Unsupervised graph alignment aims to find corresponding nodes across different graphs without supervision. Existing methods usually leverage the graph structure to aggregate features of nodes to find relations between nodes. However, the graph structure is inherently limited in pairwise relations between nodes without considering higher-order dependencies among multiple nodes. In this paper, we take advantage of the hypergraph structure to characterize higher-order structural information among nodes for better graph alignment. Specifically, we propose an optimal transport model to learn a hypergraph to capture complex relations among nodes, so that the nodes involved in one hyperedge can be adaptively based on local geometric information. In addition, inspired by the Dirichlet energy function of a hypergraph, we further refine our model to enhance the consistency between structural and feature information in each hyperedge. After that, we jointly leverage graphs and hypergraphs to extract structural and feature information to better model the relations between nodes, which is used to find node correspondences across graphs. We conduct experiments on several benchmark datasets with different settings, and the results demonstrate the effectiveness of our proposed method.

For deep regression, preserving the ordinality of the targets with respect to the feature representation improves performance across various tasks. However, a theoretical explanation for the benefits of ordinality is still lacking. This work reveals that preserving ordinality reduces the conditional entropy $H(Z|Y)$ of representation $Z$ conditional on the target $Y$. However, our findings reveal that typical regression losses fail to sufficiently reduce $H(Z|Y)$, despite its crucial role in generalization performance. With this motivation, we introduce an optimal transport-based regularizer to preserve the similarity relationships of targets in the feature space to reduce $H(Z|Y)$. Additionally, we introduce a simple yet efficient strategy of duplicating the regressor targets, also with the aim of reducing $H(Z|Y)$. Experiments on three real-world regression tasks verify the effectiveness of our strategies to improve deep regression. Code: https://github.com/needylove/Regression_tightness

Causal inference seeks to estimate the effect given a treatment such as a medicine or the dosage of a medication. To reduce the confounding bias caused by the non-randomized treatment assignment, most existing methods reduce the shift between subpopulations receiving different treatments. However, these methods split limited training samples into smaller groups, which cuts down the number of samples in each group, while precise distribution estimation and alignment highly rely on a sufficient number of training samples. In this paper, we propose a distribution alignment paradigm without data splitting, which can be naturally applied in the settings of binary and continuous treatments. To this end, we characterize the confounding bias by considering different probability measures of the same set including all the training samples, and exploit the optimal transport theory to analyze the confounding bias and outcome estimation error. Based on this, we propose to learn balanced representations by reducing the bias between the marginal distribution and the conditional distribution of a treatment. As a result, data reduction caused by splitting is avoided, and the outcome prediction model trained on one treatment group can be generalized to the entire population. The experiments on both binary and continuous treatment settings demonstrate the effectiveness of our method.

The conventional mean square error for time series forecasting is a point-wise loss function, which ignores the temporal dependency of forecasting data points and results in unstable predictions. Although other methods involve shape information loss functions, such as dynamic time warping, they assign the same weights to each matching pair and result in suboptimal results when a wrong matching pair is chosen. Besides, although the optimal transport can assign different weights for each matching pair, they easily suffer from false alignment due to the time lag. To solve these challenges, we propose a Model-Agnostic loss function via Temporally Sensitive Optimal Transport (MA-TOT) as a differentiable loss function for time series forecasting, which combines temporally sensitive Wasserstein distance for adaptive matching pair chosen and Gromov-Wasserstein distance for multi-level-similarity-measurement. Extensive experiments of several of the latest time series forecasting models with our loss function on seven real-world benchmark datasets reflect the effectiveness of our method.

Cross-network link prediction aims to predict the existence of edges between nodes in a target network by transferring knowledge from a source network with sufficient annotations. Existing methods mainly focus on associating two networks in a shared embedding space, in which the distribution discrepancy of node embeddings between two networks is reduced. However, besides the discrepancy between embeddings, the structure discrepancy also appears between networks, which has not been well investigated in existing studies. In this paper, we propose to learn cross-network relationship between nodes from different networks, and construct an augmented graph for knowledge transfer based on our learned relationship. To achieve this, we propose an optimal transport model to exploit structure information for learning node association between two networks, and then apply barycentric mapping of the graph to combine structural information of both networks according to the obtained relationship. Based on the constructed graph, we design a graph convolutional network to learn node embeddings for link prediction, so that both feature and structural information are leveraged for knowledge transfer. We conduct experiments on benchmark datasets to show the superiority of our method compared with state-of-the-art methods.

