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We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schr\"odinger-F\"ollmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process $\{X_t\}_{t\in [0,1]}$ on $\mathbb{R}^d$, $d\in \mathbb{N}_0$. This latter process is constructed such that, starting at $X_0=0$, one has $X_1\sim \pi$. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, \cite{sf_orig,jiao} consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t.~$\pi$. We show that for this methodology to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, for arbitrary $\epsilon>0$, the associated cost is $\mathcal{O}(\epsilon^{-5})$. We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t.~$\pi$, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of $\mathcal{O}(\epsilon^2)$, the associated cost is, with high probability, $\mathcal{O}(\epsilon^{-2}|\log(\epsilon)|^{2+\delta})$, for any $\delta>0$. We implement our method on several examples including Bayesian inverse problems.

In the history of first-order algorithms, Nesterov's accelerated gradient descent (NAG) is one of the milestones. However, the cause of the acceleration has been a mystery for a long time. It has not been revealed with the existence of gradient correction until the high-resolution differential equation framework proposed in [Shi et al., 2021]. In this paper, we continue to investigate the acceleration phenomenon. First, we provide a significantly simplified proof based on precise observation and a tighter inequality for $L$-smooth functions. Then, a new implicit-velocity high-resolution differential equation framework, as well as the corresponding implicit-velocity version of phase-space representation and Lyapunov function, is proposed to investigate the convergence behavior of the iterative sequence $\{x_k\}_{k=0}^{\infty}$ of NAG. Furthermore, from two kinds of phase-space representations, we find that the role played by gradient correction is equivalent to that by velocity included implicitly in the gradient, where the only difference comes from the iterative sequence $\{y_{k}\}_{k=0}^{\infty}$ replaced by $\{x_k\}_{k=0}^{\infty}$. Finally, for the open question of whether the gradient norm minimization of NAG has a faster rate $o(1/k^3)$, we figure out a positive answer with its proof. Meanwhile, a faster rate of objective value minimization $o(1/k^2)$ is shown for the case $r > 2$.

This paper deals with the grouped variable selection problem. A widely used strategy is to augment the negative log-likelihood function with a sparsity-promoting penalty. Existing methods include the group Lasso, group SCAD, and group MCP. The group Lasso solves a convex optimization problem but is plagued by underestimation bias. The group SCAD and group MCP avoid this estimation bias but require solving a nonconvex optimization problem that may be plagued by suboptimal local optima. In this work, we propose an alternative method based on the generalized minimax concave (GMC) penalty, which is a folded concave penalty that maintains the convexity of the objective function. We develop a new method for grouped variable selection in linear regression, the group GMC, that generalizes the strategy of the original GMC estimator. We present an efficient algorithm for computing the group GMC estimator and also prove properties of the solution path to guide its numerical computation and tuning parameter selection in practice. We establish error bounds for both the group GMC and original GMC estimators. A rich set of simulation studies and a real data application indicate that the proposed group GMC approach outperforms existing methods in several different aspects under a wide array of scenarios.

Removing background noise from speech audio has been the subject of considerable effort, especially in recent years due to the rise of virtual communication and amateur recordings. Yet background noise is not the only unpleasant disturbance that can prevent intelligibility: reverb, clipping, codec artifacts, problematic equalization, limited bandwidth, or inconsistent loudness are equally disturbing and ubiquitous. In this work, we propose to consider the task of speech enhancement as a holistic endeavor, and present a universal speech enhancement system that tackles 55 different distortions at the same time. Our approach consists of a generative model that employs score-based diffusion, together with a multi-resolution conditioning network that performs enhancement with mixture density networks. We show that this approach significantly outperforms the state of the art in a subjective test performed by expert listeners. We also show that it achieves competitive objective scores with just 4-8 diffusion steps, despite not considering any particular strategy for fast sampling. We hope that both our methodology and technical contributions encourage researchers and practitioners to adopt a universal approach to speech enhancement, possibly framing it as a generative task.

Most of the existing semantic segmentation approaches with image-level class labels as supervision, highly rely on the initial class activation map (CAM) generated from the standard classification network. In this paper, a novel "Progressive Patch Learning" approach is proposed to improve the local details extraction of the classification, producing the CAM better covering the whole object rather than only the most discriminative regions as in CAMs obtained in conventional classification models. "Patch Learning" destructs the feature maps into patches and independently processes each local patch in parallel before the final aggregation. Such a mechanism enforces the network to find weak information from the scattered discriminative local parts, achieving enhanced local details sensitivity. "Progressive Patch Learning" further extends the feature destruction and patch learning to multi-level granularities in a progressive manner. Cooperating with a multi-stage optimization strategy, such a "Progressive Patch Learning" mechanism implicitly provides the model with the feature extraction ability across different locality-granularities. As an alternative to the implicit multi-granularity progressive fusion approach, we additionally propose an explicit method to simultaneously fuse features from different granularities in a single model, further enhancing the CAM quality on the full object coverage. Our proposed method achieves outstanding performance on the PASCAL VOC 2012 dataset e.g., with 69.6$% mIoU on the test set), which surpasses most existing weakly supervised semantic segmentation methods. Code will be made publicly available here //github.com/TyroneLi/PPL_WSSS.

Federated learning (FL) is one of the most appealing alternatives to the standard centralized learning paradigm, allowing heterogeneous set of devices to train a machine learning model without sharing their raw data. However, FL requires a central server to coordinate the learning process, thus introducing potential scalability and security issues. In the literature, server-less FL approaches like gossip federated learning (GFL) and blockchain-enabled federated learning (BFL) have been proposed to mitigate these issues. In this work, we propose a complete overview of these three techniques proposing a comparison according to an integral set of performance indicators, including model accuracy, time complexity, communication overhead, convergence time and energy consumption. An extensive simulation campaign permits to draw a quantitative analysis. In particular, GFL is able to save the 18% of training time, the 68% of energy and the 51% of data to be shared with respect to the CFL solution, but it is not able to reach the level of accuracy of CFL. On the other hand, BFL represents a viable solution for implementing decentralized learning with a higher level of security, at the cost of an extra energy usage and data sharing. Finally, we identify open issues on the two decentralized federated learning implementations and provide insights on potential extensions and possible research directions on this new research field.

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

State-of-the-art recommendation algorithms -- especially the collaborative filtering (CF) based approaches with shallow or deep models -- usually work with various unstructured information sources for recommendation, such as textual reviews, visual images, and various implicit or explicit feedbacks. Though structured knowledge bases were considered in content-based approaches, they have been largely neglected recently due to the availability of vast amount of data, and the learning power of many complex models. However, structured knowledge bases exhibit unique advantages in personalized recommendation systems. When the explicit knowledge about users and items is considered for recommendation, the system could provide highly customized recommendations based on users' historical behaviors. A great challenge for using knowledge bases for recommendation is how to integrated large-scale structured and unstructured data, while taking advantage of collaborative filtering for highly accurate performance. Recent achievements on knowledge base embedding sheds light on this problem, which makes it possible to learn user and item representations while preserving the structure of their relationship with external knowledge. In this work, we propose to reason over knowledge base embeddings for personalized recommendation. Specifically, we propose a knowledge base representation learning approach to embed heterogeneous entities for recommendation. Experimental results on real-world dataset verified the superior performance of our approach compared with state-of-the-art baselines.