arXiv subjects

Hongteng Xu

Publications and source records attributed to Hongteng Xu.

At least 55 records · Page 3Linked to original sources

arXiv2024

Hilbert Curve Projection Distance for Distribution Comparison

Distribution comparison plays a central role in many machine learning tasks like data classification and generative modeling. In this study, we propose a novel metric, called Hilbert curve projection (HCP) distance, to measure the distance between two probability distributions with low complexity. In particular, we first project two high-dimensional probability distributions using Hilbert curve to obtain a coupling between them, and then calculate the transport distance between these two distributions in the original space, according to the coupling. We show that HCP distance is a proper metric and is well-defined for probability measures with bounded supports. Furthermore, we demonstrate that the modified empirical HCP distance with the $L_p$ cost in the $d$-dimensional space converges to its population counterpart at a rate of no more than $O(n^{-1/2\max\{d,p\}})$. To suppress the curse-of-dimensionality, we also develop two variants of the HCP distance using (learnable) subspace projections. Experiments on both synthetic and real-world data show that our HCP distance works as an effective surrogate of the Wasserstein distance with low complexity and overcomes the drawbacks of the sliced Wasserstein distance.

cs.LG↗

arXiv2023

Sliceformer: Make Multi-head Attention as Simple as Sorting in Discriminative Tasks

As one of the most popular neural network modules, Transformer plays a central role in many fundamental deep learning models, e.g., the ViT in computer vision and the BERT and GPT in natural language processing. The effectiveness of the Transformer is often attributed to its multi-head attention (MHA) mechanism. In this study, we discuss the limitations of MHA, including the high computational complexity due to its ``query-key-value'' architecture and the numerical issue caused by its softmax operation. Considering the above problems and the recent development tendency of the attention layer, we propose an effective and efficient surrogate of the Transformer, called Sliceformer. Our Sliceformer replaces the classic MHA mechanism with an extremely simple ``slicing-sorting'' operation, i.e., projecting inputs linearly to a latent space and sorting them along different feature dimensions (or equivalently, called channels). For each feature dimension, the sorting operation implicitly generates an implicit attention map with sparse, full-rank, and doubly-stochastic structures. We consider different implementations of the slicing-sorting operation and analyze their impacts on the Sliceformer. We test the Sliceformer in the Long-Range Arena benchmark, image classification, text classification, and molecular property prediction, demonstrating its advantage in computational complexity and universal effectiveness in discriminative tasks. Our Sliceformer achieves comparable or better performance with lower memory cost and faster speed than the Transformer and its variants. Moreover, the experimental results reveal that applying our Sliceformer can empirically suppress the risk of mode collapse when representing data. The code is available at \url{https://github.com/SDS-Lab/sliceformer}.

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arXiv2023

Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose a novel importance sparsification method, called \textsc{Spar-GW}, to approximate GW distance efficiently. In particular, instead of considering a dense coupling matrix, our method leverages a simple but effective sampling strategy to construct a sparse coupling matrix and update it with few computations. The proposed \textsc{Spar-GW} method is applicable to the GW distance with arbitrary ground cost, and it reduces the complexity from $O(n^4)$ to $O(n^{2+δ})$ for an arbitrary small $δ>0$. Theoretically, the convergence and consistency of the proposed estimation for GW distance are established under mild regularity conditions. In addition, this method can be extended to approximate the variants of GW distance, including the entropic GW distance, the fused GW distance, and the unbalanced GW distance. Experiments show the superiority of our \textsc{Spar-GW} to state-of-the-art methods in both synthetic and real-world tasks.

