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The FedProx algorithm is a simple yet powerful distributed proximal point optimization method widely used for federated learning (FL) over heterogeneous data. Despite its popularity and remarkable success witnessed in practice, the theoretical understanding of FedProx is largely underinvestigated: the appealing convergence behavior of FedProx is so far characterized under certain non-standard and unrealistic dissimilarity assumptions of local functions, and the results are limited to smooth optimization problems. In order to remedy these deficiencies, we develop a novel local dissimilarity invariant convergence theory for FedProx and its minibatch stochastic extension through the lens of algorithmic stability. As a result, we contribute to derive several new and deeper insights into FedProx for non-convex federated optimization including: 1) convergence guarantees independent on local dissimilarity type conditions; 2) convergence guarantees for non-smooth FL problems; and 3) linear speedup with respect to size of minibatch and number of sampled devices. Our theory for the first time reveals that local dissimilarity and smoothness are not must-have for FedProx to get favorable complexity bounds. Preliminary experimental results on a series of benchmark FL datasets are reported to demonstrate the benefit of minibatching for improving the sample efficiency of FedProx.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Wireless sensor networks are among the most promising technologies of the current era because of their small size, lower cost, and ease of deployment. With the increasing number of wireless sensors, the probability of generating missing data also rises. This incomplete data could lead to disastrous consequences if used for decision-making. There is rich literature dealing with this problem. However, most approaches show performance degradation when a sizable amount of data is lost. Inspired by the emerging field of graph signal processing, this paper performs a new study of a Sobolev reconstruction algorithm in wireless sensor networks. Experimental comparisons on several publicly available datasets demonstrate that the algorithm surpasses multiple state-of-the-art techniques by a maximum margin of 54%. We further show that this algorithm consistently retrieves the missing data even during massive data loss situations.

Nowadays, the environments of smart systems for Industry 4.0 and Internet of Things (IoT) are experiencing fast industrial upgrading. Big data technologies such as design making, event detection, and classification are developed to help manufacturing organizations to achieve smart systems. By applying data analysis, the potential values of rich data can be maximized and thus help manufacturing organizations to finish another round of upgrading. In this paper, we propose two new algorithms with respect to big data analysis, namely UFC$_{gen}$ and UFC$_{fast}$. Both algorithms are designed to collect three types of patterns to help people determine the market positions for different product combinations. We compare these algorithms on various types of datasets, both real and synthetic. The experimental results show that both algorithms can successfully achieve pattern classification by utilizing three different types of interesting patterns from all candidate patterns based on user-specified thresholds of utility and frequency. Furthermore, the list-based UFC$_{fast}$ algorithm outperforms the level-wise-based UFC$_{gen}$ algorithm in terms of both execution time and memory consumption.

This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear coupling between the large angle flapping motion and the quasi-steady aerodynamics. Then, it is transformed into a feedback control system according to the framework of imitation learning. In particular, an additional constraint is incorporated through the learning process to enhance the stability properties of the resulting controlled dynamics. Compared with conventional methods, the proposed constrained imitation learning eliminates the need to generate additional optimal trajectories on-line, without sacrificing stability. As such, the computational efficiency is substantially improved. Furthermore, this establishes the first nonlinear control system that stabilizes the coupled longitudinal and lateral dynamics of flapping wing aerial vehicle without relying on averaging or linearization. These are illustrated by numerical examples for a simulated model inspired by Monarch butterflies.

The future where the industrial shop-floors witness humans and robots working in unison and the domestic households becoming a shared space for both these agents is not very far. The scientific community has been accelerating towards that future by extending their research efforts in human-robot interaction towards human-robot collaboration. It is possible that the anthropomorphic nature of the humanoid robots could deem the most suitable for such collaborations in semi-structured, human-centered environments. Wearable sensing technologies for human agents and efficient human-aware control strategies for the humanoid robot will be key in achieving a seamless human-humanoid collaboration. This is where reliable state estimation strategies become crucial in making sense of the information coming from multiple distributed sensors attached to the human and those on the robot to augment the feedback controllers designed for the humanoid robot to aid their human counterparts. In this context, this thesis investigates the theory of Lie groups for designing state estimation techniques aimed towards humanoid locomotion and human motion estimation. [continued]

We propose a co-variance corrected random batch method for interacting particle systems. By establishing a certain entropic central limit theorem, we provide entropic convergence guarantees for the law of the entire trajectories of all particles of the proposed method to the law of the trajectories of the discrete time interacting particle system whenever the batch size $B \gg (\alpha n)^{\frac{1}{3}}$ (where $n$ is the number of particles and $\alpha$ is the time discretization parameter). This in turn implies that the outputs of these methods are nearly \emph{statistically indistinguishable} when $B$ is even moderately large. Previous works mainly considered convergence in Wasserstein distance with required stringent assumptions on the potentials or the bounds had an exponential dependence on the time horizon. This work makes minimal assumptions on the interaction potentials and in particular establishes that even when the particle trajectories diverge to infinity, they do so in the same way for both the methods. Such guarantees are very useful in light of the recent advances in interacting particle based algorithms for sampling.

End-to-End (E2E) network slicing enables wireless networks to provide diverse services on a common infrastructure. Each E2E slice, including resources of radio access network (RAN) and core network, is rented to mobile virtual network operators (MVNOs) to provide a specific service to end-users. RAN slicing, which is realized through wireless network virtualization, involves sharing the frequency spectrum and base station antennas in RAN. Similarly, in core slicing, which is achieved by network function virtualization, data center resources such as commodity servers and physical links are shared between users of different MVNOs. In this paper, we study E2E slicing with the aim of minimizing the total energy consumption. The stated optimization problem is non-convex that is solved by a sub-optimal algorithm proposed here. The simulation results show that our proposed joint power control, server and link allocation (JPSLA) algorithm achieves 30% improvement compared to the disjoint scheme, where RAN and core are sliced separately.

A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.