Unsupervised domain adaptation aims to align a labeled source domain and an unlabeled target domain, but it requires to access the source data which often raises concerns in data privacy, data portability and data transmission efficiency. We study unsupervised model adaptation (UMA), or called Unsupervised Domain Adaptation without Source Data, an alternative setting that aims to adapt source-trained models towards target distributions without accessing source data. To this end, we design an innovative historical contrastive learning (HCL) technique that exploits historical source hypothesis to make up for the absence of source data in UMA. HCL addresses the UMA challenge from two perspectives. First, it introduces historical contrastive instance discrimination (HCID) that learns from target samples by contrasting their embeddings which are generated by the currently adapted model and the historical models. With the historical models, HCID encourages UMA to learn instance-discriminative target representations while preserving the source hypothesis. Second, it introduces historical contrastive category discrimination (HCCD) that pseudo-labels target samples to learn category-discriminative target representations.

Estimating conditional average treatment effect from observational data is highly challenging due to the existence of treatment selection bias. Prevalent methods mitigate this issue by aligning distributions of different treatment groups in the latent space. However, there are two critical problems that these methods fail to address: (1) mini-batch sampling effects (MSE), which causes misalignment in non-ideal mini-batches with outcome imbalance and outliers; (2) unobserved confounder effects (UCE), which results in inaccurate discrepancy calculation due to the neglect of unobserved confounders. To tackle these problems, we propose a principled approach named Entire Space CounterFactual Regression (ESCFR), which is a new take on optimal transport in the context of causality. Specifically, based on the framework of stochastic optimal transport, we propose a relaxed masspreserving regularizer to address the MSE issue and design a proximal factual outcome regularizer to handle the UCE issue. Extensive experiments demonstrate that our proposed ESCFR can successfully tackle the treatment selection bias and achieve significantly better performance than state-of-the-art methods.

We study federated contextual linear bandits, where M agents cooperate with each other to solve a global contextual linear bandit problem with the help of a central server. We consider the asynchronous setting, where all agents work independently and the communication between one agent and the server will not trigger other agents' communication. We propose a simple algorithm named FedLinUCBbased on the principle of optimism.

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in practice, but they come at the high computational cost of solving an NP-hard combinatorial optimization problem. To reduce the computational burden, we propose to relax BMF continuously using a novel elastic-binary regularizer, from which we derive a proximal gradient algorithm. Through an extensive set of experiments, we demonstrate that our method works well in practice: On synthetic data, we show that it converges quickly, recovers the ground truth precisely, and estimates the simulated rank exactly. On real-world data, we improve upon the state of the art in recall, loss, and runtime, and a case study from the medical domain confirms that our results are easily interpretable and semantically meaningful.