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In this work, we have proposed augmented KRnets including both discrete and continuous models. One difficulty in flow-based generative modeling is to maintain the invertibility of the transport map, which is often a trade-off between effectiveness and robustness. The exact invertibility has been achieved in the real NVP using a specific pattern to exchange information between two separated groups of dimensions. KRnet has been developed to enhance the information exchange among data dimensions by incorporating the Knothe-Rosenblatt rearrangement into the structure of the transport map. Due to the maintenance of exact invertibility, a full nonlinear update of all data dimensions needs three iterations in KRnet. To alleviate this issue, we will add augmented dimensions that act as a channel for communications among the data dimensions. In the augmented KRnet, a fully nonlinear update is achieved in two iterations. We also show that the augmented KRnet can be reformulated as the discretization of a neural ODE, where the exact invertibility is kept such that the adjoint method can be formulated with respect to the discretized ODE to obtain the exact gradient. Numerical experiments have been implemented to demonstrate the effectiveness of our models.

In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal theory based methods such as maximum likelihood (ML) and normal theory based generalized least squares estimation (GLS) are unreliable. On the other hand, the asymptotically distribution free (ADF) estimator does not rely on any distribution assumption but cannot demonstrate its efficiency advantage with small and modest sample sizes. The methods which adopt misspecified loss functions including ridge GLS (RGLS) can provide better estimates and inferences than the normal theory based methods and the ADF estimator in some cases. We propose a distributionally-weighted least squares (DLS) estimator, and expect that it can perform better than the existing generalized least squares, because it combines normal theory based and ADF based generalized least squares estimation. Computer simulation results suggest that model-implied covariance based DLS (DLS_M) provided relatively accurate and efficient estimates in terms of RMSE. In addition, the empirical standard errors, the relative biases of standard error estimates, and the Type I error rates of the Jiang-Yuan rank adjusted model fit test statistic (T_JY) in DLS_M were competitive with the classical methods including ML, GLS, and RGLS. The performance of DLS_M depends on its tuning parameter a. We illustrate how to implement DLS_M and select the optimal a by a bootstrap procedure in a real data example.

This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e. where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e. optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in frequency-division duplex mode, such that CSIT is acquired via an explicit feedback of perfect CSIR. The capacity of the channel at hand is achieved by distributed linear precoding applied to Gaussian codes. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the number of transmit antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading.

Marine vehicles have been used for various scientific missions where information over features of interest is collected. In order to maximise efficiency in collecting information over a large search space, we should be able to deploy a large number of autonomous vehicles that make a decision based on the latest understanding of the target feature in the environment. In our previous work, we have presented a hierarchical framework for the multi-vessel multi-float (MVMF) problem where surface vessels drop and pick up underactuated floats in a time-minimal way. In this paper, we present the field trial results using the framework with a number of drifters and floats. We discovered a number of important aspects that need to be considered in the proposed framework, and present the potential approaches to address the challenges.

We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\ell_2$ estimation error for this problem is $O\left( \frac{s\log\left( {d}/{s}\right)}{n2^b}\right)$. Surprisingly, we show that when sample size $n$ exceeds a minimum threshold $n^*(s, d, b)$, we can achieve an $\ell_2$ estimation error of $O\left( \frac{s}{n2^b}\right)$. This implies that when $n>n^*(s, d, b)$ the convergence rate does not depend on the ambient dimension $d$ and is the same as knowing the support of the distribution beforehand. We next ask the question: ``what is the minimum $n^*(s, d, b)$ that allows dimension-free convergence?''. To upper bound $n^*(s, d, b)$, we develop novel localization schemes to accurately and efficiently localize the unknown support. For the non-interactive setting, we show that $n^*(s, d, b) = O\left( \min \left( {d^2\log^2 d}/{2^b}, {s^4\log^2 d}/{2^b}\right) \right)$. Moreover, we connect the problem with non-adaptive group testing and obtain a polynomial-time estimation scheme when $n = \tilde{\Omega}\left({s^4\log^4 d}/{2^b}\right)$. This group testing based scheme is adaptive to the sparsity parameter $s$, and hence can be applied without knowing it. For the interactive setting, we propose a novel tree-based estimation scheme and show that the minimum sample-size needed to achieve dimension-free convergence can be further reduced to $n^*(s, d, b) = \tilde{O}\left( {s^2\log^2 d}/{2^b} \right)$.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

Object detection is a fundamental and challenging problem in aerial and satellite image analysis. More recently, a two-stage detector Faster R-CNN is proposed and demonstrated to be a promising tool for object detection in optical remote sensing images, while the sparse and dense characteristic of objects in remote sensing images is complexity. It is unreasonable to treat all images with the same region proposal strategy, and this treatment limits the performance of two-stage detectors. In this paper, we propose a novel and effective approach, named deep adaptive proposal network (DAPNet), address this complexity characteristic of object by learning a new category prior network (CPN) on the basis of the existing Faster R-CNN architecture. Moreover, the candidate regions produced by DAPNet model are different from the traditional region proposal network (RPN), DAPNet predicts the detail category of each candidate region. And these candidate regions combine the object number, which generated by the category prior network to achieve a suitable number of candidate boxes for each image. These candidate boxes can satisfy detection tasks in sparse and dense scenes. The performance of the proposed framework has been evaluated on the challenging NWPU VHR-10 data set. Experimental results demonstrate the superiority of the proposed framework to the state-of-the-art.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.