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This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which depends on the information from its neighbors. The interconnection structure among the agents is described by a time-varying directed graph. While the convergence of consensus-based stochastic approximation algorithms when the interconnection among the agents is described by doubly stochastic matrices (at least in expectation) has been studied, less is known about the case when the interconnection matrix is simply stochastic. For any uniformly strongly connected graph sequences whose associated interaction matrices are stochastic, the paper derives finite-time bounds on the mean-square error, defined as the deviation of the output of the algorithm from the unique equilibrium point of the associated ordinary differential equation. For the case of interconnection matrices being stochastic, the equilibrium point can be any unspecified convex combination of the local equilibria of all the agents in the absence of communication. Both the cases with constant and time-varying step-sizes are considered. In the case when the convex combination is required to be a straight average and interaction between any pair of neighboring agents may be uni-directional, so that doubly stochastic matrices cannot be implemented in a distributed manner, the paper proposes a push-sum-type distributed stochastic approximation algorithm and provides its finite-time bound for the time-varying step-size case by leveraging the analysis for the consensus-type algorithm with stochastic matrices and developing novel properties of the push-sum algorithm.

We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally stationary segments and then compute a distance matrix between segment distributions. The segments are clustered into a learned number of discrete volatility regimes via an optimization routine. Using this framework, we determine a volatility clustering structure for financial indices, large-cap equities, exchange-traded funds and currency pairs. Our method overcomes the rigid assumptions necessary to implement many parametric regime-switching models, while effectively distilling a time series into several characteristic behaviours. Our results provide significant simplification of these time series and a strong descriptive analysis of prior behaviours of volatility. Finally, we create and validate a dynamic trading strategy that learns the optimal match between the current distribution of a time series and its past regimes, thereby making online risk-avoidance decisions in the present.

Reconfigurable intelligent surfaces (RISs) represent a promising candidate for sixth-generation (6G) wireless networks, as the RIS technology provides a new solution to control the propagation channel in order to improve the efficiency of a wireless link through enhancing the received signal power. In this paper, we propose RIS-assisted receive quadrature space-shift keying (RIS-RQSSK), which enhances the spectral efficiency of an RIS-based index modulation (IM) system by using the real and imaginary dimensions independently for the purpose of IM. Therefore, the error rate performance of the system is improved as all RIS elements reflect the incident transmit signal toward both selected receive antennas. At the receiver, a low-complexity but effective greedy detector (GD) can be employed which determines the maximum energy per dimension at the receive antennas. A max-min optimization problem is defined to maximize the received signal-to-noise ratio (SNR) components at both selected receive antennas; an analytical solution is provided based on Lagrange duality. In particular, the multi-variable optimization problem is shown to reduce to the solution of a single-variable equation, which results in a very simple design procedure. In addition, we investigate the average bit error probability (ABEP) of the proposed RIS-RQSSK system and derive a closed-form approximate upper bound on the ABEP. We also provide extensive numerical simulations to validate our derivations. Numerical results show that the proposed RIS-RQSSK scheme substantially outperforms recent prominent benchmark schemes. This enhancement considerably increases with an increasing number of receive antennas.

Heatmap-based methods dominate in the field of human pose estimation by modelling the output distribution through likelihood heatmaps. In contrast, regression-based methods are more efficient but suffer from inferior performance. In this work, we explore maximum likelihood estimation (MLE) to develop an efficient and effective regression-based methods. From the perspective of MLE, adopting different regression losses is making different assumptions about the output density function. A density function closer to the true distribution leads to a better regression performance. In light of this, we propose a novel regression paradigm with Residual Log-likelihood Estimation (RLE) to capture the underlying output distribution. Concretely, RLE learns the change of the distribution instead of the unreferenced underlying distribution to facilitate the training process. With the proposed reparameterization design, our method is compatible with off-the-shelf flow models. The proposed method is effective, efficient and flexible. We show its potential in various human pose estimation tasks with comprehensive experiments. Compared to the conventional regression paradigm, regression with RLE bring 12.4 mAP improvement on MSCOCO without any test-time overhead. Moreover, for the first time, especially on multi-person pose estimation, our regression method is superior to the heatmap-based methods. Our code is available at //github.com/Jeff-sjtu/res-loglikelihood-regression

Attention-based neural networks have achieved state-of-the-art results on a wide range of tasks. Most such models use deterministic attention while stochastic attention is less explored due to the optimization difficulties or complicated model design. This paper introduces Bayesian attention belief networks, which construct a decoder network by modeling unnormalized attention weights with a hierarchy of gamma distributions, and an encoder network by stacking Weibull distributions with a deterministic-upward-stochastic-downward structure to approximate the posterior. The resulting auto-encoding networks can be optimized in a differentiable way with a variational lower bound. It is simple to convert any models with deterministic attention, including pretrained ones, to the proposed Bayesian attention belief networks. On a variety of language understanding tasks, we show that our method outperforms deterministic attention and state-of-the-art stochastic attention in accuracy, uncertainty estimation, generalization across domains, and robustness to adversarial attacks. We further demonstrate the general applicability of our method on neural machine translation and visual question answering, showing great potential of incorporating our method into various attention-related tasks.

We investigate how the final parameters found by stochastic gradient descent are influenced by over-parameterization. We generate families of models by increasing the number of channels in a base network, and then perform a large hyper-parameter search to study how the test error depends on learning rate, batch size, and network width. We find that the optimal SGD hyper-parameters are determined by a "normalized noise scale," which is a function of the batch size, learning rate, and initialization conditions. In the absence of batch normalization, the optimal normalized noise scale is directly proportional to width. Wider networks, with their higher optimal noise scale, also achieve higher test accuracy. These observations hold for MLPs, ConvNets, and ResNets, and for two different parameterization schemes ("Standard" and "NTK"). We observe a similar trend with batch normalization for ResNets. Surprisingly, since the largest stable learning rate is bounded, the largest batch size consistent with the optimal normalized noise scale decreases as the width increases.

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.

The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two of the most famous variational models in image segmentation and image restoration, respectively. They have ubiquitous applications in image processing. In this paper, we explore the linkage between these two important models. We prove that for two-phase segmentation problem the optimal solution of the PCMS model can be obtained by thresholding the minimizer of the ROF model. This linkage is still valid for multiphase segmentation under mild assumptions. Thus it opens a new segmentation paradigm: image segmentation can be done via image restoration plus thresholding. This new paradigm, which circumvents the innate non-convex property of the PCMS model, therefore improves the segmentation performance in both efficiency (much faster than state-of-the-art methods based on PCMS model, particularly when the phase number is high) and effectiveness (producing segmentation results with better quality) due to the flexibility of the ROF model in tackling degraded images, such as noisy images, blurry images or images with information loss. As a by-product of the new paradigm, we derive a novel segmentation method, coined thresholded-ROF (T-ROF) method, to illustrate the virtue of manipulating image segmentation through image restoration techniques. The convergence of the T-ROF method under certain conditions is proved, and elaborate experimental results and comparisons are presented.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.