The problem of sparsity pattern or support set recovery refers to estimating the set of nonzero coefficients of an unknown vector beta* isin Ropf p based on a set of n noisy observations. It arises ...in a variety of settings, including subset selection in regression, graphical model selection, signal denoising, compressive sensing, and constructive approximation. The sample complexity of a given method for subset recovery refers to the scaling of the required sample size n as a function of the signal dimension p, sparsity index k (number of non-zeroes in beta*), as well as the minimum value beta min of beta* over its support and other parameters of measurement matrix. This paper studies the information-theoretic limits of sparsity recovery: in particular, for a noisy linear observation model based on random measurement matrices drawn from general Gaussian measurement matrices, we derive both a set of sufficient conditions for exact support recovery using an exhaustive search decoder, as well as a set of necessary conditions that any decoder, regardless of its computational complexity, must satisfy for exact support recovery. This analysis of fundamental limits complements our previous work on sharp thresholds for support set recovery over the same set of random measurement ensembles using the polynomial-time Lasso method (lscr 1 -constrained quadratic programming).
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. ...It arises in various application domains, including distributed tracking and localization, multi-agent coordination, estimation in sensor networks, and large-scale machine learning. We develop and analyze distributed algorithms based on dual subgradient averaging, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our analysis allows us to clearly separate the convergence of the optimization algorithm itself and the effects of communication dependent on the network structure. We show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network, and confirm this prediction's sharpness both by theoretical lower bounds and simulations for various networks. Our approach includes the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardn4516420ess of these problems. Given the extensive use of ...convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is important. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We introduce a new notion of discrepancy between functions, and use it to reduce problems of stochastic convex optimization to statistical parameter estimation, which can be lower bounded using information-theoretic methods. Using this approach, we improve upon known results and obtain tight minimax complexity estimates for various function classes.
A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The ...decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting "LP decoder" generalizes our previous work on turbo-like codes. A precise combinatorial characterization of when the LP decoder succeeds is provided, based on pseudocodewords associated with the factor graph. Our definition of a pseudocodeword unifies other such notions known for iterative algorithms, including "stopping sets," "irreducible closed walks," "trellis cycles," "deviation sets," and "graph covers." The fractional distance d/sub frac/ of a code is introduced, which is a lower bound on the classical distance. It is shown that the efficient LP decoder will correct up to /spl lceil/d/sub frac//2/spl rceil/-1 errors and that there are codes with d/sub frac/=/spl Omega/(n/sup 1-/spl epsi//). An efficient algorithm to compute the fractional distance is presented. Experimental evidence shows a similar performance on low-density parity-check (LDPC) codes between LP decoding and the min-sum and sum-product algorithms. Methods for tightening the LP relaxation to improve performance are also provided.
We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent ...positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By ...decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: a) a tree-relaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and b) a tree-reweighted max-product message-passing algorithm that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the mode-finding problem and a reweighted form of the max-product (min-sum) message-passing algorithm.
Sonic Hedgehog (SHH) signaling at primary cilia drives the proliferation and progression of a subset of medulloblastomas, the most common malignant paediatric brain tumor. Severe side effects ...associated with conventional treatments and resistance to targeted therapies has led to the need for new strategies. SHH signaling is dependent on primary cilia for signal transduction suggesting the potential for cilia destabilizing mechanisms as a therapeutic target. INPP5E is an inositol polyphosphate 5-phosphatase that hydrolyses PtdIns(4,5)P
and more potently, the phosphoinositide (PI) 3-kinase product PtdIns(3,4,5)P
. INPP5E promotes SHH signaling during embryonic development via PtdIns(4,5)P
hydrolysis at cilia, that in turn regulates the cilia recruitment of the SHH suppressor GPR161. However, the role INPP5E plays in cancer is unknown and the contribution of PI3-kinase signaling to cilia function is little characterized. Here, we reveal INPP5E promotes SHH signaling in SHH medulloblastoma by negatively regulating a cilia-compartmentalized PI3-kinase signaling axis that maintains primary cilia on tumor cells. Conditional deletion of Inpp5e in a murine model of constitutively active Smoothened-driven medulloblastoma slowed tumor progression, suppressed cell proliferation, reduced SHH signaling and promoted tumor cell cilia loss. PtdIns(3,4,5)P
, its effector pAKT and the target pGSK3β, which when non-phosphorylated promotes cilia assembly/stability, localized to tumor cell cilia. The number of PtdIns(3,4,5)P
/pAKT/pGSK3β-positive cilia was increased in cultured Inpp5e-null tumor cells relative to controls. PI3-kinase inhibition or expression of wild-type, but not catalytically inactive HA-INPP5E partially rescued cilia loss in Inpp5e-null tumor cells in vitro. INPP5E mRNA and copy number were reduced in human SHH medulloblastoma compared to other molecular subtypes and consistent with the murine model, reduced INPP5E was associated with improved overall survival. Therefore our study identifies a compartmentalized PtdIns(3,4,5)P
/AKT/GSK3β signaling axis at cilia in SHH-dependent medulloblastoma that is regulated by INPP5E to maintain tumor cell cilia, promote SHH signaling and thereby medulloblastoma progression.
Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms ...can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of n and radicn, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy e using O((n 1.5 radiclogn) logisin -1 ) radio transmissions, which yields a radicn/ log n factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.
Specimen collection: An essential tool Rocha, L. A.; Aleixo, A.; Allen, G. ...
Science (American Association for the Advancement of Science),
05/2014, Volume:
344, Issue:
6186
Journal Article
PDBe: Protein Data Bank in Europe Velankar, S; Alhroub, Y; Best, C ...
Nucleic acids research,
01/2012, Volume:
40, Issue:
D1
Journal Article
Peer reviewed
Open access
The Protein Data Bank in Europe (PDBe; pdbe.org) is a partner in the Worldwide PDB organization (wwPDB; wwpdb.org) and as such actively involved in managing the single global archive of ...biomacromolecular structure data, the PDB. In addition, PDBe develops tools, services and resources to make structure-related data more accessible to the biomedical community. Here we describe recently developed, extended or improved services, including an animated structure-presentation widget (PDBportfolio), a widget to graphically display the coverage of any UniProt sequence in the PDB (UniPDB), chemistry- and taxonomy-based PDB-archive browsers (PDBeXplore), and a tool for interactive visualization of NMR structures, corresponding experimental data as well as validation and analysis results (Vivaldi).
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