cs.LG↗

arXiv2023

Text2Poster: Laying out Stylized Texts on Retrieved Images

Poster generation is a significant task for a wide range of applications, which is often time-consuming and requires lots of manual editing and artistic experience. In this paper, we propose a novel data-driven framework, called \textit{Text2Poster}, to automatically generate visually-effective posters from textual information. Imitating the process of manual poster editing, our framework leverages a large-scale pretrained visual-textual model to retrieve background images from given texts, lays out the texts on the images iteratively by cascaded auto-encoders, and finally, stylizes the texts by a matching-based method. We learn the modules of the framework by weakly- and self-supervised learning strategies, mitigating the demand for labeled data. Both objective and subjective experiments demonstrate that our Text2Poster outperforms state-of-the-art methods, including academic research and commercial software, on the quality of generated posters.

cs.MM↗

arXiv2022

Regularized Optimal Transport Layers for Generalized Global Pooling Operations

Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical fundamentals, its practical implementations often depend on empirical mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In this work, we develop a novel and generalized global pooling framework through the lens of optimal transport. The proposed framework is interpretable from the perspective of expectation-maximization. Essentially, it aims at learning an optimal transport across sample indices and feature dimensions, making the corresponding pooling operation maximize the conditional expectation of input data. We demonstrate that most existing pooling methods are equivalent to solving a regularized optimal transport (ROT) problem with different specializations, and more sophisticated pooling operations can be implemented by hierarchically solving multiple ROT problems. Making the parameters of the ROT problem learnable, we develop a family of regularized optimal transport pooling (ROTP) layers. We implement the ROTP layers as a new kind of deep implicit layer. Their model architectures correspond to different optimization algorithms. We test our ROTP layers in several representative set-level machine learning scenarios, including multi-instance learning (MIL), graph classification, graph set representation, and image classification. Experimental results show that applying our ROTP layers can reduce the difficulty of the design and selection of global pooling -- our ROTP layers may either imitate some existing global pooling methods or lead to some new pooling layers fitting data better. The code is available at \url{https://github.com/SDS-Lab/ROT-Pooling}.

cs.LG↗

arXiv2022

ImDrug: A Benchmark for Deep Imbalanced Learning in AI-aided Drug Discovery

The last decade has witnessed a prosperous development of computational methods and dataset curation for AI-aided drug discovery (AIDD). However, real-world pharmaceutical datasets often exhibit highly imbalanced distribution, which is overlooked by the current literature but may severely compromise the fairness and generalization of machine learning applications. Motivated by this observation, we introduce ImDrug, a comprehensive benchmark with an open-source Python library which consists of 4 imbalance settings, 11 AI-ready datasets, 54 learning tasks and 16 baseline algorithms tailored for imbalanced learning. It provides an accessible and customizable testbed for problems and solutions spanning a broad spectrum of the drug discovery pipeline such as molecular modeling, drug-target interaction and retrosynthesis. We conduct extensive empirical studies with novel evaluation metrics, to demonstrate that the existing algorithms fall short of solving medicinal and pharmaceutical challenges in the data imbalance scenario. We believe that ImDrug opens up avenues for future research and development, on real-world challenges at the intersection of AIDD and deep imbalanced learning.

cs.LG↗

arXiv2022

Revisiting Global Pooling through the Lens of Optimal Transport

Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through the lens of optimal transport. We demonstrate that most existing global pooling methods are equivalent to solving some specializations of an unbalanced optimal transport (UOT) problem. Making the parameters of the UOT problem learnable, we unify various global pooling methods in the same framework, and accordingly, propose a generalized global pooling layer called UOT-Pooling (UOTP) for neural networks. Besides implementing the UOTP layer based on the classic Sinkhorn-scaling algorithm, we design a new model architecture based on the Bregman ADMM algorithm, which has better numerical stability and can reproduce existing pooling layers more effectively. We test our UOTP layers in several application scenarios, including multi-instance learning, graph classification, and image classification. Our UOTP layers can either imitate conventional global pooling layers or learn some new pooling mechanisms leading to better performance.

cs.LG↗

arXiv2022

Predicting Protein-Ligand Binding Affinity via Joint Global-Local Interaction Modeling

