State estimation is a critical foundational module in robotics applications, where robustness and performance are paramount. Although in recent years, many works have been focusing on improving one of the most widely adopted state estimation methods, visual inertial odometry (VIO), by incorporating multiple cameras, these efforts predominantly address synchronous camera systems. Asynchronous cameras, which offer simpler hardware configurations and enhanced resilience, have been largely overlooked. To fill this gap, this paper presents VINS-Multi, a novel multi-camera-IMU state estimator for asynchronous cameras. The estimator comprises parallel front ends, a front end coordinator, and a back end optimization module capable of handling asynchronous input frames. It utilizes the frames effectively through a dynamic feature number allocation and a frame priority coordination strategy. The proposed estimator is integrated into a customized quadrotor platform and tested in multiple realistic and challenging scenarios to validate its practicality. Additionally, comprehensive benchmark results are provided to showcase the robustness and superior performance of the proposed estimator.

Alternatively, if the algorithm performs well against any of the existing AC ones then it would be good to see its performance in various settings and detailed explanation of its properties. The latter would be useful in its own right whether or not it is related to summarizing posterior distribution's characteristics. A few specific comments: Line 19: It is correct to say that the MAP might not be good in situations where the posterior is diffuse, I guess you mean uniform-like? It might also be multimodal, skewed (mode and mean differ), high variance,for example, so the MAP is not necessarily a good choice although it depends on the (underlying) loss function. Line 52: Since a Dirichlet Process is a discrete random probability measure, when sampling from it it induces a random partition (the ties will belong to the same cluster).

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

Federated learning learns from scattered data by fusing collaborative models from local nodes. However, the conventional coordinate-based model averaging by FedAvg ignored the random information encoded per parameter and may suffer from structural feature misalignment. In this work, we propose Fed2, a feature-aligned federated learning framework to resolve this issue by establishing a firm structure-feature alignment across the collaborative models. Fed2 is composed of two major designs: First, we design a feature-oriented model structure adaptation method to ensure explicit feature allocation in different neural network structures. Applying the structure adaptation to collaborative models, matchable structures with similar feature information can be initialized at the very early training stage. During the federated learning process, we then propose a feature paired averaging scheme to guarantee aligned feature distribution and maintain no feature fusion conflicts under either IID or non-IID scenarios. Eventually, Fed2 could effectively enhance the federated learning convergence performance under extensive homo- and heterogeneous settings, providing excellent convergence speed, accuracy, and computation/communication efficiency.

Federated learning learns from scattered data by fusing collaborative models from local nodes. However, due to chaotic information distribution, the model fusion may suffer from structural misalignment with regard to unmatched parameters. In this work, we propose a novel federated learning framework to resolve this issue by establishing a firm structure-information alignment across collaborative models. Specifically, we design a feature-oriented regulation method ({$\Psi$-Net}) to ensure explicit feature information allocation in different neural network structures. Applying this regulating method to collaborative models, matchable structures with similar feature information can be initialized at the very early training stage. During the federated learning process under either IID or non-IID scenarios, dedicated collaboration schemes further guarantee ordered information distribution with definite structure matching, so as the comprehensive model alignment. Eventually, this framework effectively enhances the federated learning applicability to extensive heterogeneous settings, while providing excellent convergence speed, accuracy, and computation/communication efficiency.

Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC) methods for posterior inference. The most widely used MCMC strategies rely on an element wise Gibbs update of the feature allocation matrix. These element wise updates can be inefficient as features are typically strongly correlated. To overcome this problem we have developed a Gibbs sampler that can update an entire row of the feature allocation matrix in a single move. However, this sampler is impractical for models with a large number of features as the computational complexity scales exponentially in the number of features. We develop a Particle Gibbs sampler that targets the same distribution as the row wise Gibbs updates, but has computational complexity that only grows linearly in the number of features. We compare the performance of our proposed methods to the standard Gibbs sampler using synthetic data from a range of feature allocation models. Our results suggest that row wise updates using the PG methodology can significantly improve the performance of samplers for feature allocation models.

We present a consensus Monte Carlo algorithm that scales existing Bayesian nonparametric models for clustering and feature allocation to big data. The algorithm is valid for any prior on random subsets such as partitions and latent feature allocation, under essentially any sampling model. Motivated by three case studies, we focus on clustering induced by a Dirichlet process mixture sampling model, inference under an Indian buffet process prior with a binomial sampling model, and with a categorical sampling model. We assess the proposed algorithm with simulation studies and show results for inference with three datasets: an MNIST image dataset, a dataset of pancreatic cancer mutations, and a large set of electronic health records (EHR). Supplementary materials for this article are available online.

Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We present an alternative notion of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges. We demonstrate that edge-exchangeable models, unlike models that are traditionally vertex exchangeable, can exhibit sparsity. To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox (2015), models within our framework are stationary across steps of the graph sequence. In particular, our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure.

Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual network datasets continue to grow in size, it is necessary to develop models that accurately represent the real-life scaling properties of networks. One behavior of interest is having a power law in the degree distribution. However, other types of power laws that have been observed empirically and considered for applications such as clustering and feature allocation models have not been studied as frequently in models for graph data. In this paper, we enumerate desirable asymptotic behavior that may be of interest for modeling graph data, including sparsity and several types of power laws. We outline a general framework for graph generative models using completely random measures; by contrast to the pioneering work of Caron and Fox (2015), we consider instantiating more of the existing atoms of the random measure as the dataset size increases rather than adding new atoms to the measure. We see that these two models can be complementary; they respectively yield interpretations as (1) time passing among existing members of a network and (2) new individuals joining a network. We detail a particular instance of this framework and show simulated results that suggest this model exhibits some desirable asymptotic power-law behavior.

A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability for random graphs in contrast to the established notion of infinite exchangeability for random graphs --- which has traditionally relied on exchangeability of nodes (rather than edges) in a graph. We show that, unlike node exchangeability, edge exchangeability encompasses models that are known to provide a projective sequence of random graphs that circumvent the Aldous-Hoover Theorem and exhibit sparsity, i.e., sub-quadratic growth of the number of edges with the number of nodes. We show how edge-exchangeability of graphs relates naturally to existing notions of exchangeability from clustering (a.k.a. partitions) and other familiar combinatorial structures.