Stark C. Draper

Tharindu Adikari, Stark Draper

We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some average distortion constraint, and the reconstructions at two terminals must be identical with high probability. In this paper, we develop inner and outer bounds to the achievable rate distortion region of the CSR problem for a doubly symmetric binary source. We employ existing achievability results for Steinberg's common reconstruction and Wyner-Ziv's source coding with side information problems, and an achievability result for the lossy version of Korner-Marton's modulo-two sum computation problem.

Omid Vaheb, Sebastien Fabbro, Stark Draper

In astronomical imaging, the low photon count of exposures necessitates extensive post-processing steps, including contamination removal and denoising. This paper evaluates deep-learning denoising methods that can be trained without clean ground-truth images and assesses their utility for detection11 oriented analysis of astronomical data. We adapt and compare Noise2Noise, Stein's Unbiased Risk Estimator, and blind-spot-based methods using synthetic data and real observations from the Hubble Space Telescope (HST) and the Canada-France-Hawaii Telescope (CFHT). Performance is evaluated using object-detection metrics, including correct detection rate and false alarm rate, together with image-based metrics and pixel-distribution diagnostics. The results show that these methods can improve faint-source detectability relative to the original noisy images, with encouraging gains on HST data after domain-consistent initialization, while transfer to CFHT data is more limited, highlighting the importance of instrument/domain similarity for unsupervised adaptation.

Nafiseh Ghoroghchian, Rajasekhar Anguluri, Gautam Dasarathy et al.

We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average controllability of the fine-scale system can be well approximated by average controllability of the (synthesized, reduced-order) coarse-scale system. To this end, we require knowledge of some inherent parametric structure of the fine-scale network that makes this type of approximation possible. Therefore, we assume that the underlying fine-scale network is generated by the stochastic block model (SBM) -- often studied in community detection. We then provide an algorithm that directly estimates the average controllability of the fine-scale system using a coarse summary of SBM. Our analysis indicates the necessity of underlying structure (e.g., in-built communities) to be able to quantify accurately the controllability from coarsely characterized networked dynamics. We also compare our method to that of the reduced-order method and highlight the regimes where both can outperform each other. Finally, we provide simulations to confirm our theoretical results for different scalings of network size and density, and the parameter that captures how much community-structure is retained in the coarse summary.

Yuanxin Guo, Stark C. Draper, Wei Yu

This paper proposes modulo quantization (MQ) coding as a simple, structured, and low-complexity scheme for channels with primitive (i.e., noiseless digital) relay links and correlated Gaussian noises across terminals. The key component of MQ coding is the modulo quantization operation, which maps a real-valued symbol to its uniform-quantization index taken modulo a fixed integer. This operation allows effective exploitation of the common noise component shared across the terminals. For the Gaussian primitive relay channel with perfectly correlated noises, where a relay has a finite-capacity link to the receiver, MQ coding can be shown to achieve the capacity of this channel. For the Gaussian primitive diamond channel with perfectly correlated noises, where two relays can forward information through finite-capacity links to a receiver that has no direct observation of the transmitted signal, MQ coding yields novel achievability bounds that improve upon previously known bounds and coincide with the cut-set upper bound in certain signal-to-noise ratio (SNR) regimes. In scenarios with highly but non-perfectly correlated noises, MQ coding can approach the performance of compress-forward (CF) at significantly lower complexity, while surpassing decode-forward (DF) for the Gaussian primitive relay channel in certain SNR ranges. For the Gaussian primitive diamond channel with non-perfectly correlated noises, MQ can outperform both CF and DF at moderate SNR.

Shahrzad Kiani, Nupur Kulkarni, Adam Dziedzic et al.

Federated learning (FL) with differential privacy (DP) provides a framework for collaborative machine learning, enabling clients to train a shared model while adhering to strict privacy constraints. The framework allows each client to have an individual privacy guarantee, e.g., by adding different amounts of noise to each client's model updates. One underlying assumption is that all clients spend their privacy budgets uniformly over time (learning rounds). However, it has been shown in the literature that learning in early rounds typically focuses on more coarse-grained features that can be learned at lower signal-to-noise ratios while later rounds learn fine-grained features that benefit from higher signal-to-noise ratios. Building on this intuition, we propose a time-adaptive DP-FL framework that expends the privacy budget non-uniformly across both time and clients. Our framework enables each client to save privacy budget in early rounds so as to be able to spend more in later rounds when additional accuracy is beneficial in learning more fine-grained features. We theoretically prove utility improvements in the case that clients with stricter privacy budgets spend budgets unevenly across rounds, compared to clients with more relaxed budgets, who have sufficient budgets to distribute their spend more evenly. Our practical experiments on standard benchmark datasets support our theoretical results and show that, in practice, our algorithms improve the privacy-utility trade-offs compared to baseline schemes.

