Daily Papers

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

Large language models (LLMs) such as ChatGPT have exhibited remarkable performance in generating human-like texts. However, machine-generated texts (MGTs) may carry critical risks, such as plagiarism issues, misleading information, or hallucination issues. Therefore, it is very urgent and important to detect MGTs in many situations. Unfortunately, it is challenging to distinguish MGTs and human-written texts because the distributional discrepancy between them is often very subtle due to the remarkable performance of LLMs. In this paper, we seek to exploit maximum mean discrepancy (MMD) to address this issue in the sense that MMD can well identify distributional discrepancies. However, directly training a detector with MMD using diverse MGTs will incur a significantly increased variance of MMD since MGTs may contain multiple text populations due to various LLMs. This will severely impair MMD's ability to measure the difference between two samples. To tackle this, we propose a novel multi-population aware optimization method for MMD called MMD-MP, which can avoid variance increases and thus improve the stability to measure the distributional discrepancy. Relying on MMD-MP, we develop two methods for paragraph-based and sentence-based detection, respectively. Extensive experiments on various LLMs, \eg, GPT2 and ChatGPT, show superior detection performance of our MMD-MP. The source code is available at https://github.com/ZSHsh98/MMD-MP.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels K(x,y) = - |x-y|^r, r in (0,2) have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for r=1, a simple sorting algorithm can be applied to reduce the complexity from O(MN+N^2) to O((M+N)log(M+N)) for two measures with M and N support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number P of slices. We show that the resulting error has complexity O(d/P), where d is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

Wireless sensing has recently found widespread applications in diverse environments, including homes, offices, and public spaces. By analyzing patterns in channel state information (CSI), it is possible to infer human actions for tasks such as person identification, gesture recognition, and fall detection. However, CSI is highly sensitive to environmental changes, where even minor alterations can significantly distort the CSI patterns. This sensitivity often leads to performance degradation or outright failure when applying wireless sensing models trained in one environment to another. To address this challenge, Domain Alignment (DAL) has been widely adopted for cross-domain classification tasks, as it focuses on aligning the global distributions of the source and target domains in feature space. Despite its popularity, DAL often neglects inter-category relationships, which can lead to misalignment between categories across domains, even when global alignment is achieved. To overcome these limitations, we propose K-Nearest Neighbors Maximum Mean Discrepancy (KNN-MMD), a novel few-shot method for cross-domain wireless sensing. Our approach begins by constructing a help set using KNN from the target domain, enabling local alignment between the source and target domains within each category using MMD. Additionally, we address a key instability issue commonly observed in cross-domain methods, where model performance fluctuates sharply between epochs. Further, most existing methods struggle to determine an optimal stopping point during training due to the absence of labeled data from the target domain. Our method resolves this by excluding the support set from the target domain during training and employing it as a validation set to determine the stopping criterion.The dataset and code are publicly available at https://github.com/RS2002/KNN-MMD .

We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized alpha-divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories.

We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous properties like efficient computation via slicing and sorting. We approximate the joint distribution of the ground truth and the observations using discrete Wasserstein gradient flows and establish an error bound for the posterior distributions. Further, we prove that our particle flow is indeed a Wasserstein gradient flow of an appropriate functional. The power of our method is demonstrated by numerical examples including conditional image generation and inverse problems like superresolution, inpainting and computed tomography in low-dose and limited-angle settings.

Multimodal recommendation systems are increasingly becoming foundational technologies for e-commerce and content platforms, enabling personalized services by jointly modeling users' historical behaviors and the multimodal features of items (e.g., visual and textual). However, most existing methods rely on either static fusion strategies or graph-based local interaction modeling, facing two critical limitations: (1) insufficient ability to model fine-grained cross-modal associations, leading to suboptimal fusion quality; and (2) a lack of global distribution-level consistency, causing representational bias. To address these, we propose MambaRec, a novel framework that integrates local feature alignment and global distribution regularization via attention-guided learning. At its core, we introduce the Dilated Refinement Attention Module (DREAM), which uses multi-scale dilated convolutions with channel-wise and spatial attention to align fine-grained semantic patterns between visual and textual modalities. This module captures hierarchical relationships and context-aware associations, improving cross-modal semantic modeling. Additionally, we apply Maximum Mean Discrepancy (MMD) and contrastive loss functions to constrain global modality alignment, enhancing semantic consistency. This dual regularization reduces mode-specific deviations and boosts robustness. To improve scalability, MambaRec employs a dimensionality reduction strategy to lower the computational cost of high-dimensional multimodal features. Extensive experiments on real-world e-commerce datasets show that MambaRec outperforms existing methods in fusion quality, generalization, and efficiency. Our code has been made publicly available at https://github.com/rkl71/MambaRec.

