1,037 research outputs found

    The Necessary And Sufficient Condition for Generalized Demixing

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    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

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    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

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    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

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    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

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    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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