Generative adversarial network (GAN) has achieved remarkable success in generating high-quality synthetic data by learning the underlying distributions of target data. Recent efforts have been devoted to utilizing optimal transport (OT) to tackle the gradient vanishing and instability issues in GAN. They use the Wasserstein distance as a metric to measure the discrepancy between the generator distribution and the real data distribution. However, most optimal transport GANs define loss functions in Euclidean space, which limits their capability in handling high-order statistics that are of much interest in a variety of practical applications. In this article, we propose a computational framework to alleviate this issue from both theoretical and practical perspectives. Particularly, we generalize the optimal transport-based GAN from Euclidean space to the reproducing kernel Hilbert space (RKHS) and propose Hilbert Optimal Transport GAN (HOT-GAN). First, we design HOT-GAN with a Hilbert embedding that allows the discriminator to tackle more informative and high-order statistics in RKHS. Second, we prove that HOT-GAN has a closed-form kernel reformulation in RKHS that can achieve a tractable objective under the GAN framework. Third, HOT-GAN's objective enjoys the theoretical guarantee of differentiability with respect to generator parameters, which is beneficial to learn powerful generators via adversarial kernel learning. Extensive experiments are conducted, showing that our proposed HOT-GAN consistently outperforms the representative GAN works.

In recommendation systems, the existence of the missing-not-at-random (MNAR) problem results in the selection bias issue, degrading the recommendation performance ultimately. A common practice to address MNAR is to treat missing entries from the so-called “exposure” perspective, i.e., modeling how an item is exposed (provided) to a user. Most of the existing approaches use heuristic models or re-weighting strategy on observed ratings to mimic the missing-at-random setting. However, little research has been done to reveal how the ratings are missing from a causal perspective. To bridge the gap, we propose an unbiased and robust method called DENC ( De-Bias Network Confounding in Recommendation ), inspired by confounder analysis in causal inference. In general, DENC provides a causal analysis on MNAR from both the inherent factors (e.g., latent user or item factors) and auxiliary network’s perspective. Particularly, the proposed exposure model in DENC can control the social network confounder meanwhile preserve the observed exposure information. We also develop a deconfounding model through the balanced representation learning to retain the primary user and item features, which enables DENC generalize well on the rating prediction. Extensive experiments on three datasets validate that our proposed model outperforms the state-of-the-art baselines.

Traditional recommendation models trained on observational interaction data have generated large impacts in a wide range of applications, it faces bias problems that cover users’ true intent and thus deteriorate the recommendation effectiveness. Existing methods track this problem as eliminating bias for the robust recommendation, e.g., by re-weighting training samples or learning disentangled representations. The disentangled representation methods as the state-of-the-art eliminate bias by revealing cause-effect of the bias generation. However, how to design the semantic-aware and unbiased representations for users’ true intents is largely unexplored. To bridge the gap, we are the first to propose an unbiased and semantic-aware disentanglement learning calledCaDSI(CausalDisentanglement forSemantics-AwareIntent Learning) from a causal perspective. Particularly, CaDSI explicitly models the causal relations underlying recommendation task, and thus produces semantic-aware representations via disentangling users’ true intents aware of specific item context. Moreover, the causal intervention mechanism is designed to eliminate confounding bias stemming from context information, which further aligns the semantic-aware representation with users’ true intent. Extensive experiments and case studies both validate the robustness and interpretability of our proposed model.

Treatment effect estimation helps answer questions, such as whether a specific treatment affects the outcome of interest. One fundamental issue in this research is to alleviate the treatment assignment bias among those treated units and controlled units. Classical causal inference methods resort to the propensity score estimation, which unfortunately tends to be misspecified when only limited overlapping exists between the treated and the controlled units. Moreover, existing supervised methods mainly consider the treatment assignment information underlying the factual space, and thus, their performance of counterfactual inference may be degraded due to overfitting of the factual results. To alleviate those issues, we build on the optimal transport theory and propose a novel causal optimal transport (CausalOT) model to estimate an individual treatment effect (ITE). With the proposed propensity measure, CausalOT can infer the counterfactual outcome by solving a novel regularized optimal transport problem, which allows the utilization of global information on observational covariates to alleviate the issue of limited overlapping. In addition, a novel counterfactual loss is designed for CausalOT to align the factual outcome distribution with the counterfactual outcome distribution. Most importantly, we prove the theoretical generalization bound for the counterfactual error of CausalOT. Empirical studies on benchmark datasets confirm that the proposed CausalOT outperforms state-of-the-art causal inference methods.

Off-policy learning has drawn huge attention in recommender systems (RS), which provides an opportunity for reinforcement learning to abandon the expensive online training. However, off-policy learning from logged data suffers biases caused by the policy shift between the target policy and the logging policy. Consequently, most off-policy learning resorts to inverse propensity scoring (IPS) which however tends to be over-fitted over exposed (or recommended) items and thus fails to explore unexposed items.

