Pranava Singhal

Pranava Singhal, Waqar Mirza, Ajit Rajwade et al.

In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works have used such a decomposition to estimate the joint density from lower-dimensional marginals, which can be estimated more reliably with the same number of samples. We combine two key ideas: dictionaries to represent 1-D densities, and random projections to estimate the joint distribution from 1-D marginals, explored separately in prior work. Our algorithm benefits from improved sample complexity over the previous dictionary-based approach by using 1-D marginals for reconstruction. We evaluate the performance of our method on estimating synthetic probability densities and compare it with the previous dictionary-based approach and Gaussian Mixture Models (GMMs). Our algorithm outperforms these other approaches in all the experimental settings.

Pranava Singhal, Shashi Raj Pandey, Petar Popovski

The standard client selection algorithms for Federated Learning (FL) are often unbiased and involve uniform random sampling of clients. This has been proven sub-optimal for fast convergence under practical settings characterized by significant heterogeneity in data distribution, computing, and communication resources across clients. For applications having timing constraints due to limited communication opportunities with the parameter server (PS), the client selection strategy is critical to complete model training within the fixed budget of communication rounds. To address this, we develop a biased client selection strategy, GreedyFed, that identifies and greedily selects the most contributing clients in each communication round. This method builds on a fast approximation algorithm for the Shapley Value at the PS, making the computation tractable for real-world applications with many clients. Compared to various client selection strategies on several real-world datasets, GreedyFed demonstrates fast and stable convergence with high accuracy under timing constraints and when imposing a higher degree of heterogeneity in data distribution, systems constraints, and privacy requirements.