AI-generated videos have achieved near-perfect visual realism (e.g., Sora), urgently necessitating reliable detection mechanisms. However, detecting such videos faces significant challenges in modeling high-dimensional spatiotemporal dynamics and identifying subtle anomalies that violate physical laws. In this paper, we propose a physics-driven AI-generated video detection paradigm based on probability flow conservation principles. Specifically, we propose a statistic called Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, explicitly capturing deviations from natural video dynamics. Leveraging pre-trained diffusion models, we develop an NSG estimator through spatial gradients approximation and motion-aware temporal modeling without complex motion decomposition while preserving physical constraints. Building on this, we propose an NSG-based video detection method (NSG-VD) that computes the Maximum Mean Discrepancy (MMD) between NSG features of the test and real videos as a detection metric. Last, we derive an upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies due to distributional shifts. Extensive experiments confirm that NSG-VD outperforms state-of-the-art baselines by 16.00% in Recall and 10.75% in F1-Score, validating the superior performance of NSG-VD. The source code is available at https://github.com/ZSHsh98/NSG-VD.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a varphi-divergence to an empirical distribution. However, the use of varphi-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples that are highly diverse and representative of the underlying distribution. However, one of the main limitations of diffusion models is the complexity of sample generation, since a large number of inference timesteps is required to faithfully capture the data distribution. In this paper, we present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. This allows the finetuned model to significantly improve the speed-quality trade-off, by substantially increasing fidelity in inference regimes with few steps or, equivalently, by reducing the required number of steps to reach a target fidelity, thus paving the way for a more practical adoption of diffusion models in a wide range of applications. We evaluate our approach on unconditional image generation with extensive experiments across the CIFAR-10, CelebA, ImageNet and LSUN-Church datasets. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models, and outperforms state-of-the-art techniques for accelerated sampling. Code is available at: https://github.com/diegovalsesia/MMD-DDM.

We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss functions raised by recent work: we show that gradient estimators used in the optimization process for both MMD GANs and Wasserstein GANs are unbiased, but learning a discriminator based on samples leads to biased gradients for the generator parameters. We also discuss the issue of kernel choice for the MMD critic, and characterize the kernel corresponding to the energy distance used for the Cramer GAN critic. Being an integral probability metric, the MMD benefits from training strategies recently developed for Wasserstein GANs. In experiments, the MMD GAN is able to employ a smaller critic network than the Wasserstein GAN, resulting in a simpler and faster-training algorithm with matching performance. We also propose an improved measure of GAN convergence, the Kernel Inception Distance, and show how to use it to dynamically adapt learning rates during GAN training.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

Effective cross-modal retrieval requires robust alignment of heterogeneous data types. Most existing methods focus on bi-modal retrieval tasks and rely on distributional alignment techniques such as Kullback-Leibler divergence, Maximum Mean Discrepancy, and correlation alignment. However, these methods often suffer from critical limitations, including numerical instability, sensitivity to hyperparameters, and their inability to capture the full structure of the underlying distributions. In this paper, we introduce the Cauchy-Schwarz (CS) divergence, a hyperparameter-free measure that improves both training stability and retrieval performance. We further propose a novel Generalized CS (GCS) divergence inspired by H\"older's inequality. This extension enables direct alignment of three or more modalities within a unified mathematical framework through a bidirectional circular comparison scheme, eliminating the need for exhaustive pairwise comparisons. Extensive experiments on six benchmark datasets demonstrate the effectiveness of our method in both bi-modal and tri-modal retrieval tasks. The code of our CS/GCS divergence is publicly available at https://github.com/JiahaoZhang666/CSD.

