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On the Convergence of FedAvg on Non-IID Data
TLDR
This paper analyzes the convergence of Federated Averaging on non-iid data and establishes a convergence rate of $\mathcal{O}(\frac{1}{T})$ for strongly convex and smooth problems, where $T$ is the number of SGDs.
Distributed Power-law Graph Computing: Theoretical and Empirical Analysis
TLDR
A novel vertex-cut method, called degree-based hashing (DBH), is proposed, which makes effective use of the skewed degree distributions for GP and theoretically proves that DBH can achieve lower communication cost than existing methods and can simultaneously guarantee good workload balance.
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
TLDR
A more general error bound is established for the adaptive column/row sampling algorithm, based on which more accurate CUR and Nystrom algorithms with expected relative-error bounds are proposed.
Nonconvex Relaxation Approaches to Robust Matrix Recovery
TLDR
A nonconvex optimization model for handing the low-rank matrix recovery problem and an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA.
Support Matrix Machines
TLDR
This work proposes a new classification method that is defined as a hinge loss plus a so-called spectral elastic net penalty which is a spectral extension of the conventional elastic net over a matrix, and proposes an alternating direction method of multipliers (ADMM) algorithm for solving the problem.
Wishart Mechanism for Differentially Private Principal Components Analysis
TLDR
A new input perturbation mechanism for publishing a covariance matrix to achieve $(\epsilon,0)$-differential privacy and uses a Wishart distribution to generate matrix noise to apply this mechanism to principal component analysis.
Communication Efficient Decentralized Training with Multiple Local Updates
TLDR
This work analyzes the Periodic Decentralized Stochastic Gradient Descent algorithm, a straightforward combination of federated averaging and decentralized SGD, and proves that PD-SGD converges to a critical point.
CPSG-MCMC: Clustering-Based Preprocessing method for Stochastic Gradient MCMC
TLDR
An effective subsampling strategy to reduce the variance based on a failed attempt to do importance sampling by partitioning the dataset with k-means clustering algorithm in a preprocessing step and using the fixed clustering throughout the entire MCMC simulation.
Colorization by Matrix Completion
TLDR
This paper develops a robust colorization model and resorts to an augmented Lagrange multiplier algorithm for solving the model, based on the fact that a matrix can be represented as a low-rank matrix plus a sparse matrix.
Probabilistic Relational PCA
TLDR
By explicitly modeling covariance between instances as derived from the relational information, a novel probabilistic dimensionality reduction method is proposed, called Probabilistic relational PCA (PRPCA), for relational data analysis.
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