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Full-Text Articles in Mathematics
From Quantifying And Propagating Uncertainty To Quantifying And Propagating Both Uncertainty And Reliability: Practice-Motivated Approach To Measurement Planning And Data Processing, Niklas R. Winnewisser, Vladik Kreinovich, Olga Kosheleva
From Quantifying And Propagating Uncertainty To Quantifying And Propagating Both Uncertainty And Reliability: Practice-Motivated Approach To Measurement Planning And Data Processing, Niklas R. Winnewisser, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
When we process data, it is important to take into account that data comes with uncertainty. There exist techniques for quantifying uncertainty and propagating this uncertainty through the data processing algorithms. However, most of these techniques do not take into account that in real world, measuring instruments are not 100% reliable -- they sometimes malfunction and produce values which are far off from the measured values of the corresponding quantities. How can we take into account both uncertainty and reliability? In this paper, we consider several possible scenarios, and we show, for each scenario, what is the natural way to …
Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich
Fast -- Asymptotically Optimal -- Methods For Determining The Optimal Number Of Features, Saied Tizpaz-Niari, Luc Longpré, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In machine learning -- and in data processing in general -- it is very important to select the proper number of features. If we select too few, we miss important information and do not get good results, but if we select too many, this will include many irrelevant ones that only bring noise and thus again worsen the results. The usual method of selecting the proper number of features is to add features one by one until the quality stops improving and starts deteriorating again. This method works, but it often takes too much time. In this paper, we propose …
Combining Interval, Probabilistic, And Other Types Of Uncertainty In Engineering Applications, Andrew Martin Pownuk
Combining Interval, Probabilistic, And Other Types Of Uncertainty In Engineering Applications, Andrew Martin Pownuk
Open Access Theses & Dissertations
In many practical application, we process measurement results and expert estimates. Measurements and expert estimates are never absolutely accurate, their result are slightly different from the actual (unknown) values of the corresponding quantities. It is therefore desirable to analyze how this measurement and estimation inaccuracy affects the results of data processing.
There exist numerous methods for estimating the accuracy of the results of data processing under different models of measurement and estimation inaccuracies: probabilistic, interval, and fuzzy. To be useful in engineering applications, these methods should provide accurate estimate for the resulting uncertainty, should not take too much computation time, …
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu
Departmental Technical Reports (CS)
In many real-life situations, we are interested in the values of physical quantities x1, ..., xn which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y1, ..., ym which are related to the desired quantities by a known relation, and use these measurement results to estimate xi. The corresponding data processing algorithms are sometimes very complex and time-consuming, so a natural question is: are simpler (and, thus, faster) algorithms possible for solving this data processing problem? In this paper, we show that by using …