11 research outputs found
On the Burer-Monteiro method for general semidefinite programs
Consider a semidefinite program (SDP) involving an positive
semidefinite matrix . The Burer-Monteiro method uses the substitution to obtain a nonconvex optimization problem in terms of an
matrix . Boumal et al. showed that this nonconvex method provably solves
equality-constrained SDPs with a generic cost matrix when , where is the number of constraints. In this note we extend
their result to arbitrary SDPs, possibly involving inequalities or multiple
semidefinite constraints. We derive similar guarantees for a fixed cost matrix
and generic constraints. We illustrate applications to matrix sensing and
integer quadratic minimization.Comment: 10 page
SDP Relaxation with Randomized Rounding for Energy Disaggregation
We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations randomized rounding, as well as a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results both in synthetic and real-world datasets demonstrate the superiority of our method
SDP Relaxation with Randomized Rounding for Energy Disaggregation
We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations randomized rounding, as well as a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results both in synthetic and real-world datasets demonstrate the superiority of our method
Approximation Bounds for Sparse Programs
We show that sparsity constrained optimization problems over low dimensional
spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to
derive both data-driven bounds on the duality gap, and an efficient
primalization procedure to recover feasible points satisfying these bounds.
These error bounds are proportional to the rate of growth of the objective with
the target cardinality, which means in particular that the relaxation is nearly
tight as soon as the target cardinality is large enough so that only
uninformative features are added
Structured Dictionary Learning for Energy Disaggregation
The increased awareness regarding the impact of energy consumption on the
environment has led to an increased focus on reducing energy consumption.
Feedback on the appliance level energy consumption can help in reducing the
energy demands of the consumers. Energy disaggregation techniques are used to
obtain the appliance level energy consumption from the aggregated energy
consumption of a house. These techniques extract the energy consumption of an
individual appliance as features and hence face the challenge of distinguishing
two similar energy consuming devices. To address this challenge we develop
methods that leverage the fact that some devices tend to operate concurrently
at specific operation modes. The aggregated energy consumption patterns of a
subgroup of devices allow us to identify the concurrent operating modes of
devices in the subgroup. Thus, we design hierarchical methods to replace the
task of overall energy disaggregation among the devices with a recursive
disaggregation task involving device subgroups. Experiments on two real-world
datasets show that our methods lead to improved performance as compared to
baseline. One of our approaches, Greedy based Device Decomposition Method
(GDDM) achieved up to 23.8%, 10% and 59.3% improvement in terms of
micro-averaged f score, macro-averaged f score and Normalized Disaggregation
Error (NDE), respectively.Comment: 10 Page
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
Photonics is the platform of choice to build a modular, easy-to-network
quantum computer operating at room temperature. However, no concrete
architecture has been presented so far that exploits both the advantages of
qubits encoded into states of light and the modern tools for their generation.
Here we propose such a design for a scalable and fault-tolerant photonic
quantum computer informed by the latest developments in theory and technology.
Central to our architecture is the generation and manipulation of
three-dimensional hybrid resource states comprising both bosonic qubits and
squeezed vacuum states. The proposal enables exploiting state-of-the-art
procedures for the non-deterministic generation of bosonic qubits combined with
the strengths of continuous-variable quantum computation, namely the
implementation of Clifford gates using easy-to-generate squeezed states.
Moreover, the architecture is based on two-dimensional integrated photonic
chips used to produce a qubit cluster state in one temporal and two spatial
dimensions. By reducing the experimental challenges as compared to existing
architectures and by enabling room-temperature quantum computation, our design
opens the door to scalable fabrication and operation, which may allow photonics
to leap-frog other platforms on the path to a quantum computer with millions of
qubits.Comment: 38 pages, many figures. Comments welcom