Recommender systems seek to present candidate items for users based on their potential preferences. Beneficial from the powerful ability of the graph model to leverage structural information, the graph based approach has drawn much attention in the community of recommendation. However, existing graph based methods usually use interaction data or some heuristic rules to construct the graph, without considering implicit relations involved in features and higher-order dependencies of users and items. In this paper, we propose a novel graph collaborative filtering method based on the theory of optimal transport, which is devoted to extracting features and dependencies of users and items to reveal implicit relations between them. Specifically, we model users and items as two distributions and propose an optimal transport model to characterize strong relations between them. By incorporating feature and dependency information of users and items, we learn implicit relations and features of users and items in a unified learning model. Based on the learned relations and original interaction data, we design a dual-stream graph convolutional network to enhance the representation learning for users and items, boosting the performance of recommendation. The experimental results on two real-world datasets demonstrate the effectiveness of our method. We also conduct ablation studies to evaluate the effects of the learned features and relations obtained from our optimal transport model.

Although graph neural networks have achieved great success in the task of molecular property prediction in recent years, their generalization ability under out-of-distribution (OOD) settings is still under-explored. Most of the existing methods rely on learning discriminative representations for prediction, often assuming that the underlying semantic components are correctly identified. However, this assumption does not always hold, leading to potential misidentifications that affect model robustness. Different from these discriminative-based methods, we propose a generative model to ensure the Semantic-Components Identifiability, named SCI. We demonstrate that the latent variables in this generative model can be explicitly identified into semantic-relevant (SR) and semantic-irrelevant (SI) components, which contributes to better OOD generalization by involving minimal change properties of causal mechanisms. Specifically, we first formulate the data generation process from the atom level to the molecular level, where the latent space is split into SI substructures, SR substructures, and SR atom variables. Sequentially, to reduce misidentification, we restrict the minimal changes of the SR atom variables and add a semantic latent substructure regularization to mitigate the variance of the SR substructure under augmented domain changes. Under mild assumptions, we prove the block-wise identifiability of the SR substructure and the comment-wise identifiability of SR atom variables. Experimental studies achieve state-of-the-art performance and show general improvement on 21 datasets in 3 mainstream benchmarks. Moreover, the visualization results of the proposed SCI method provide insightful case studies and explanations for the prediction results.

Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.). However, this i.i.d. assumption is often violated due to the inherent dependencies among the event sequences. Fortunately, in practice, we find these dependencies can be modeled by a topological network, suggesting a potential solution to the non-i.i.d. problem by introducing the prior topological network into Granger causal discovery. This observation prompts us to tackle two ensuing challenges: 1) how to model the event sequences while incorporating both the prior topological network and the latent Granger causal structure, and 2) how to learn the Granger causal structure. To this end, we devise a unified topological neural Poisson auto-regressive model with two processes. In the generation process, we employ a variant of the neural Poisson process to model the event sequences, considering influences from both the topological network and the Granger causal structure. In the inference process, we formulate an amortized inference algorithm to infer the latent Granger causal structure. We encapsulate these two processes within a unified likelihood function, providing an end-to-end framework for this task. Experiments on simulated and real-world data demonstrate the effectiveness of our approach.

