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Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been developed for this task, typically based either on universal data compression algorithms, or on statistical estimators of the underlying process distribution. In this work, we propose a fully-Bayesian approach for entropy estimation. Building on the recently introduced Bayesian Context Trees (BCT) framework for modelling discrete time series as variable-memory Markov chains, we show that it is possible to sample directly from the induced posterior on the entropy rate. This can be used to estimate the entire posterior distribution, providing much richer information than point estimates. We develop theoretical results for the posterior distribution of the entropy rate, including proofs of consistency and asymptotic normality. The practical utility of the method is illustrated on both simulated and real-world data, where it is found to outperform state-of-the-art alternatives.

Cell-free massive MIMO is emerging as a promising technology for future wireless communication systems, which is expected to offer uniform coverage and high spectral efficiency compared to classical cellular systems. We study in this paper how cell-free massive MIMO can support federated edge learning. Taking advantage of the additive nature of the wireless multiple access channel, over-the-air computation is exploited, where the clients send their local updates simultaneously over the same communication resource. This approach, known as over-the-air federated learning (OTA-FL), is proven to alleviate the communication overhead of federated learning over wireless networks. Considering channel correlation and only imperfect channel state information available at the central server, we propose a practical implementation of OTA-FL over cell-free massive MIMO. The convergence of the proposed implementation is studied analytically and experimentally, confirming the benefits of cell-free massive MIMO for OTA-FL.

Neural Architecture Search (NAS) for automatically finding the optimal network architecture has shown some success with competitive performances in various computer vision tasks. However, NAS in general requires a tremendous amount of computations. Thus reducing computational cost has emerged as an important issue. Most of the attempts so far has been based on manual approaches, and often the architectures developed from such efforts dwell in the balance of the network optimality and the search cost. Additionally, recent NAS methods for image restoration generally do not consider dynamic operations that may transform dimensions of feature maps because of the dimensionality mismatch in tensor calculations. This can greatly limit NAS in its search for optimal network structure. To address these issues, we re-frame the optimal search problem by focusing at component block level. From previous work, it's been shown that an effective denoising block can be connected in series to further improve the network performance. By focusing at block level, the search space of reinforcement learning becomes significantly smaller and evaluation process can be conducted more rapidly. In addition, we integrate an innovative dimension matching modules for dealing with spatial and channel-wise mismatch that may occur in the optimal design search. This allows much flexibility in optimal network search within the cell block. With these modules, then we employ reinforcement learning in search of an optimal image denoising network at a module level. Computational efficiency of our proposed Denoising Prior Neural Architecture Search (DPNAS) was demonstrated by having it complete an optimal architecture search for an image restoration task by just one day with a single GPU.

The unsupervised anomaly localization task faces the challenge of missing anomaly sample training, detecting multiple types of anomalies, and dealing with the proportion of the area of multiple anomalies. A separate teacher-student feature imitation network structure and a multi-scale processing strategy combining an image and feature pyramid are proposed to solve these problems. A network module importance search method based on gradient descent optimization is proposed to simplify the network structure. The experimental results show that the proposed algorithm performs better than the feature modeling anomaly localization method on the real industrial product detection dataset in the same period. The multi-scale strategy can effectively improve the effect compared with the benchmark method.

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial extension of the Bai-Silverstein theorem (BST) (2004). The latter has strongly influenced the development of high-dimensional statistics, especially in applications of random matrix theory to statistics. However, the assumption of uniform boundedness of the population covariance matrices has seriously limited the applications of the BST. The aim of this paper is to remove the barriers for the applications of the BST. The new CLT, allows spiked eigenvalues to exist, which may be bounded or tend to infinity. An important feature of our result is that the roles of either spiked eigenvalues or the bulk eigenvalues predominate in the CLT, depending on which variance is nonnegligible in the summation of the variances. The CLT for LSS is then applied to compare four linear hypothesis tests: The Wilk's likelihood ratio test, the Lawly-Hotelling trace test, the Bartlett-Nanda-Pillai trace test, and Roy's largest root test. We also derive and analyze their power function under particular alternatives.

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum likelihood estimator achieves the minimax lower bound. However, this optimization-based estimator is computationally intractable because the objective function is highly nonconvex and the feasible set involves discrete structures. To address the computational challenge, we propose a Bayesian approach to estimate high-dimensional Gaussian mixtures whose cluster centers exhibit sparsity using a continuous spike-and-slab prior. Posterior inference can be efficiently computed using an easy-to-implement Gibbs sampler. We further prove that the posterior contraction rate of the proposed Bayesian method is minimax optimal. The mis-clustering rate is obtained as a by-product using tools from matrix perturbation theory. The proposed Bayesian sparse Gaussian mixture model does not require pre-specifying the number of clusters, which can be adaptively estimated via the Gibbs sampler. The validity and usefulness of the proposed method is demonstrated through simulation studies and the analysis of a real-world single-cell RNA sequencing dataset.

We consider a sequential decision making task where we are not allowed to evaluate parameters that violate an a priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown constraint and allow evaluations only in regions that are safe with high probability. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. Moreover, the way in which they exploit regularity assumptions about the constraint introduces an additional critical hyperparameter. In this paper, we propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate. Our approach is naturally applicable to continuous domains and does not require additional hyperparameters. We theoretically analyze the method and show that we do not violate the safety constraint with high probability and that we explore by learning about the constraint up to arbitrary precision. Empirical evaluations demonstrate improved data-efficiency and scalability.

Efficient and accurate detection of subtle motion generated from small objects in noisy environments, as needed for vital sign monitoring, is challenging, but can be substantially improved with magnification. We developed a complex Gabor filter-based decomposition method to amplify phases at different spatial wavelength levels to magnify motion and extract 1D motion signals for fundamental frequency estimation. The phase-based complex Gabor filter outputs are processed and then used to train machine learning models that predict respiration and heart rate with greater accuracy. We show that our proposed technique performs better than the conventional temporal FFT-based method in clinical settings, such as sleep laboratories and emergency departments, as well for a variety of human postures.

Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

It is a common paradigm in object detection frameworks to treat all samples equally and target at maximizing the performance on average. In this work, we revisit this paradigm through a careful study on how different samples contribute to the overall performance measured in terms of mAP. Our study suggests that the samples in each mini-batch are neither independent nor equally important, and therefore a better classifier on average does not necessarily mean higher mAP. Motivated by this study, we propose the notion of Prime Samples, those that play a key role in driving the detection performance. We further develop a simple yet effective sampling and learning strategy called PrIme Sample Attention (PISA) that directs the focus of the training process towards such samples. Our experiments demonstrate that it is often more effective to focus on prime samples than hard samples when training a detector. Particularly, On the MSCOCO dataset, PISA outperforms the random sampling baseline and hard mining schemes, e.g. OHEM and Focal Loss, consistently by more than 1% on both single-stage and two-stage detectors, with a strong backbone ResNeXt-101.