Sequential recommendation (SR) aims to model the sequential dependencies in users' historical interactions to better capture their evolving interests. However, existing SR approaches primarily rely on collaborative data, which leads to limitations such as the cold-start problem and sub-optimal performance. Meanwhile, despite the success of large language models (LLMs), their application in industrial recommender systems is hindered by high inference latency, inability to capture all distribution statistics, and catastrophic forgetting. To this end, we propose a novel Pre-train, Align, and Disentangle (PAD) paradigm to empower recommendation models with LLMs. Specifically, we first pre-train both the SR and LLM models to get collaborative and textual embeddings. Next, a characteristic recommendation-anchored alignment loss is proposed using multi-kernel maximum mean discrepancy with Gaussian kernels. Finally, a triple-experts architecture, consisting aligned and modality-specific experts with disentangled embeddings, is fine-tuned in a frequency-aware manner. Experiments conducted on three public datasets demonstrate the effectiveness of PAD, showing significant improvements and compatibility with various SR backbone models, especially on cold items. The implementation code and datasets will be publicly available.

Cross-modal alignment is crucial for multimodal representation fusion due to the inherent heterogeneity between modalities. While Transformer-based methods have shown promising results in modeling inter-modal relationships, their quadratic computational complexity limits their applicability to long-sequence or large-scale data. Although recent Mamba-based approaches achieve linear complexity, their sequential scanning mechanism poses fundamental challenges in comprehensively modeling cross-modal relationships. To address this limitation, we propose AlignMamba, an efficient and effective method for multimodal fusion. Specifically, grounded in Optimal Transport, we introduce a local cross-modal alignment module that explicitly learns token-level correspondences between different modalities. Moreover, we propose a global cross-modal alignment loss based on Maximum Mean Discrepancy to implicitly enforce the consistency between different modal distributions. Finally, the unimodal representations after local and global alignment are passed to the Mamba backbone for further cross-modal interaction and multimodal fusion. Extensive experiments on complete and incomplete multimodal fusion tasks demonstrate the effectiveness and efficiency of the proposed method.

This paper studies attack detection for discrete-time linear systems with stochastic process noise that produce both a vulnerable (i.e., attackable) linear measurement and a secured (i.e., unattackable) quadratic measurement. The motivating application of this model is a dynamic-game setting where the quadratic measurement is interpreted as a system-level utility or reward, and control inputs into the linear system are interpreted as control policies that, once applied, are known to all game participants and which steer the system towards a game-theoretic equilibrium (e.g., Nash equilibrium). To detect attacks on the linear channel, we develop a novel quadratic-utility-aware observer that leverages the secured quadratic output and enforces measurement consistency via a projection step. We establish three properties for this observer: feasibility of the true state, prox-regularity of the quadratic-constraint set, and a monotone error-reduction guarantee in the noise-free case. To detect adversarial manipulation, we compare linear and quadratic observer trajectories using a wild bootstrap maximum mean discrepancy (MMD) test that provides valid inference under temporal dependence. We validate our framework using numerical experiments of a pursuit-evasion game, where the quadratic observer preserves estimation accuracy under linear-sensor attacks, while the statistical test detects distributional divergence between the observers' trajectories.

Skeleton-based multi-entity action recognition is a challenging task aiming to identify interactive actions or group activities involving multiple diverse entities. Existing models for individuals often fall short in this task due to the inherent distribution discrepancies among entity skeletons, leading to suboptimal backbone optimization. To this end, we introduce a Convex Hull Adaptive Shift based multi-Entity action recognition method (CHASE), which mitigates inter-entity distribution gaps and unbiases subsequent backbones. Specifically, CHASE comprises a learnable parameterized network and an auxiliary objective. The parameterized network achieves plausible, sample-adaptive repositioning of skeleton sequences through two key components. First, the Implicit Convex Hull Constrained Adaptive Shift ensures that the new origin of the coordinate system is within the skeleton convex hull. Second, the Coefficient Learning Block provides a lightweight parameterization of the mapping from skeleton sequences to their specific coefficients in convex combinations. Moreover, to guide the optimization of this network for discrepancy minimization, we propose the Mini-batch Pair-wise Maximum Mean Discrepancy as the additional objective. CHASE operates as a sample-adaptive normalization method to mitigate inter-entity distribution discrepancies, thereby reducing data bias and improving the subsequent classifier's multi-entity action recognition performance. Extensive experiments on six datasets, including NTU Mutual 11/26, H2O, Assembly101, Collective Activity and Volleyball, consistently verify our approach by seamlessly adapting to single-entity backbones and boosting their performance in multi-entity scenarios. Our code is publicly available at https://github.com/Necolizer/CHASE .

