This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client drift--is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms

Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering sparse vectors from linear measurements. A well-known analysis of Tropp and Gilbert shows that OMP can recover a k-sparse n-dimensional real vector from m 4k log(n) noise-free random linear measurements with a probability that goes to one as n goes to infinity. This work shows strengthens this result by showing that a lower number of measurements, m 2k log(n-k), is in fact sufficient for asymptotic recovery. Moreover, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m 2k log(n-k) exactly matches the number of measurements required by the more complex lasso for signal recovery.

AI has played a role in overcoming COVID especially in drug discovery and other related areas in fighting the pandemic. AI investment in drug design and drug discovery has increased significantly The percentage of graduates undertaking a PhD in AI has increased There is a big uptake in generative AI in the ability to compose text, audio, and images to a sufficiently high standard that humans have a hard time telling the difference between synthetic and non-synthetic outputs for some constrained applications of the technology. AI has a diversity challenge China overtakes the US in AI journal citations After surpassing the US in the total number of journal publications several years ago, China now also leads in journal citations; however, the US has consistently (and significantly) more AI conference papers (which are also more heavily cited) than China over the last decade. Surveillance technologies are fast, cheap, and increasingly ubiquitous The technologies necessary for large-scale surveillance are rapidly maturing, with techniques for image classification, face recognition, video analysis, and voice identification all seeing significant progress in 2020. AI ethics lacks benchmarks and consensus Though a number of groups are producing a range of qualitative or normative outputs in the AI ethics domain, the field generally lacks benchmarks that can be used to measure or assess the relationship between broader societal discussions about technology development and the development of the technology itself.

A new analysis of code-sharing platform GitHub has shown that India has eclipsed even the US when it comes to writing AI code. The new analysis conducted by the OECD of data from Microsoft-owned code-sharing platform GitHub reveals another contender in the AI race: India, which has succeeded in equipping its vast technology talent base with AI skills. The data is gathered from public AI-related code repositories or repos that are hosted on the platform. Examining the location from where contributions, or'commits', to these AI repos are made reveals that in 2019, India overtook the US as the principal source of AI-related code. In 2020, it accounted for 30% of all commits, double the US figure.

A new analysis of the upper body of famed fossil'Little Foot,' a near-complete skeleton of a hominin that lived 3.67 million years ago, reveals she was a creature adapted to living in trees. Scientists at the University of Southern California (USC) examined Little Foot's shoulder assembly, showing it supported arms well suited for hanging from branches and moving up and down trees – similar to that of apes. The latest analysis'provides the best evidence yet of how human ancestors used their arms more than 3 million years ago,' said Kristian J. Carlson, lead author of the study. The findings also suggests the structural similarities in the shoulder between humans and African apes are much more recent, and persisted much longer, than previously believed. A new analysis of the upper body of famed fossil'Little Foot,' a near-complete skeleton of a hominin that lived 3.67 million years ago, reveals she was a creature adapted to living in trees Little Foot was discovered in South Africa in 1994 and has allowed scientists to travel back in time to learn more about the evolution of humans.

Virtually all state-of-the-art methods for training supervised machine learning models are variants of SGD enhanced with a number of additional tricks, such as minibatching, momentum, and adaptive stepsizes. One of the tricks that works so well in practice that it is used as default in virtually all widely used machine learning software is {\em random reshuffling (RR)}. However, the practical benefits of RR have until very recently been eluding attempts at being satisfactorily explained using theory. Motivated by recent development due to Mishchenko, Khaled and Richt\'{a}rik (2020), in this work we provide the first analysis of SVRG under Random Reshuffling (RR-SVRG) for general finite-sum problems. First, we show that RR-SVRG converges linearly with the rate $\mathcal{O}(\kappa^{3/2})$ in the strongly-convex case, and can be improved further to $\mathcal{O}(\kappa)$ in the big data regime (when $n > \mathcal{O}(\kappa)$), where $\kappa$ is the condition number. This improves upon the previous best rate $\mathcal{O}(\kappa^2)$ known for a variance reduced RR method in the strongly-convex case due to Ying, Yuan and Sayed (2020). Second, we obtain the first sublinear rate for general convex problems. Third, we establish similar fast rates for Cyclic-SVRG and Shuffle-Once-SVRG. Finally, we develop and analyze a more general variance reduction scheme for RR, which allows for less frequent updates of the control variate. We corroborate our theoretical results with suitably chosen experiments on synthetic and real datasets.

Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering sparse vectors from linear measurements. A well-known analysis of Tropp and Gilbert shows that OMP can recover a k-sparse n-dimensional real vector from m 4k log(n) noise-free random linear measurements with a probability that goes to one as n goes to infinity. This work shows strengthens this result by showing that a lower number of measurements, m 2k log(n-k), is in fact sufficient for asymptotic recovery. Moreover, this number of measurements is also sufficient for detection of the sparsity pattern (support) of the vector with measurement errors provided the signal-to-noise ratio (SNR) scales to infinity. The scaling m 2k log(n-k) exactly matches the number of measurements required by the more complex lasso for signal recovery.