Shahrzad Kiani, Franziska Boenisch, Stark C. Draper

Federated Learning (FL) is the standard protocol for collaborative learning. In FL, multiple workers jointly train a shared model. They exchange model updates calculated on their data, while keeping the raw data itself local. Since workers naturally form groups based on common interests and privacy policies, we are motivated to extend standard FL to reflect a setting with multiple, potentially overlapping groups. In this setup where workers can belong and contribute to more than one group at a time, complexities arise in understanding privacy leakage and in adhering to privacy policies. To address the challenges, we propose differential private overlapping grouped learning (DPOGL), a novel method to implement privacy guarantees within overlapping groups. Under the honest-but-curious threat model, we derive novel privacy guarantees between arbitrary pairs of workers. These privacy guarantees describe and quantify two key effects of privacy leakage in DP-OGL: propagation delay, i.e., the fact that information from one group will leak to other groups only with temporal offset through the common workers and information degradation, i.e., the fact that noise addition over model updates limits information leakage between workers. Our experiments show that applying DP-OGL enhances utility while maintaining strong privacy compared to standard FL setups.

Tharindu Adikari, Stark Draper

We consider decentralized consensus optimization when workers sample data from non-identical distributions and perform variable amounts of work due to slow nodes known as stragglers. The problem of non-identical distributions and the problem of variable amount of work have been previously studied separately. In our work we analyze them together under a unified system model. We study the convergence of the optimization algorithm when combining worker outputs under two heuristic methods: (1) weighting equally, and (2) weighting by the amount of work completed by each. We prove convergence of the two methods under perfect consensus, assuming straggler statistics are independent and identical across all workers for all iterations. Our numerical results show that under approximate consensus the second method outperforms the first method for both convex and non-convex objective functions. We make use of the theory on minimum variance unbiased estimator (MVUE) to evaluate the existence of an optimal method for combining worker outputs. While we conclude that neither of the two heuristic methods are optimal, we also show that an optimal method does not exist.

Tharindu B. Adikari, Stark C. Draper

An increasing bottleneck in decentralized optimization is communication. Bigger models and growing datasets mean that decentralization of computation is important and that the amount of information exchanged is quickly growing. While compression techniques have been introduced to cope with the latter, none has considered leveraging the temporal correlations that exist in consecutive vector updates. An important example is distributed momentum-SGD where temporal correlation is enhanced by the low-pass-filtering effect of applying momentum. In this paper we design and analyze compression methods that exploit temporal correlation in systems both with and without error-feedback. Experiments with the ImageNet dataset demonstrate that our proposed methods offer significant reduction in the rate of communication at only a negligible increase in computation complexity. We further analyze the convergence of SGD when compression is applied with error-feedback. In the literature, convergence guarantees are developed only for compressors that provide error-bounds point-wise, i.e., for each input to the compressor. In contrast, many important codes (e.g. rate-distortion codes) provide error-bounds only in expectation and thus provide a more general guarantee. In this paper we prove the convergence of SGD under an expected error assumption by establishing a bound for the minimum gradient norm.

Sankalp Gilda, Stark C. Draper, Sebastien Fabbro et al.

We leverage state-of-the-art machine learning methods and a decade's worth of archival data from CFHT to predict observatory image quality (IQ) from environmental conditions and observatory operating parameters. Specifically, we develop accurate and interpretable models of the complex dependence between data features and observed IQ for CFHT's wide-field camera, MegaCam. Our contributions are several-fold. First, we collect, collate and reprocess several disparate data sets gathered by CFHT scientists. Second, we predict probability distribution functions (PDFs) of IQ and achieve a mean absolute error of $\sim0.07''$ for the predicted medians. Third, we explore the data-driven actuation of the 12 dome "vents" installed in 2013-14 to accelerate the flushing of hot air from the dome. We leverage epistemic and aleatoric uncertainties in conjunction with probabilistic generative modeling to identify candidate vent adjustments that are in-distribution (ID); for the optimal configuration for each ID sample, we predict the reduction in required observing time to achieve a fixed SNR. On average, the reduction is $\sim12\%$. Finally, we rank input features by their Shapley values to identify the most predictive variables for each observation. Our long-term goal is to construct reliable and real-time models that can forecast optimal observatory operating parameters to optimize IQ. We can then feed such forecasts into scheduling protocols and predictive maintenance routines. We anticipate that such approaches will become standard in automating observatory operations and maintenance by the time CFHT's successor, the Maunakea Spectroscopic Explorer, is installed in the next decade.

