Space-optimal Heavy Hitters with Strong Error Bounds

The problem of finding heavy hitters and approximating the frequencies of items is at the heart of many problems in data stream analysis. It has been observed that several proposed solutions to this problem can outperform their worst-case guarantees on real data. This leads to the question of whether some stronger bounds can be guaranteed. We answer this in the positive by showing that a class of "counter-based algorithms" (including the popular and very space-efficient FREQUENT and SPACESAVING algorithms) provide much stronger approximation guarantees than previously known. Specifically, we show that errors in the approximation of individual elements do not depend on the frequencies of the most frequent elements, but only on the frequency of the remaining "tail." This shows that counter-based methods are the most space-efficient (in fact, space-optimal) algorithms having this strong error bound. This tail guarantee allows these algorithms to solve the "sparse recovery" problem. Here, the goal is to recover a faithful representation of the vector of frequencies, f. We prove that using space O(k), the algorithms construct an approximation f* to the frequency vector f so that the L1 error ||f -- f*||[subscript 1] is close to the best possible error min[subscript f2] ||f2 -- f||[subscript 1], where f2 ranges over all vectors with at most k non-zero entries. This improves the previously best known space bound of about O(k log n) for streams without element deletions (where n is the size of the domain from which stream elements are drawn). Other consequences of the tail guarantees are results for skewed (Zipfian) data, and guarantees for accuracy of merging multiple summarized streams.David & Lucile Packard Foundation (Fellowship)Center for Massive Data Algorithmics (MADALGO)National Science Foundation (U.S.). (Grant number CCF-0728645

Bankruptcy risk forecasting for the metallurgical branch in Romania

All investment decisions require a thorough analysis of the retrospective evolution of the entities from the concerned area, in order to estimate the long-term evolution perspectives. In this context, the present study analyzes the evolution of the entities from the Romanian metallurgical sector based on the accounting and financial information published for the period 2008 - 2012 and, in fact, it justifies the situation from the perspective of users (managers, investors, auditors) and of the economic environment specific to Romania. Starting from this premise we created a regression model particularly useful in forecasting the evolution of the ability to deal with debt for the entities from the Romanian metallurgical sector

Determinant factors for the growing of shareholders’ equity in the metallurgical sector in Romania

The article provides a statistical monograph of the financial position and performance for the period 2008 – 2012 of the entities from the Romanian metallurgical sector whose financial statements in the period 2004 – 2012 have become the object of the financial audit. There are tested five types of regression models in order to separately determine the evolution of equity in accordance with the variation of turnover, total assets, average number of employees and net result. After determining the most appropriate simple regression model, one proceeds at establishing a multiple regression model which would simultaneously reflect the evolution of equity in accordance with the above mentioned variables. The study’s importance is enhanced by certain statistically-based concrete measures which management should consider in order to increase the shareholders’ equity