Publications

@inproceedings{brofos_bias-variance_2019,
title = {A Bias-Variance Decomposition for Bayesian Deep Learning},
author = {James A Brofos and Rui Shu and Roy R Lederman},
year = {2019},
date = {2019-12-01},
pages = {14},
abstract = {We exhibit a decomposition of the Kullback-Leibler divergence into terms corresponding to bias, variance, and irreducible error. Our particular focus in this work is Bayesian deep learning and in this domain we illustrate the application of this decomposition to adversarial example identification, to image segmentation, and to malware detection. We empirically demonstrate qualitative similarities between the variance decomposition and mutual information.},
keywords = {Bayesian Deep Learning, Bayesian Inference, Deep Learning},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{boumal_heterogeneous_2018,
title = {Heterogeneous multireference alignment: A single pass approach},
author = {N Boumal and T Bendory and Roy R Lederman and A Singer},
doi = {10.1109/CISS.2018.8362313},
year = {2018},
date = {2018-01-01},
booktitle = {2018 52nd Annual Conference on Information Sciences and Systems (CISS)},
pages = {1--6},
abstract = {Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where K signals must be estimated, and each observation comes from one of those signals, unknown to us. This is a simplified model for the heterogeneity problem notably arising in cryo-electron microscopy. We propose an algorithm which estimates the K signals without estimating either the shifts or the classes of the observations. It requires only one pass over the data and is based on low-order moments that are invariant under cyclic shifts. Given sufficiently many measurements, one can estimate these invariant features averaged over the K signals. We then design a smooth, non-convex optimization problem to compute a set of signals which are consistent with the estimated averaged features. We find that, in many cases, the proposed approach estimates the set of signals accurately despite non-convexity, and conjecture the number of signals K that can be resolved as a function of the signal length L is on the order of √L.},
keywords = {bispectrum, concave programming, cryo-EM, cyclic shifts, Discrete Fourier transforms, estimation theory, expectation-maximization, Gaussian mixture models, heterogeneity, heterogeneous MRA, Heterogeneous multireference alignment, Multireference alignment, Noise measurement, non-convex optimization, nonconvex optimization problem, Optimization, Reliability, signal estimation, signal processing, Signal resolution, Signal to noise ratio, single pass approach, Standards},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{aldroubi_dynamical_2017,
title = {Dynamical sampling with random noise},
author = {Akram Aldroubi and L Huang and I Krishtal and Roy R Lederman},
doi = {10.1109/SAMPTA.2017.8024372},
year = {2017},
date = {2017-01-01},
booktitle = {2017 International Conference on Sampling Theory and Applications (SampTA)},
pages = {409--412},
abstract = {In this paper we consider a system of dynamical sampling, i.e. sampling a signal f that evolves in time under the action of an evolution operator A. We discuss the error in the recovery of the original signal when the samples are corrupted by additive, independent and identically distributed (i.i.d) noise. We focus on the study of the mean squared error E(∥ϵn∥22) between the original signal and the reconstructed signal obtained by solving a least squares problem. In the theoretical part, we give a formula for E(∥ϵn∥22) and prove that E(∥ϵn∥22) decreases as the number of the samples increases. In addition, we discuss several numerical experiments that verify the theoretical results.},
keywords = {Dynamical Sampling, evolution operator, signal reconstruction, signal recovery, signal sampling},
pubstate = {published},
tppubtype = {inproceedings}
}

@inproceedings{lederman_alternating_2015,
title = {Alternating diffusion for common manifold learning with application to sleep stage assessment},
author = {Roy R Lederman and Ronen Talmon and Hau-tieng Wu and Yu-Lun Lo and Ronald R Coifman},
doi = {10.1109/ICASSP.2015.7179075},
year = {2015},
date = {2015-01-01},
booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages = {5758--5762},
abstract = {In this paper, we address the problem of multimodal signal processing and present a manifold learning method to extract the common source of variability from multiple measurements. This method is based on alternating-diffusion and is particularly adapted to time series. We show that the common source of variability is extracted from multiple sensors as if it were the only source of variability, extracted by a standard manifold learning method from a single sensor, without the influence of the sensor-specific variables. In addition, we present application to sleep stage assessment. We demonstrate that, indeed, through alternating-diffusion, the sleep information hidden inside multimodal respiratory signals can be better captured compared to single-modal methods.},
note = {ISSN: 2379-190X},
keywords = {Alternating Diffusion, Common variable, diffusion maps, Kernel, learning (artificial intelligence), Manifolds, multimodal, multimodal respiratory signals, multimodal signal processing, Physiology, Sensitivity, Sensor phenomena and characterization, signal processing, sleep, sleep stage assessment, standard manifold learning method, time series},
pubstate = {published},
tppubtype = {inproceedings}
}