Hypergraph captures high-order information in structured data and obtains much attention in machine learning and data mining. Existing approaches mainly learn representations for hypervertices by transforming a hypergraph to a standard graph, or learn representations for hypervertices and hyperedges in separate spaces. In this paper, we propose a hypergraph expansion method to transform a hypergraph to a standard graph while preserving high-order information. Different from previous hypergraph expansion approaches like clique expansion and star expansion, we transform both hypervertices and hyperedges in the hypergraph to vertices in the expanded graph, and construct connections between hypervertices or hyperedges, so that richer relationships can be used in graph learning. Based on the expanded graph, we propose a learning model to embed hypervertices and hyperedges in a joint representation space. Compared with the method of learning separate spaces for hypervertices and hyperedges, our method is able to capture common knowledge involved in hypervertices and hyperedges, and also improve the data efficiency and computational efficiency. To better leverage structure information, we minimize the graph reconstruction loss to preserve the structure information in the model. We perform experiments on both hypervertex classification and hyperedge classification tasks to demonstrate the effectiveness of our proposed method.

Clustering is one of the most fundamental problems in machine learning and data mining, and many algorithms have been proposed in the past decades. Among them, subspace clustering and spectral clustering are the most famous approaches. In this paper, we provide an explanation for subspace clustering and spectral clustering from the perspective of optimal transport. Optimal transport studies how to move samples from one distribution to another distribution with minimal transport cost, and has shown a powerful ability to extract geometric information. By considering a self optimal transport model with only one group of samples, we observe that both subspace clustering and spectral clustering can be explained in the framework of optimal transport, and the optimal transport matrix bridges the spaces of features and spectral embeddings. Inspired by this connection, we propose a spectral optimal transport barycenter model, which learns spectral embeddings by solving a barycenter problem equipped with an optimal transport discrepancy and guidance of data. Based on our proposed model, we take advantage of optimal transport to exploit both feature and metric information involved in data for learning coupled spectral embeddings and affinity matrix in a unified model. We develop an alternating optimization algorithm to solve the resultant problems, and conduct experiments in different settings to evaluate the performance of our proposed methods.

Estimating treatment effects from observational data suffers from the issue of confounding bias, which is induced by the imbalanced confounder distributions between the treated and control groups. As an effective approach, re-weighting learns a group of sample weights to balance the confounder distributions. Existing methods of re-weighting highly rely on a propensity score model or moment alignment. However, for complex real-world data, it is difficult to obtain an accurate propensity score prediction. Although moment alignment is free of learning a propensity score model, accurate estimation for high-order moments is computationally difficult and still remains an open challenge, and first and second-order moments are insufficient to align the distributions and easy to be misled by outliers. In this paper, we exploit geometry to capture the intrinsic structure involved in data for balancing the confounder distributions, so that confounding bias can be reduced even with outliers. To achieve this, we construct a connection between treatment effect estimation and optimal transport, a powerful tool to capture geometric information. After that, we propose an optimal transport model to learn sample weights by extracting geometry from confounders, in which geometric information between groups and within groups is leveraged for better confounder balancing. A projected mirror descent algorithm is employed to solve the derived optimization problem. Experimental studies on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Causal effect estimation under networked interference is an important but challenging problem. Available parametric methods are limited in their model space, while previous semiparametric methods, e.g., leveraging neural networks to fit only one single nuisance function, may still encounter misspecification problems under networked interference without appropriate assumptions on the data generation process. To mitigate bias stemming from misspecification, we propose a novel doubly robust causal effect estimator under networked interference, by adapting the targeted learning technique to the training of neural networks. Specifically, we generalize the targeted learning technique into the networked interference setting and establish the condition under which an estimator achieves double robustness. Based on the condition, we devise an end-to-end causal effect estimator by transforming the identified theoretical condition into a targeted loss. Moreover, we provide a theoretical analysis of our designed estimator, revealing a faster convergence rate compared to a single nuisance model. Extensive experimental results on two real-world networks with semisynthetic data demonstrate the effectiveness of our proposed estimators.

