regression network is proposed to estimate a global depth scale factor explicitly, and the predicted scale factor can indicate the maximum depth values. Second, rather than using a single-stage pose estimation strategy as in previous methods, we propose to utilize a residual pose estimation module to estimate relative camera poses across consecutive frames iteratively. Third, to incorporate extensive coordinates guidance for our residual pose estimation module, we propose to perform coordinate convolutional encoding directly over the inputs to pose networks. The proposed method is validated on a variety of benchmark indoor datasets, i.e., EuRoC MAV, NYUv2, ScanNet and 7-Scenes, demonstrating the state-of-the-art performance.

Transferring Knowledge with Attention Distillation for Multi-Domain Image-to-Image Translation

Gradient-based attention modeling has been used widely as a way to visualize and understand convolutional neural networks. However, exploiting these visual explanations during the training of generative adversarial networks (GANs) is an unexplored area in computer vision research. Indeed, we argue that this kind of information can be used to influence GANs training in a positive way. For this reason, in this paper, it is shown how gradient based attentions can be used as knowledge to be conveyed in a teacher-student paradigm for multi-domain image-to-image translation tasks in order to improve the results of the student architecture. Further, it is demonstrated how "pseudo"-attentions can also be employed during training when teacher and student networks are trained on different domains which share some similarities. The approach is validated on multi-domain facial attributes transfer and human expression synthesis showing both qualitative and quantitative results.