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Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex-valued. We study the popular recovery method of \ell 1-regularized least squares or LASSO. While several studies have shown that LASSO provides desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to solve the complex-valued LASSO problem and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP. Our theoretical results are concerned with the case of i.i.d. Gaussian sensing matrices. Simulations confirm that our results hold for a larger class of random matrices. [ABSTRACT FROM AUTHOR]

In this paper, we describe the problem of recommending conference sessions to attendees and show how novel extensions to traditional model-based recommender systems, as suggested in Adomavicius and Tuzhilin [CHECK END OF SENTENCE], can address this problem. We introduce Recommendation Engine by CONjoint Decomposition of ITems and USers (RECONDITUS)—a technique that is an extension of preference-based recommender systems to recommend items from a new disjoint set to users from a new disjoint set. The assumption being that preferences exhibited by users with known usage behavior (e.g., past conference session attendance), which can be abstracted by projections of user and item matrices, will be similar to ones of new (different) users where the basic environment and item domain are the same (e.g., new conference). RECONDITUS requires no item ratings, but operates on observed user behavior such as past conference session attendance. The RECONDITUS paradigm consists of projections of both user and item data, and the learning of relationships in projected space. Once established, the relationships enable predicting new relationships and provide associated recommendations. The approach can encompass several traditional data mining problems where both clustering and prediction are necessary. RECONDITUS has been evaluated using data from the Oracle OpenWorld conference. [ABSTRACT FROM AUTHOR]