Most studies on causal inference tackle the issue of confounding bias by reducing the distribution shift between the control and treated groups. However, it remains an open question to adopt an appropriate metric for distribution shift in practice. In this paper, we define a generic balancing error on reweighted samples to characterize the confounding bias, and study the connection between the balancing error and the Wasserstein discrepancy derived from the theory of optimal transport. We not only regard the Wasserstein discrepancy as the metric of distribution shift, but also explore the association between the balancing error and the underlying cost function involved in the Wasserstein discrepancy. Motivated by this, we propose to reduce the balancing error under the framework of optimal transport with learnable marginal distributions and the cost function, which is implemented by jointly learning weights and representations associated with factual outcomes. The experiments on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Sequential recommendation aims to choose the most suitable items for a user at a specific timestamp given historical behaviors. Existing methods usually model the user behavior sequence based on transition-based methods such as Markov chain. However, these methods also implicitly assume that the users are independent of each other without considering the influence between users. In fact, this influence plays an important role in sequence recommendation since the behavior of a user is easily affected by others. Therefore, it is desirable to aggregate both user behaviors and the influence between users, which are evolved temporally and involved in the heterogeneous graph of users and items. In this article, we incorporate dynamic user-item heterogeneous graphs to propose a novel sequential recommendation framework. As a result, the historical behaviors as well as the influence between users can be taken into consideration. To achieve this, we first formalize sequential recommendation as a problem to estimate conditional probability given temporal dynamic heterogeneous graphs and user behavior sequences. After that, we exploit the conditional random field to aggregate the heterogeneous graphs and user behaviors for probability estimation and employ the pseudo-likelihood approach to derive a tractable objective function. Finally, we provide scalable and flexible implementations of the proposed framework. Experimental results on three real-world datasets not only demonstrate the effectiveness of our proposed method but also provide some insightful discoveries on the sequential recommendation.

Estimating causal effects from observational network data is a significant but challenging problem. Existing works in causal inference for observational network data lack an analysis of the generalization bound, which can theoretically provide support for alleviating the complex confounding bias and practically guide the design of learning objectives in a principled manner. To fill this gap, we derive a generalization bound for causal effect estimation in network scenarios by exploiting 1) the reweighting schema based on joint propensity score and 2) the representation learning schema based on Integral Probability Metric (IPM). We provide two perspectives on the generalization bound in terms of reweighting and representation learning, respectively. Motivated by the analysis of the bound, we propose a weighting regression method based on the joint propensity score augmented with representation learning. Extensive experimental studies on two real-world networks with semi-synthetic data demonstrate the effectiveness of our algorithm.

Multi-source domain adaptation (MSDA) aims to leverage the knowledge in multiple source domains to assist the prediction in a target domain, where the source and target domains have different data distributions. This paper presents a MSDA model to investigate both domain discrepancy and domain relevance, whose interactions are also exploited to gradually refine the learning performance. Particularly, the proposed model contains two components, i.e., feature spaces learning and transferred weights learning. The former one minimizes the domain discrepancy and the latter one evaluates the domain relevance. Experimental results on several real-world datasets demonstrate the effectiveness of the proposed model.

Domain adaptation aims at extracting knowledge from auxiliary source domains to assist the learning task in a target domain. Since the distributions of the source and target domains are different, directly using source data to build a classifier for the target domain may hamper the classification performance on the target data. In this paper, we propose to find a feature subset that is both transferable and discriminative, so that both the domain discrepancy and the classification loss measured on the selected features can be reduced. To achieve this, we formulate a new sparse learning model that is able to jointly reduce the domain discrepancy and select informative features for classification. Extensive experiments on real-world data sets demonstrate the effectiveness of the proposed method.

In many practical datasets, such as co-citation and co-authorship, relationships across the samples are more complex than pair-wise. Hypergraphs provide a flexible and natural representation for such complex correlations and thus obtain increasing attention in the machine learning and data mining communities. Existing deep learning-based hypergraph approaches seek to learn the latent vertex representations based on either vertices or hyperedges from previous layers and focus on reducing the cross-entropy error over labeled vertices to obtain a classifier. In this paper, we propose a novel model called Hypergraph Collaborative Network (HCoN), which takes the information from both previous vertices and hyperedges into consideration to achieve informative latent representations and further introduces the hypergraph reconstruction error as a regularizer to learn an effective classifier. We evaluate the proposed method on two cases, i.e., semi-supervised vertex and hyperedge classifications. We carry out the experiments on several benchmark datasets and compare our method with several state-of-the-art approaches. Experimental results demonstrate that the performance of the proposed method is better than that of the baseline methods.

