3 research outputs found
Analog Coding Frame-work
Analog coding is a low-complexity method to combat erasures, based on linear
redundancy in the signal space domain. Previous work examined "band-limited
discrete Fourier transform (DFT)" codes for Gaussian channels with erasures or
impulses. We extend this concept to source coding with "erasure
side-information" at the encoder and show that the performance of band-limited
DFT can be significantly improved using irregular spectrum, and more generally,
using equiangular tight frames (ETF). Frames are overcomplete bases and are
widely used in mathematics, computer science, engineering, and statistics since
they provide a stable and robust decomposition. Design of frames with favorable
properties of random subframes is motivated in variety of applications,
including code-devision multiple access (CDMA), compressed sensing and analog
coding. We present a novel relation between deterministic frames and random
matrix theory. We show empirically that the MANOVA ensemble offers a universal
description of the spectra of randomly selected subframes with constant aspect
ratios, taken from deterministic near-ETFs. Moreover, we derive an analytic
framework and bring a formal validation for some of the empirical results,
specifically that the asymptotic form for the moments of high orders of subsets
of ETF agree with that of MANOVA. Finally, when exploring over-complete bases,
the Welch bound is a lower bound on the root mean square cross correlation
between vectors. We extend the Welch bound to an erasure setting, in which a
reduced frame, composed of a random subset of Bernoulli selected vectors, is of
interest. The lower bound involves moment of the reduced frame, and it is tight
for ETFs and asymptotically coincides with the MANOVA moments. This result
offers a novel perspective on the superiority of ETFs over other frames
An ETF view of Dropout regularization
Dropout is a popular regularization technique in deep learning. Yet, the
reason for its success is still not fully understood. This paper provides a new
interpretation of Dropout from a frame theory perspective. By drawing a
connection to recent developments in analog channel coding, we suggest that for
a certain family of autoencoders with a linear encoder, optimizing the encoder
with dropout regularization leads to an equiangular tight frame (ETF). Since
this optimization is non-convex, we add another regularization that promotes
such structures by minimizing the cross-correlation between filters in the
network. We demonstrate its applicability in convolutional and fully connected
layers in both feed-forward and recurrent networks. All these results suggest
that there is indeed a relationship between dropout and ETF structure of the
regularized linear operations.Comment: Accepted to BMVC 202
Coding Method for Parallel Iterative Linear Solver
Computationally intensive distributed and parallel computing is often
bottlenecked by a small set of slow workers known as stragglers. In this paper,
we utilize the emerging idea of "coded computation" to design a novel
error-correcting-code inspired technique for solving linear inverse problems
under specific iterative methods in a parallelized implementation affected by
stragglers. Example applications include inverse problems in machine learning
on graphs, such as personalized PageRank and sampling on graphs. We provably
show that our coded-computation technique can reduce the mean-squared error
under a computational deadline constraint. In fact, the ratio of mean-squared
error of replication-based and coded techniques diverges to infinity as the
deadline increases. Our experiments for personalized PageRank performed on real
systems and real social networks show that this ratio can be as large as
. Further, unlike coded-computation techniques proposed thus far, our
strategy combines outputs of all workers, including the stragglers, to produce
more accurate estimates at the computational deadline. This also ensures that
the accuracy degrades "gracefully" in the event that the number of stragglers
is large.Comment: submitte