Nafiseh Ghoroghchian, Gautam Dasarathy, Stark C. Draper

We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at low-resolution, each measurement integrating across multiple graph nodes. Such low-resolution measurements effectively induce a coarse graph with its own communities. Our objective is to develop conditions on the graph structure, the quantity, and properties of measurements, under which we can recover the community organization in this coarse graph. In this paper, we build on the stochastic block model by mathematically formalizing the coarsening process, and characterizing its impact on the community members and connections. Through this novel setup and modeling, we characterize an error bound for community recovery. The error bound yields simple and closed-form asymptotic conditions to achieve the perfect recovery of the coarse graph communities.

Nuwan Ferdinand, Haider Al-Lawati, Stark C. Draper et al.

Distributed optimization is vital in solving large-scale machine learning problems. A widely-shared feature of distributed optimization techniques is the requirement that all nodes complete their assigned tasks in each computational epoch before the system can proceed to the next epoch. In such settings, slow nodes, called stragglers, can greatly slow progress. To mitigate the impact of stragglers, we propose an online distributed optimization method called Anytime Minibatch. In this approach, all nodes are given a fixed time to compute the gradients of as many data samples as possible. The result is a variable per-node minibatch size. Workers then get a fixed communication time to average their minibatch gradients via several rounds of consensus, which are then used to update primal variables via dual averaging. Anytime Minibatch prevents stragglers from holding up the system without wasting the work that stragglers can complete. We present a convergence analysis and analyze the wall time performance. Our numerical results show that our approach is up to 1.5 times faster in Amazon EC2 and it is up to five times faster when there is greater variability in compute node performance.

Tharindu Adikari, Stark C. Draper

We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large datasets. While boundary trees use an Euclidean measure of similarity, the Differentiable Boundary Tree algorithm by Zoran et al.(2017) was introduced to learn low-dimensional representations of complex input data, on which semantic similarity can be calculated to train boundary trees. As is pointed out by its authors, the differentiable boundary tree approach contains a few limitations that prevents it from scaling to large datasets. In this paper, we introduce Differentiable Boundary Sets, an algorithm that overcomes the computational issues of the differentiable boundary tree scheme and also improves its classification accuracy and data representability. Our algorithm is efficiently implementable with existing tools and offers a significant reduction in training time. We test and compare the algorithms on the well known MNIST handwritten digits dataset and the newer Fashion-MNIST dataset by Xiao et al.(2017).

Nuwan Ferdinand, Stark Draper

In this paper, we focus on approaches to parallelizing stochastic gradient descent (SGD) wherein data is farmed out to a set of workers, the results of which, after a number of updates, are then combined at a central master node. Although such synchronized SGD approaches parallelize well in idealized computing environments, they often fail to realize their promised computational acceleration in practical settings. One cause is slow workers, termed stragglers, who can cause the fusion step at the master node to stall, which greatly slowing convergence. In many straggler mitigation approaches work completed by these nodes, while only partial, is discarded completely. In this paper, we propose an approach to parallelizing synchronous SGD that exploits the work completed by all workers. The central idea is to fix the computation time of each worker and then to combine distinct contributions of all workers. We provide a convergence analysis and optimize the combination function. Our numerical results demonstrate an improvement of several factors of magnitude in comparison to existing methods.

Patrick Eschenfeldt, Dan Schmidt, Stark Draper et al.

We introduce a new type of graphical model that we call a "memory factor network" (MFN). We show how to use MFNs to model the structure inherent in many types of data sets. We also introduce an associated message-passing style algorithm called "proactive message passing"' (PMP) that performs inference on MFNs. PMP comes with convergence guarantees and is efficient in comparison to competing algorithms such as variants of belief propagation. We specialize MFNs and PMP to a number of distinct types of data (discrete, continuous, labelled) and inference problems (interpolation, hypothesis testing), provide examples, and discuss approaches for efficient implementation.

Tzu-Han Chou, Stark C. Draper, Akbar M. Sayeed

This paper investigates generation of a secret key from a reciprocal wireless channel. In particular we consider wireless channels that exhibit sparse structure in the wideband regime and the impact of the sparsity on the secret key capacity. We explore this problem in two steps. First, we study key generation from a state-dependent discrete memoryless multiple source. The state of source captures the effect of channel sparsity. Secondly, we consider a wireless channel model that captures channel sparsity and correlation between the legitimate users' channel and the eavesdropper's channel. Such dependency can significantly reduce the secret key capacity. According to system delay requirements, two performance measures are considered: (i) ergodic secret key capacity and (ii) outage probability. We show that in the wideband regime when a white sounding sequence is adopted, a sparser channel can achieve a higher ergodic secret key rate than a richer channel can. For outage performance, we show that if the users generate secret keys at a fraction of the ergodic capacity, the outage probability will decay exponentially in signal bandwidth. Moreover, a larger exponent is achieved by a richer channel.