The growth rate of pulmonary nodules is a critical clue to the cancerous diagnosis. It is essential to monitor their dynamic progressions during pulmonary nodule management. To facilitate the prosperity of research on nodule growth prediction, we organized and published a temporal dataset called NLSTt with consecutive computed tomography (CT) scans. Based on the self-built dataset, we develop a visual learner to predict the growth for the following CT scan qualitatively and further propose a model to predict the growth rate of pulmonary nodules quantitatively, so that better diagnosis can be achieved with the help of our predicted results. To this end, in this work, we propose a parameterized Gempertz-guided morphological autoencoder (GM-AE) to generate any future-time-span high-quality visual appearances of pulmonary nodules from the baseline CT scan. Specifically, we parameterize a popular mathematical model for tumor growth kinetics, Gompertz, to predict future masses and volumes of pulmonary nodules. Then, we exploit the expected growth rate on the mass and volume to guide decoders generating future shape and texture of pulmonary nodules. We introduce two branches in an autoencoder to encourage shape-aware and textural-aware representation learning and integrate the generated shape into the textural-aware branch to simulate the future morphology of pulmonary nodules. We conduct extensive experiments on the self-built NLSTt dataset to demonstrate the superiority of our GM-AE to its competitive counterparts. Experiment results also reveal the learnable Gompertz function enjoys promising descriptive power in accounting for inter-subject variability of the growth rate for pulmonary nodules. Besides, we evaluate our GM-AE model on an in-house dataset to validate its generalizability and practicality. We make its code publicly available along with the published NLSTt dataset.

Domain adaptation (DA) aims to transfer knowledge from one source domain to another different but related target domain. The mainstream approach embeds adversarial learning into deep neural networks (DNNs) to either learn domain-invariant features to reduce the domain discrepancy or generate data to fill in the domain gap. However, these adversarial DA (ADA) approaches mainly consider the domain-level data distributions, while ignoring the differences among components contained in different domains. Therefore, components that are not related to the target domain are not filtered out. This can cause a negative transfer. In addition, it is difficult to make full use of the relevant components between the source and target domains to enhance DA. To address these limitations, we propose a general two-stage framework, named multicomponent ADA (MCADA). This framework trains the target model by first learning a domain-level model and then fine-tuning that model at the component-level. In particular, MCADA constructs a bipartite graph to find the most relevant component in the source domain for each component in the target domain. Since the nonrelevant components are filtered out for each target component, fine-tuning the domain-level model can enhance positive transfer. Extensive experiments on several real-world datasets demonstrate that MCADA has significant advantages over state-of-the-art methods.

Recommendation systems provide personalized service to users and aim at suggesting to them items that they may prefer. There is an increasing requirement of next-item recommendation systems to infer a user's next favor item based on his/her historical selection of items. In this article, we study the next-item recommendation under the cold-start situation, where the users in the system share no interaction with the new items. Specifically, we seek to address the problem from the perspective of zero-shot learning (ZSL), which classifies samples whose classes are unseen during training. To this end, we crystallize the relationship and setting from ZSL to cold-start next-item recommendation, and further propose a novel model called User-Item Matching and Auto-encoders (UIMA) which learns the latent embeddings for both users and items by exploiting user historical preferences and item attributes. Concretely, UIMA consists of three components, i.e., two auto-encoders for learning user and item embeddings and a matching network to explore the relationship between the learned user and item embeddings. We perform experiments on several cold-start next-item recommendation datasets, including movies, music, and bookmarks. Promising results demonstrate the effectiveness of the proposed method for cold-start next-item recommendation.

