1,037 research outputs found
The Necessary And Sufficient Condition for Generalized Demixing
Demixing is the problem of identifying multiple structured signals from a
superimposed observation. This work analyzes a general framework, based on
convex optimization, for solving demixing problems. We present a new solution
to determine whether or not a specific convex optimization problem built for
generalized demixing is successful. This solution will also bring about the
possibility to estimate the probability of success by the approximate kinematic
formula
Decontamination of Mutual Contamination Models
Many machine learning problems can be characterized by mutual contamination
models. In these problems, one observes several random samples from different
convex combinations of a set of unknown base distributions and the goal is to
infer these base distributions. This paper considers the general setting where
the base distributions are defined on arbitrary probability spaces. We examine
three popular machine learning problems that arise in this general setting:
multiclass classification with label noise, demixing of mixed membership
models, and classification with partial labels. In each case, we give
sufficient conditions for identifiability and present algorithms for the
infinite and finite sample settings, with associated performance guarantees.Comment: Published in JMLR. Subsumes arXiv:1602.0623
Blind Demixing for Low-Latency Communication
In the next generation wireless networks, lowlatency communication is
critical to support emerging diversified applications, e.g., Tactile Internet
and Virtual Reality. In this paper, a novel blind demixing approach is
developed to reduce the channel signaling overhead, thereby supporting
low-latency communication. Specifically, we develop a low-rank approach to
recover the original information only based on a single observed vector without
any channel estimation. Unfortunately, this problem turns out to be a highly
intractable non-convex optimization problem due to the multiple non-convex
rankone constraints. To address the unique challenges, the quotient manifold
geometry of product of complex asymmetric rankone matrices is exploited by
equivalently reformulating original complex asymmetric matrices to the
Hermitian positive semidefinite matrices. We further generalize the geometric
concepts of the complex product manifolds via element-wise extension of the
geometric concepts of the individual manifolds. A scalable Riemannian
trust-region algorithm is then developed to solve the blind demixing problem
efficiently with fast convergence rates and low iteration cost. Numerical
results will demonstrate the algorithmic advantages and admirable performance
of the proposed algorithm compared with the state-of-art methods.Comment: 14 pages, accepted by IEEE Transaction on Wireless Communicatio
Equilibrium properties of highly asymmetric star-polymer mixtures
We employ effective interaction potentials to study the equilibrium structure
and phase behavior of highly asymmetric mixtures of star polymers. We consider
in particular the influence of the addition of a component with a small number
of arms and a small size on a concentrated solution of large stars with a high
functionality. By employing liquid integral equation theories we examine the
evolution of the correlation functions of the big stars upon addition of the
small ones, finding a loss of structure that can be attributed to a weakening
of the repulsions between the large stars due to the presence of the small
ones. We analyze this phenomenon be means of a generalized depletion mechanism
which is supported by computer simulations. By applying thermodynamic
perturbation theory we draw the phase diagram of the asymmetric mixture,
finding that the addition of small stars melts the crystal formed by the big
ones. A systematic comparison between the two- and effective one-component
descriptions of the mixture that corroborates the reliability of the
generalized depletion picture is also carried out.Comment: 26 pages, 9 figures, submitted to Phys. Rev.
Phase diagram of symmetric binary mixtures at equimolar and non-equimolar concentrations: a systematic investigation
We consider symmetric binary mixtures consisting of spherical particles with
equal diameters interacting via a hard-core plus attractive tail potential with
strengths epsilon_{ij}, i,j=1,2, such that epsilon_{11} = epsilon_{22} >
epsilon_{12}. The phase diagram of the system at all densities and
concentrations is investigated as a function of the unlike-to-like interaction
ratio delta = epsilon_{12}/epsilon_{11} by means of the hierarchical reference
theory (HRT). The results are related to those of previous investigations
performed at equimolar concentration, as well as to the topology of the
mean-field critical lines. As delta is increased in the interval 0 < delta < 1,
we find first a regime where the phase diagram at equal species concentration
displays a tricritical point, then one where both a tricritical and a
liquid-vapor critical point are present. We did not find any clear evidence of
the critical endpoint topology predicted by mean-field theory as delta
approaches 1, at least up to delta=0.8, which is the largest value of delta
investigated here. Particular attention was paid to the description of the
critical-plus-tricritical point regime in the whole density-concentration
plane. In this situation, the phase diagram shows, in a certain temperature
interval, a coexistence region that encloses an island of homogeneous,
one-phase fluid.Comment: 27 pages + 20 figure
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