The prediction of protein-ligand binding affinity is of great significance for discovering lead compounds in drug research. Facing this challenging task, most existing prediction methods rely on the topological and/or spatial structure of molecules and the local interactions while ignoring the multi-level inter-molecular interactions between proteins and ligands, which often lead to sub-optimal performance. To solve this issue, we propose a novel global-local interaction (GLI) framework to predict protein-ligand binding affinity. In particular, our GLI framework considers the inter-molecular interactions between proteins and ligands, which involve not only the high-energy short-range interactions between closed atoms but also the low-energy long-range interactions between non-bonded atoms. For each pair of protein and ligand, our GLI embeds the long-range interactions globally and aggregates local short-range interactions, respectively. Such a joint global-local interaction modeling strategy helps to improve prediction accuracy, and the whole framework is compatible with various neural network-based modules. Experiments demonstrate that our GLI framework outperforms state-of-the-art methods with simple neural network architectures and moderate computational costs.

q-bio.BM↗

arXiv2022

Explainable Legal Case Matching via Inverse Optimal Transport-based Rationale Extraction

As an essential operation of legal retrieval, legal case matching plays a central role in intelligent legal systems. This task has a high demand on the explainability of matching results because of its critical impacts on downstream applications -- the matched legal cases may provide supportive evidence for the judgments of target cases and thus influence the fairness and justice of legal decisions. Focusing on this challenging task, we propose a novel and explainable method, namely \textit{IOT-Match}, with the help of computational optimal transport, which formulates the legal case matching problem as an inverse optimal transport (IOT) problem. Different from most existing methods, which merely focus on the sentence-level semantic similarity between legal cases, our IOT-Match learns to extract rationales from paired legal cases based on both semantics and legal characteristics of their sentences. The extracted rationales are further applied to generate faithful explanations and conduct matching. Moreover, the proposed IOT-Match is robust to the alignment label insufficiency issue commonly in practical legal case matching tasks, which is suitable for both supervised and semi-supervised learning paradigms. To demonstrate the superiority of our IOT-Match method and construct a benchmark of explainable legal case matching task, we not only extend the well-known Challenge of AI in Law (CAIL) dataset but also build a new Explainable Legal cAse Matching (ELAM) dataset, which contains lots of legal cases with detailed and explainable annotations. Experiments on these two datasets show that our IOT-Match outperforms state-of-the-art methods consistently on matching prediction, rationale extraction, and explanation generation.

cs.IR↗

arXiv2022

Interventional Multi-Instance Learning with Deconfounded Instance-Level Prediction

When applying multi-instance learning (MIL) to make predictions for bags of instances, the prediction accuracy of an instance often depends on not only the instance itself but also its context in the corresponding bag. From the viewpoint of causal inference, such bag contextual prior works as a confounder and may result in model robustness and interpretability issues. Focusing on this problem, we propose a novel interventional multi-instance learning (IMIL) framework to achieve deconfounded instance-level prediction. Unlike traditional likelihood-based strategies, we design an Expectation-Maximization (EM) algorithm based on causal intervention, providing a robust instance selection in the training phase and suppressing the bias caused by the bag contextual prior. Experiments on pathological image analysis demonstrate that our IMIL method substantially reduces false positives and outperforms state-of-the-art MIL methods.

cs.CV↗

arXiv2022

BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation

Many representative graph neural networks, e.g., GPR-GNN and ChebNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose BernNet, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-$K$ Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.

cs.LG↗

arXiv2021

Learning Graphon Autoencoders for Generative Graph Modeling

Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.

cs.LG↗

arXiv2021

A Hypergradient Approach to Robust Regression without Correspondence

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring instruments may not be able to maintain the correspondence between the samples and the measurements. Due to the combinatorial nature of the problem, most existing methods are only applicable when the sample size is small, and limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework -- ROBOT -- for the shuffled regression problem, which is applicable to large data and complex nonlinear models. Specifically, we reformulate the regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression, and therefore allows us to find a better descent direction for the model parameter by differentiating through the data correspondence. ROBOT can be further extended to the inexact correspondence setting, where there may not be an exact alignment between the input and output data. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.