One of the main challenges in multi-source domain adaptation is how to reduce the domain discrepancy between each source domain and a target domain, and then evaluate the domain relevance to determine how much knowledge should be transferred from different source domains to the target domain. However, most prior approaches barely consider both discrepancies and relevance among domains. In this paper, we propose an algorithm, called Iterative Refinement based on Feature Selection and the Wasserstein distance (IRFSW), to solve semi-supervised domain adaptation with multiple sources. Specifically, IRFSW aims to explore both the discrepancies and relevance among domains in an iterative learning procedure, which gradually refines the learning performance until the algorithm stops. In each iteration, for each source domain and the target domain, we develop a sparse model to select features in which the domain discrepancy and training loss are reduced simultaneously. Then a classifier is constructed with the selected features of the source and labeled target data. After that, we exploit optimal transport over the selected features to calculate the transferred weights. The weight values are taken as the ensemble weights to combine the learned classifiers to control the amount of knowledge transferred from source domains to the target domain. Experimental results validate the effectiveness of the proposed method.

Domain adaptation aims at extracting knowledge from auxiliary source domains to assist the learning task in a target domain. In classification problems, since the distributions of the source and target domains are different, directly using source data to build a classifier for the target domain may hamper the classification performance on the target data. Fortunately, in many tasks, there can be some features that are transferable, i.e., the source and target domains share similar properties. On the other hand, it is common that the source data contain noisy features which may degrade the learning performance in the target domain. This issue, however, is barely studied in existing works. In this paper, we propose to find a feature subset that is transferable across the source and target domains. As a result, the domain discrepancy measured on the selected features can be reduced. Moreover, we seek to find the most discriminative features for classification. To achieve the above goals, we formulate a new sparse learning model that is able to jointly reduce the domain discrepancy and select informative features for classification. We develop two optimization algorithms to address the derived learning problem. Extensive experiments on real-world data sets demonstrate the effectiveness of the proposed method.

Heterogeneous domain adaptation (HDA) is a challenging problem because of the different feature representations in the source and target domains. Most HDA methods search for mapping matrices from the source and target domains to discover latent features for learning. However, these methods barely consider the reconstruction error to measure the information loss during the mapping procedure. In this paper, we propose to jointly capture the information and match the source and target domain distributions in the latent feature space. In the learning model, we propose to minimize the reconstruction loss between the original and reconstructed representations to preserve information during transformation and reduce the Maximum Mean Discrepancy between the source and target domains to align their distributions. The resulting minimization problem involves two projection variables with orthogonal constraints that can be solved by the generalized gradient flow method, which can preserve orthogonal constraints in the computational procedure. We conduct extensive experiments on several image classification datasets to demonstrate that the effectiveness and efficiency of the proposed method are better than those of state-of-the-art HDA methods.

When encountering a dubious diagnostic case, medical instance retrieval can help radiologists make evidence-based diagnoses by finding images containing instances similar to a query case from a large image database. The similarity between the query case and retrieved similar cases is determined by visual features extracted from pathologically abnormal regions. However, the manifestation of these regions often lacks specificity, i.e., different diseases can have the same manifestation, and different manifestations may occur at different stages of the same disease. To combat the manifestation ambiguity in medical instance retrieval, we propose a novel deep framework called Y-Net, encoding images into compact hash-codes generated from convolutional features by feature aggregation. Y-Net can learn highly discriminative convolutional features by unifying the pixel-wise segmentation loss and classification loss. The segmentation loss allows exploring subtle spatial differences for good spatial-discriminability while the classification loss utilizes class-aware semantic information for good semantic-separability. As a result, Y-Net can enhance the visual features in pathologically abnormal regions and suppress the disturbing of the background during model training, which could effectively embed discriminative features into the hash-codes in the retrieval stage. Extensive experiments on two medical image datasets demonstrate that Y-Net can alleviate the ambiguity of pathologically abnormal regions and its retrieval performance outperforms the state-of-the-art method by an average of 9.27% on the returned list of 10.

