The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fraction of errors is impossible if the measurement rate and the per-sample signal-to-noise ratio (SNR) are finite constants, independent of the vector length. In this paper, it is shown that recovery with an arbitrarily small but constant fraction of errors is, however, possible, and that in some cases computationally simple estimators are near-optimal. Bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector for several different recovery algorithms. The tightness of the bounds, in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing information-theoretic necessary bounds. Near optimality is shown for a wide variety of practically motivated signal models

Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector. The tightness of the bounds in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing achievable bounds. Near optimality is shown for a wide variety of practically motivated signal models

"Compressed" Compressed Sensing

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller number of samples is sufficient when there exists prior knowledge about the distribution of the unknown vector, or when only partial recovery is needed. An information-theoretic lower bound with connections to free probability theory and an upper bound corresponding to a computationally simple thresholding estimator are derived. It is shown that in certain cases (e.g. discrete valued vectors or large distortions) the number of samples can be decreased. Interestingly though, it is also shown that in many cases no reduction is possible

The Impact of Contracting Out on the Costs of Refuse Collection Services - The Case of Ireland

This paper examines the impact of contracting out on the costs incurred by local authorities in providing refuse collection services. Using original survey data for the Republic of Ireland, three methods of estimating the impact of tendering are adopted. Crude comparisons of costs before and after tendering and the costs of local authorities versus private contractors indicate that tendering can yield savings of between 34 and 45 per cent. Using multivariate regression analysis to enable us to control for service characteristics confirms cost savings of around 45 per cent. The bulk of these cost savings are attributed to real efficiency gains as a result of contracting out.

“Utilization, Development and Conservation” of Natural Resources for the Maximum Benefit of Alaskans: Scrutinizing Alaska’s Permitting Regime for Large Mines

This Article disputes analyses and conclusions presented in an article about Pebble Mine published in the Alaska Law Review’s June 2008 issue. This Article discusses the history of mining in Alaska and the Pebble Project and describes the permitting regime applicable to mining exploration or development projects as it has been developed by the Alaska Legislature and the United States Congress, implemented by state and federal administrative agencies, and interpreted by federal and state courts. The Authors argue that the mining industry in Alaska has not historically proved detrimental to the fishing industry and that numerous and adequate legal safeguards are provided by the existing permitting regime. They also dispute the previous article’s conclusion that development of the Pebble resource would harm fisheries. This Article concludes that a change in state law by which the owners of the Pebble resource are barred from developing the known deposit would effect a compensable regulatory taking

Variational bayes for estimating the parameters of a hidden Potts model

Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets

Cryptocurrency-Remittance Transfers Futuristic Technologies & Poverty Alleviation

The methodologies used to transfer remittances to Sub-Saharan Africa are currently predisposing their citizens to be dealt unethically large surcharges which are relatively greater than any other location in the world. These African nation\u27s average remittance transaction fees were greater than 13% in 2006 and could become the greatest benefactor if a more efficient methodology of remittance currency transferring were to be created. For instance, if Sub-Saharan African citizens began to utilize cryptocurrencies instead of standard transfer companies like Western Union and MoneyGram; transfer fees could be reduced to as little as (.025%) which would directly send more funds to the people that need it the most. The methodologies within this paper consist of a semi-log poverty regression that utilized an econometric structure similar to the previous literature. In addition to previous regression analyses conducted by Gupta (2009), Giuliano (2008), Adams & Page (2005), and Ravallion (1997); I attempt to include variables in attempt to determine the role that technological integration has towards poverty mitigation. My econometric semi log regression analyzes 18 nations with Africa. These nations were specifically chosen in reference to their relatively large association with remittance transfers. Within this analysis of poverty within Sub Saharan Africa, a strong correlation between remittance transactions and poverty reduction is found. More specifically, the results also suggest that remittances transactions directly assist the most impoverished citizens within a nation most efficiently and that an increased technological infrastructure played a significant role within poverty mitigation. These conclusions should further incentives developing nations across the world to investigate how cryptocurrencies could effectively mitigate poverty

UI-Design driven model-based testing

Testing interactive systems is notoriously difficult. Not only do we need to ensure that the functionality of the developed system is correct with respect to the requirements and specifications, we also need to ensure that the user interface to the system is correct (enables a user to access the functionality correctly) and is usable. These different requirements of interactive system testing are not easily combined within a single testing strategy. We investigate the use of models of interactive systems, which have been derived from design artefacts, as the basis for generating tests for an implemented system. We give a model-based method for testing interactive systems which has low overhead in terms of the models required and which enables testing of UI and system functionality from the perspective of user interaction