On the Sample Information About Parameter and Prediction

The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive information is defined similarly and used for model selection and optimal designs, though to a lesser extent. The parameter and predictive information measures are proper utility functions and have been also used in combination. Yet the relationship between the two measures and the effects of conditional dependence between the observable quantities on the Bayesian information measures remain unexplored. We address both issues. The relationship between the two information measures is explored through the information provided by the sample about the parameter and prediction jointly. The role of dependence is explored along with the interplay between the information measures, prior and sampling design. For the conditionally independent sequence of observable quantities, decompositions of the joint information characterize Lindley's measure as the sample information about the parameter and prediction jointly and the predictive information as part of it. For the conditionally dependent case, the joint information about parameter and prediction exceeds Lindley's measure by an amount due to the dependence. More specific results are shown for the normal linear models and a broad subfamily of the exponential family. Conditionally independent samples provide relatively little information for prediction, and the gap between the parameter and predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ultrafast Analog Fourier Transform Using 2-D LC Lattice

We describe how a 2-D rectangular lattice of inductors and capacitors can serve as an analog Fourier transform device, generating an approximate discrete Fourier transform (DFT) of an arbitrary input vector of fixed length. The lattice displays diffractive and refractive effects and mimics the combined optical effects of a thin-slit aperture and lens. Diffraction theories in optics are usually derived for 3-D media, whereas our derivations proceed in 2-D. Analytical and numerical results show agreement between lattice output and the true DFT. Potentially, this lattice can be used for an extremely low latency and high throughput analog signal processing device. The lattice can be fabricated on-chip with frequency of operation of more than 10 GHz

Dissimilarity-based Sparse Subset Selection

Finding an informative subset of a large collection of data points or models is at the center of many problems in computer vision, recommender systems, bio/health informatics as well as image and natural language processing. Given pairwise dissimilarities between the elements of a `source set' and a `target set,' we consider the problem of finding a subset of the source set, called representatives or exemplars, that can efficiently describe the target set. We formulate the problem as a row-sparsity regularized trace minimization problem. Since the proposed formulation is, in general, NP-hard, we consider a convex relaxation. The solution of our optimization finds representatives and the assignment of each element of the target set to each representative, hence, obtaining a clustering. We analyze the solution of our proposed optimization as a function of the regularization parameter. We show that when the two sets jointly partition into multiple groups, our algorithm finds representatives from all groups and reveals clustering of the sets. In addition, we show that the proposed framework can effectively deal with outliers. Our algorithm works with arbitrary dissimilarities, which can be asymmetric or violate the triangle inequality. To efficiently implement our algorithm, we consider an Alternating Direction Method of Multipliers (ADMM) framework, which results in quadratic complexity in the problem size. We show that the ADMM implementation allows to parallelize the algorithm, hence further reducing the computational time. Finally, by experiments on real-world datasets, we show that our proposed algorithm improves the state of the art on the two problems of scene categorization using representative images and time-series modeling and segmentation using representative~models

The Exchange Rate and Consumer Prices in Pakistan: Is Rupee Devaluation In Inflationary?

This paper challenges the popular view that devaluation of the rupee is inflationary. Recent developments in the theoretical literature are reviewed to explain why consumer prices would be unresponsive to exchange rate changes in the short run. Then empirical tests are conducted for Pakistan during the period 1982 to 2001 to examine whether inflation is systematically related to changes in the exchange rate. The empirical analysis finds no association between rupee devaluations and inflation in Pakistan. It appears, therefore, that concerns about the inflationary consequences of rupee devaluation are unsupported by the facts

Conditions of Full Disclosure:The Blockchain Remuneration Model

One of the fundamental applications for a practically useful system of money is remuneration. Information pertaining to the amount of compensation awarded to different individuals is often considered sensitive, commanding a certain degree of privacy. As Bitcoin and similarly designed cryptocurrencies evolve into a recognized medium of exchange for larger swaths of the world economy, an increasing number of people will earn income in the form of blockchain-based payments. The nature of these transactions is such that the minute details of an affected individuals compensation package and spending habits will be exposed to public scrutiny. In some cases this violates cultural norms which respect the confidentiality of salaries, yet in other cases it could be regarded as providing the benefits associated with greater transparency. In this work we analyse the Bitcoin blockchain record of periodic payments accruing to an individual address in exchange for goods or services rendered. For differing levels of available information we seek to determine the extent of insights that can be gleaned about the transacting counter-parties and the privacy implications this entails