Sparse principal component analysis (SPCA) produces principal components with sparse loadings, which is very important for handling data with many irrelevant features and also critical to interpret the results. To deal with orthogonal constraints, most previous approaches address SPCA with several components using techniques such as deflation technique and convex relaxations. However, the deflation technique usually suffers from suboptimal solutions due to poor approximations. On the other hand, the convex relaxations are often computationally expensive. To address the above issues, in this paper, we propose to address SPCA over the Stiefel manifold directly, and develop a stabilized Alternating Direction Method of Multipliers (SADMM) to handle the nonconvex orthogonal constraints. Compared to traditional ADMM, the proposed SADMM method converges well with a wide range of parameters and obtains a better solution. We also theoretically study the convergence property of the proposed SADMM method. Furthermore, most existing methods ignore an inherent drawback of SPCA - the importance of different components is not considered when doing feature selection, which often makes the selected features nonoptimal. To address this, we further propose a two-stage method which considers the importance of different components to select the most important features. Empirical studies on both synthetic and real-world datasets show that the proposed algorithms achieve better performance compared to existing state-of-the-art methods.

Multi-source domain adaptation has received considerable attention due to its effectiveness of leveraging the knowledge from multiple related sources with different distributions to enhance the learning performance. One of the fundamental challenges in multi-source domain adaptation is how to determine the amount of knowledge transferred from each source domain to the target domain. To address this issue, we propose a new algorithm, called Domain-attention Conditional Wasserstein Distance (DCWD), to learn transferred weights for evaluating the relatedness across the source and target domains. In DCWD, we design a new conditional Wasserstein distance objective function by taking the label information into consideration to measure the distance between a given source domain and the target domain. We also develop an attention scheme to compute the transferred weights of different source domains based on their conditional Wasserstein distances to the target domain. After that, the transferred weights can be used to reweight the source data to determine their importance in knowledge transfer. We conduct comprehensive experiments on several real-world data sets, and the results demonstrate the effectiveness and efficiency of the proposed method.

The issue of data imbalance occurs in many real-world applications especially in medical diagnosis, where normal cases are usually much more than the abnormal cases. To alleviate this issue, one of the most important approaches is the oversampling method, which seeks to synthesize minority class samples to balance the numbers of different classes. However, existing methods barely consider global geometric information involved in the distribution of minority class samples, and thus may incur distribution mismatching between real and synthetic samples. In this paper, relying on optimal transport (Villani 2008), we propose an oversampling method by exploiting global geometric information of data to make synthetic samples follow a similar distribution to that of minority class samples. Moreover, we introduce a novel regularization based on synthetic samples and shift the distribution of minority class samples according to loss information. Experiments on toy and real-world data sets demonstrate the efficacy of our proposed method in terms of multiple metrics.

In this article, we study the problem of online heterogeneous transfer learning, where the objective is to make predictions for a target data sequence arriving in an online fashion, and some offline labeled instances from a heterogeneous source domain are provided as auxiliary data. The feature spaces of the source and target domains are completely different, thus the source data cannot be used directly to assist the learning task in the target domain. To address this issue, we take advantage of unlabeled co-occurrence instances as intermediate supplementary data to connect the source and target domains, and perform knowledge transition from the source domain into the target domain. We propose a novel online heterogeneous transfer learning algorithm called O nline H eterogeneous K nowledge T ransition (OHKT) for this purpose. In OHKT, we first seek to generate pseudo labels for the co-occurrence data based on the labeled source data, and then develop an online learning algorithm to classify the target sequence by leveraging the co-occurrence data with pseudo labels. Experimental results on real-world data sets demonstrate the effectiveness and efficiency of the proposed algorithm.

Cartoon-to-photo facial translation could be widely used in different applications, such as law enforcement and anime remaking. Nevertheless, current general-purpose image-to-image models \ygyan{usually} %can only produce blurry or unrelated results in this task. In this paper, we propose a Cartoon-to-Photo facial translation with Generative Adversarial Networks (\name) for inverting cartoon faces to generate photo-realistic and related face images. In order to produce convincing faces with intact facial parts, we exploit global and local discriminators to capture global facial features and three local facial regions, respectively. Moreover, we use a specific content network to capture and preserve face characteristic and identity between cartoons and photos. As a result, the proposed approach can generate convincing high-quality faces that satisfy both the characteristic and identity constraints of input cartoon faces. Compared with recent works on unpaired image-to-image translation, our proposed method is able to generate more realistic and correlative images.

