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Group Lasso with Overlap and Graph Lasso
"... We propose a new penalty function which, when used as regularization for empirical risk minimization procedures, leads to sparse estimators. The support of the sparse vector is typically a union of potentially overlapping groups of covariates defined a priori, or a set of covariates which tend to be ..."
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Cited by 117 (14 self)
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We propose a new penalty function which, when used as regularization for empirical risk minimization procedures, leads to sparse estimators. The support of the sparse vector is typically a union of potentially overlapping groups of covariates defined a priori, or a set of covariates which tend to be connected to each other when a graph of covariates is given. We study theoretical properties of the estimator, and illustrate its behavior on simulated and breast cancer gene expression data. 1.
Dynamic Allocation of Subcarriers and 1 Transmit Powers in an OFDMA Cellular Network
"... This paper considers the problem of minimizing outage probabilities in the downlink of a multiuser, multicell OFDMA cellular network with frequency selective fading, imperfect channel state information and frequency hopping. The task is to determine the allocation of powers and subcarriers for users ..."
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This paper considers the problem of minimizing outage probabilities in the downlink of a multiuser, multicell OFDMA cellular network with frequency selective fading, imperfect channel state information and frequency hopping. The task is to determine the allocation of powers and subcarriers for users to ensure that the user outage probabilities are as low as possible. We formulate a minmax outage probability problem and solve it under the constraint that the transmit power spectrum at each base station is flat. In particular, we obtain a subchannel allocation algorithm that has complexity O(L log L) in L, the number of users in the cell. We also consider suboptimal but implementable approaches with and without the flat transmit power spectrum constraint. We conclude that the flat transmit spectrum approach has merit, and warrants further study. Index Terms Cellular network, resource allocation, power control, orthogonal frequency division multiple access (OFDMA), subcarrier allocation, power spectrum, fading channels, outage capacity, fast frequency hopping, interference averaging. I.
FROM ORDIENTS TO OPTIMIZATION: SUBSTITUTION EFFECTS WITHOUT DIFFERENTIABILITY
, 2009
"... This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradient for functions (utilities). The main motivation for this study is to replace the binary relation at the center stage of economic analysis, rather than its representation (whenever i ..."
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This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradient for functions (utilities). The main motivation for this study is to replace the binary relation at the center stage of economic analysis, rather than its representation (whenever it exists). Moreover, ordients have a natural economic interpretation as marginal rates of substitution. Some examples of ordientable binary relations include the lexicographic order, binary relations resulting from the sequential applications of multiple rationales or binary relations with differentiable representations. We characterize the constrained maxima of binary relations through ordients and provide an implicit function theorem and an envelope theorem.