cs.LG↗

arXiv2021

Hawkes Processes on Graphons

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that are associated with Granger causality graphs, our model leverages an uncountable event type space and samples the graphs with different sizes from a nonparametric model called {\it graphon}. Given those graphs, we can generate the corresponding Hawkes processes and simulate event sequences. Learning this graphon-based Hawkes process model helps to 1) infer the underlying relations shared by different Hawkes processes; and 2) simulate event sequences with different event types but similar dynamics. We learn the proposed model by minimizing the hierarchical optimal transport distance between the generated event sequences and the observed ones, leading to a novel reward-augmented maximum likelihood estimation method. We analyze the properties of our model in-depth and demonstrate its rationality and effectiveness in both theory and experiments.

cs.LG↗

arXiv2020

Zero-Shot Recognition via Optimal Transport

We propose an optimal transport (OT) framework for generalized zero-shot learning (GZSL), seeking to distinguish samples for both seen and unseen classes, with the assist of auxiliary attributes. The discrepancy between features and attributes is minimized by solving an optimal transport problem. {Specifically, we build a conditional generative model to generate features from seen-class attributes, and establish an optimal transport between the distribution of the generated features and that of the real features.} The generative model and the optimal transport are optimized iteratively with an attribute-based regularizer, that further enhances the discriminative power of the generated features. A classifier is learned based on the features generated for both the seen and unseen classes. In addition to generalized zero-shot learning, our framework is also applicable to standard and transductive ZSL problems. Experiments show that our optimal transport-based method outperforms state-of-the-art methods on several benchmark datasets.

cs.LG↗

arXiv2020

Learning to Recommend from Sparse Data via Generative User Feedback

Traditional collaborative filtering (CF) based recommender systems tend to perform poorly when the user-item interactions/ratings are highly scarce. To address this, we propose a learning framework that improves collaborative filtering with a synthetic feedback loop (CF-SFL) to simulate the user feedback. The proposed framework consists of a "recommender" and a "virtual user". The "recommender" is formulated as a CF model, recommending items according to observed user preference. The "virtual user" estimates rewards from the recommended items and generates a \emph{feedback} in addition to the observed user preference. The "recommender" connected with the "virtual user" constructs a closed loop, that recommends users with items and imitates the \emph{unobserved} feedback of the users to the recommended items. The synthetic feedback is used to augment the observed user preference and improve recommendation results. Theoretically, such model design can be interpreted as inverse reinforcement learning, which can be learned effectively via rollout (simulation). Experimental results show that the proposed framework is able to enrich the learning of user preference and boost the performance of existing collaborative filtering methods on multiple datasets.

cs.IR↗

arXiv2020

Learning Graphons via Structured Gromov-Wasserstein Barycenters

We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs. Furthermore, we develop several enhancements and extensions of the basic algorithm, $e.g.$, the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. The code is available at https://github.com/HongtengXu/SGWB-Graphon.

cs.LG↗

arXiv2020

Learning Autoencoders with Relational Regularization

A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a \emph{relational regularization} on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, allowing one to flexibly learn a structured prior distribution associated with the generative model. Moreover, it helps co-training of multiple autoencoders even if they have heterogeneous architectures and incomparable latent spaces. We implement the framework with two scalable algorithms, making it applicable for both probabilistic and deterministic autoencoders. Our relational regularized autoencoder (RAE) outperforms existing methods, $e.g.$, the variational autoencoder, Wasserstein autoencoder, and their variants, on generating images. Additionally, our relational co-training strategy for autoencoders achieves encouraging results in both synthesis and real-world multi-view learning tasks. The code is at https://github.com/HongtengXu/ Relational-AutoEncoders.

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