5 research outputs found
Online Matrix Completion with Side Information
We give an online algorithm and prove novel mistake and regret bounds for
online binary matrix completion with side information. The mistake bounds we
prove are of the form . The term is
analogous to the usual margin term in SVM (perceptron) bounds. More
specifically, if we assume that there is some factorization of the underlying
matrix into where the rows of are interpreted
as "classifiers" in and the rows of as "instances" in
, then is the maximum (normalized) margin over all
factorizations consistent with the observed matrix. The
quasi-dimension term measures the quality of side information. In the
presence of vacuous side information, . However, if the side
information is predictive of the underlying factorization of the matrix, then
in an ideal case, where is the number of distinct row
factors and is the number of distinct column factors. We additionally
provide a generalization of our algorithm to the inductive setting. In this
setting, we provide an example where the side information is not directly
specified in advance. For this example, the quasi-dimension is now bounded
by
Annual Report 2017-2018
LETTER FROM THE DEAN
I am pleased to share with you the College of Computing and Digital Media’s (CDM) 2017-18 annual report, highlighting the many achievements across our community. It was a big year. We began offering five new programs (two bachelor’s, two master’s, and one PhD) across our three schools, in addition to several new certificate programs through our Institute for Professional Development. We built new, cutting-edge spaces to support these and other programs— most notably a 4,500 square-foot makerspace, a robotics and medical engineering lab, an augmented and virtual reality lab, and plans for a cyber-physical systems project lab. Our faculty continued to pursue their research and creative agendas, offering collaborative opportunities with students and partners. CDM students and alumni were celebrated for their many achievements— everything from leading the winning teams at the U.S. Cyber Challenge and Campus 1871 to showcasing their games at juried festivals and winning national screenwriting competitions. We encouraged greater research and teaching collaboration, both between our own schools and with units outside CDM. Design and Computing faculty are working together on an NSA grant for smart home devices that considers both software and interface/design, as well as a new grant-funded game lab. One Project Bluelight film team collaborated with The Theatre School and the School of Music while CDM and College of Science and Health faculty joined forces to research the links between traumatic brain injury, domestic violence, and deep games. It has been exciting and inspiring to witness the accomplishments of our innovative and dedicated community. We are proud to provide the space and resources for them to do their exceptional work.
David MillerDean, College of Computing and Digital Mediahttps://via.library.depaul.edu/cdmannual/1001/thumbnail.jp
Recommended from our members
Parameterized algorithms of fundamental NP-hard problems: a survey
Parameterized computation theory has developed rapidly over the last two decades. In theoretical computer science, it has attracted considerable attention for its theoretical value and significant guidance in many practical applications. We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems. All of these problems have been widely applied in various areas, such as Internet of Things, Wireless Sensor Networks, Artificial Intelligence, Bioinformatics, Big Data, and so on. In this paper, we are focused on the algorithms’ main idea and algorithmic techniques, and omit the details of them
Complexity of Combinatorial Matrix Completion With Diameter Constraints
We thoroughly study a novel and still basic combinatorial matrix completion
problem: Given a binary incomplete matrix, fill in the missing entries so that
the resulting matrix has a specified maximum diameter (that is, upper-bounding
the maximum Hamming distance between any two rows of the completed matrix) as
well as a specified minimum Hamming distance between any two of the matrix
rows. This scenario is closely related to consensus string problems as well as
to recently studied clustering problems on incomplete data.
We obtain an almost complete complexity dichotomy between polynomial-time
solvable and NP-hard cases in terms of the minimum distance lower bound and the
number of missing entries per row of the incomplete matrix. Further, we develop
polynomial-time algorithms for maximum diameter three, which are based on
Deza's theorem from extremal set theory. On the negative side we prove
NP-hardness for diameter at least four. For the parameter number of missing
entries per row, we show polynomial-time solvability when there is only one
missing entry and NP-hardness when there can be at least two missing entries.
In general, our algorithms heavily rely on Deza's theorem and the
correspondingly identified sunflower structures pave the way towards solutions
based on computing graph factors and solving 2-SAT instances
Parameterized Algorithms for the Matrix Completion Problem
We consider two matrix completion problems, in
which we are given a matrix with missing entries
and the task is to complete the matrix in a way
that (1) minimizes the rank, or (2) minimizes the
number of distinct rows. We study the parameterized
complexity of the two aforementioned
problems with respect to several parameters of interest,
including the minimum number of matrix
rows, columns, and rows plus columns needed to
cover all missing entries. We obtain new algorithmic
results showing that, for the bounded domain
case, both problems are fixed-parameter tractable
with respect to all aforementioned parameters. We
complement these results with a lower-bound result
for the unbounded domain case that rules out
fixed-parameter tractability w.r.t. some of the parameters
under consideration