Heterogeneous domain adaptation (HDA) aims to exploit knowledge from a heterogeneous source domain to improve the learning performance in a target domain. Since the feature spaces of the source and target domains are different, the transferring of knowledge is extremely difficult. In this paper, we propose a novel semi-supervised algorithm for HDA by exploiting the theory of optimal transport (OT), a powerful tool originally designed for aligning two different distributions. To match the samples between heterogeneous domains, we propose to preserve the semantic consistency between heterogeneous domains by incorporating label information into the entropic Gromov-Wasserstein discrepancy, which is a metric in OT for different metric spaces, resulting in a new semi-supervised scheme. Via the new scheme, the target and transported source samples with the same label are enforced to follow similar distributions. Lastly, based on the Kullback-Leibler metric, we develop an efficient algorithm to optimize the resultant problem. Comprehensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

In this paper, we study the online heterogeneous transfer (OHT) learning problem, where the target data of interest arrive in an online manner, while the source data and auxiliary co-occurrence data are from offline sources and can be easily annotated. OHT is very challenging, since the feature spaces of the source and target domains are different. To address this, we propose a novel technique called OHT by hedge ensemble by exploiting both offline knowledge and online knowledge of different domains. To this end, we build an offline decision function based on a heterogeneous similarity that is constructed using labeled source data and unlabeled auxiliary co-occurrence data. After that, an online decision function is learned from the target data. Last, we employ a hedge weighting strategy to combine the offline and online decision functions to exploit knowledge from the source and target domains of different feature spaces. We also provide a theoretical analysis regarding the mistake bounds of the proposed approach. Comprehensive experiments on three real-world data sets demonstrate the effectiveness of the proposed technique.

Deep learning has achieved unprecedented practical success in many applications. Despite its empirical success, however, the theoretical understanding of deep neural networks still remains a major open problem. In this paper, we explore properties of two-layered ReLU networks. For simplicity, we assume that the optimal model parameters (also called ground-truth parameters) are known. We then assume that a network receives Gaussian input and is trained by minimizing the expected squared loss between the prediction function of the network and a target function. To conduct the analysis, we propose a normal equation for critical points, and study the invariances under three kinds of transformations, namely, scale transformation, rotation transformation and perturbation transformation. We prove that these transformations can keep the loss of a critical point invariant, thus can incur flat regions. Consequently, how to escape from flat regions is vital in training neural networks.

Domain adaptation aims to reduce the effort on collecting and annotating target data by leveraging knowledge from a different source domain. The domain adaptation problem will become extremely challenging when the feature spaces of the source and target domains are different, which is also known as the heterogeneous domain adaptation (HDA) problem. In this paper, we propose a novel HDA method to find the optimal discriminative correlation subspace for the source and target data. The discriminative correlation subspace is inherited from the canonical correlation subspace between the source and target data, and is further optimized to maximize the discriminative ability for the target domain classifier. We formulate a joint objective in order to simultaneously learn the discriminative correlation subspace and the target domain classifier. We then apply an alternating direction method of multiplier (ADMM) algorithm to address the resulting non-convex optimization problem. Comprehensive experiments on two real-world data sets demonstrate the effectiveness of the proposed method compared to the state-of-the-art methods.

Transfer learning techniques have been broadly applied in applications where labeled data in a target domain are difficult to obtain while a lot of labeled data are available in related source domains. In practice, there can be multiple source domains that are related to the target domain, and how to combine them is still an open problem. In this paper, we seek to leverage labeled data from multiple source domains to enhance classification performance in a target domain where the target data are received in an online fashion. This problem is known as the online transfer learning problem. To achieve this, we propose novel online transfer learning paradigms in which the source and target domains are leveraged adaptively. We consider two different problem settings: homogeneous transfer learning and heterogeneous transfer learning. The proposed methods work in an online manner, where the weights of the source domains are adjusted dynamically. We provide the mistake bounds of the proposed methods and perform comprehensive experiments on real-world data sets to demonstrate the effectiveness of the proposed algorithms.