Metaverse has stretched the real world into unlimited space. There will be more live concerts in Metaverse. The task of singer identification is to identify the song belongs to which singer. However, there has been a tough problem in singer identification, which is the different live effects. The studio version is different from the live version, the data distribution of the training set and the test set are different, and the performance of the classifier decreases. This paper proposes the use of the domain adaptation method to solve the live effect in singer identification. Three methods of domain adaptation combined with Convolutional Recurrent Neural Network (CRNN) are designed, which are Maximum Mean Discrepancy (MMD), gradient reversal (Revgrad), and Contrastive Adaptation Network (CAN). MMD is a distance-based method, which adds domain loss. Revgrad is based on the idea that learned features can represent different domain samples. CAN is based on class adaptation, it takes into account the correspondence between the categories of the source domain and target domain. Experimental results on the public dataset of Artist20 show that CRNN-MMD leads to an improvement over the baseline CRNN by 0.14. The CRNN-RevGrad outperforms the baseline by 0.21. The CRNN-CAN achieved state of the art with the F1 measure value of 0.83 on album split.

As with many machine learning problems, the progress of image generation methods hinges on good evaluation metrics. One of the most popular is the Frechet Inception Distance (FID). FID estimates the distance between a distribution of Inception-v3 features of real images, and those of images generated by the algorithm. We highlight important drawbacks of FID: Inception's poor representation of the rich and varied content generated by modern text-to-image models, incorrect normality assumptions, and poor sample complexity. We call for a reevaluation of FID's use as the primary quality metric for generated images. We empirically demonstrate that FID contradicts human raters, it does not reflect gradual improvement of iterative text-to-image models, it does not capture distortion levels, and that it produces inconsistent results when varying the sample size. We also propose an alternative new metric, CMMD, based on richer CLIP embeddings and the maximum mean discrepancy distance with the Gaussian RBF kernel. It is an unbiased estimator that does not make any assumptions on the probability distribution of the embeddings and is sample efficient. Through extensive experiments and analysis, we demonstrate that FID-based evaluations of text-to-image models may be unreliable, and that CMMD offers a more robust and reliable assessment of image quality.

We propose an innovative machine learning-based technique to address the problem of channel acquisition at the base station in frequency division duplex systems. In this context, the base station reconstructs the full channel state information in the downlink frequency range based on limited downlink channel state information feedback from the mobile terminal. The channel state information recovery is based on a convolutional neural network which is trained exclusively on collected channel state samples acquired in the uplink frequency domain. No acquisition of training samples in the downlink frequency range is required at all. Finally, after a detailed presentation and analysis of the proposed technique and its performance, the "transfer learning'' assumption of the convolutional neural network that is central to the proposed approach is validated with an analysis based on the maximum mean discrepancy metric.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We present a novel unsupervised domain adaption method for person re-identification (reID) that generalizes a model trained on a labeled source domain to an unlabeled target domain. We introduce a camera-driven curriculum learning (CaCL) framework that leverages camera labels of person images to transfer knowledge from source to target domains progressively. To this end, we divide target domain dataset into multiple subsets based on the camera labels, and initially train our model with a single subset (i.e., images captured by a single camera). We then gradually exploit more subsets for training, according to a curriculum sequence obtained with a camera-driven scheduling rule. The scheduler considers maximum mean discrepancies (MMD) between each subset and the source domain dataset, such that the subset closer to the source domain is exploited earlier within the curriculum. For each curriculum sequence, we generate pseudo labels of person images in a target domain to train a reID model in a supervised way. We have observed that the pseudo labels are highly biased toward cameras, suggesting that person images obtained from the same camera are likely to have the same pseudo labels, even for different IDs. To address the camera bias problem, we also introduce a camera-diversity (CD) loss encouraging person images of the same pseudo label, but captured across various cameras, to involve more for discriminative feature learning, providing person representations robust to inter-camera variations. Experimental results on standard benchmarks, including real-to-real and synthetic-to-real scenarios, demonstrate the effectiveness of our framework.