Abstract Causal inference is capable of estimating the treatment effect (i.e., the causal effect oftreatmenton theoutcome) to benefit the decision making in various domains. One fundamental challenge in this research is that the treatment assignment bias in observational data. To increase the validity of observational studies on causal inference, representation-based methods as the state-of-the-art have demonstrated the superior performance of treatment effect estimation. Most representation-based methods assume all observed covariates are pre-treatment (i.e., not affected by the treatment) and learn a balanced representation from these observed covariates for estimating treatment effect. Unfortunately, this assumption is often too strict a requirement in practice, as some covariates are changed by doing an intervention on treatment (i.e., post-treatment). By contrast, the balanced representation learned from unchanged covariates thus biases the treatment effect estimation. In light of this, we propose a deep treatment-adaptive architecture (DTANet) that can address the post-treatment covariates and provide a unbiased treatment effect estimation. Generally speaking, the contributions of this work are threefold. First, our theoretical results guarantee DTANet can identify treatment effect from observations. Second, we introduce a novel regularization of orthogonality projection to ensure that the learned confounding representation is invariant and not being contaminated by the treatment, meanwhile mediate variable representation is informative and discriminative for predicting the outcome. Finally, we build on the optimal transport and learn a treatment-invariant representation for the unobserved confounders to alleviate the confounding bias.

Underwriting is an important process in insurance and is concerned with accepting individuals into insurance policy with tolerable claim risk. Underwriting is a tedious and labor intensive process relying on underwriters' domain knowledge and experience, thus is labor intensive and prone to error. Machine learning models are recently applied to automate the underwriting process and thus to ease the burden on the underwriters as well as improve underwriting accuracy. However, observational data used for underwriting modelling is high dimensional, sparse and incomplete, due to the dynamic evolving nature (e.g., upgrade) of business information systems. Simply applying traditional supervised learning methods e.g., logistic regression or Gradient boosting on such highly incomplete data usually leads to the unsatisfactory underwriting result, thus requiring practical data imputation for training quality improvement. In this paper, rather than choosing off-the-shelf solutions tackling the complex data missing problem, we propose an innovative Generative Adversarial Nets (GAN) framework that can capture the missing pattern from a causal perspective. Specifically, we design a structural causal model to learn the causal relations underlying the missing pattern of data. Then, we devise a Causality-aware Generative network (CaGen) using the learned causal relationship prior to generating missing values, and correct the imputed values via the adversarial learning. We also show that CaGen significantly improves the underwriting prediction in real-world insurance applications.

The Sinkhorn divergence has become a very popular metric to compare probability distributions in optimal transport. However, most works resort to the Sinkhorn divergence in Euclidean space, which greatly blocks their applications in complex data with nonlinear structure. It is therefore of theoretical demand to empower the Sinkhorn divergence with the capability of capturing nonlinear structures. We propose a theoretical and computational framework to bridge this gap. In this paper, we extend the Sinkhorn divergence in Euclidean space to the reproducing kernel Hilbert space, which we term "Hilbert Sinkhorn divergence" (HSD). In particular, we can use kernel matrices to derive a closed form expression of the HSD that is proved to be a tractable convex optimization problem. We also prove several attractive statistical properties of the proposed HSD, i.e., strong consistency, asymptotic behavior and sample complexity. Empirically, our method yields state-of-the-art performances on image classification and topological data analysis.

Persistence diagram (PD) has been considered as a compact descriptor for topological data analysis (TDA). Unfortunately, PD cannot be directly used in machine learning methods since it is a multiset of points. Recent efforts have been devoted to transforming PDs into vectors to accommodate machine learning methods. However, they share one common shortcoming: the mapping of PDs to a feature representation depends on a pre-defined polynomial. To address this limitation, this paper proposes an algebraic representation for PDs, i.e., polynomial representation. In this work, we discover a set of general polynomials that vanish on vectorized PDs and extract the task-adapted feature representation from these polynomials. We also prove two attractive properties of the proposed polynomial representation, i.e., stability and linear separability. Experiments also show that our method compares favorably with state-of-the-art TDA methods.

Matrix recovery aims to learn a low-rank structure from high dimensional data, which arises in numerous learning applications. As a popular heuristic to matrix recovery, convex relaxation involves iterative calling of singular value decomposition (SVD). Riemannian optimization based method can alleviate such expensive cost in SVD for improved scalability, which however is usually degraded by the unknown rank. This paper proposes a novel algorithm RIST that exploits the algebraic variety of low-rank manifold for matrix recovery. Particularly, RIST utilizes an efficient scheme that automatically estimate the potential rank on the real algebraic variety and tracks the favorable Riemannian submanifold. Moreover, RIST utilizes the second-order geometric characterization and achieves provable superlinear convergence, which is superior to the linear convergence of most existing methods. Extensive comparison experiments demonstrate the accuracy and ef- ficiency of RIST algorithm.