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Algorithms For Calculating Variance
Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values. Naïve algorithm A formula for calculating the variance of an entire population of size ''N'' is: :\sigma^2 = \overline - \bar x^2 = \frac - \left(\frac\right)^2 Using Bessel's correction to calculate an unbiased estimate of the population variance from a finite sample of ''n'' observations, the formula is: :s^2 = \left(\frac n - \left( \frac n \right)^2\right) \cdot \frac . Therefore, a naïve algorithm to calculate the estimated variance is given by the following: * Let * For each datum : ** ** ** * This algorithm can easily be adapted to compute the variance of a finite population: simply divide by ''n'' instead of ''n'' − 1 on the l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Statistics
Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is fast developing. The view that the broader concept of computing must be taught as part of general statistical education is gaining momentum. As in Statistics, traditional statistics the goal is to transform raw data into knowledge,Edward Wegman, Wegman, Edward J. �Computational Statistics: A New Agenda for Statistical Theory and Practice.�� Journal of the Washington Academy of Sciences', vol. 78, no. 4, 1988, pp. 310–322. ''JSTOR'' but the focus lies on computer intensive statistical methods, such as cases with very large Sample size determination, sample size and non-homogeneous data sets. The terms 'computational statistics' and 'statis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ..., the area in which online algorithms are developed is called online optimization. As an example, consider the sorting algorithms selection sort and insertion sort: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Cluster
A computer cluster is a set of computers that work together so that they can be viewed as a single system. Unlike grid computers, computer clusters have each node set to perform the same task, controlled and scheduled by software. The newest manifestation of cluster computing is cloud computing. The components of a cluster are usually connected to each other through fast local area networks, with each node (computer used as a server) running its own instance of an operating system. In most circumstances, all of the nodes use the same hardware and the same operating system, although in some setups (e.g. using Open Source Cluster Application Resources (OSCAR)), different operating systems can be used on each computer, or different hardware. Clusters are usually deployed to improve performance and availability over that of a single computer, while typically being much more cost-effective than single computers of comparable speed or availability. Computer clusters emerged as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphics Processing Unit
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs were later found to be useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. History 1970s Arcade system boards have used specialized graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advanced Vector Extensions
Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge New Instructions) are SIMD extensions to the x86 instruction set architecture for microprocessors from Intel and Advanced Micro Devices (AMD). They were proposed by Intel in March 2008 and first supported by Intel with the Sandy Bridge microarchitecture shipping in Q1 2011 and later by AMD with the Bulldozer microarchitecture shipping in Q4 2011. AVX provides new features, new instructions, and a new coding scheme. AVX2 (also known as Haswell New Instructions) expands most integer commands to 256 bits and introduces new instructions. They were first supported by Intel with the Haswell microarchitecture, which shipped in 2013. AVX-512 expands AVX to 512-bit support using a new EVEX prefix encoding proposed by Intel in July 2013 and first supported by Intel with the Knights Landing co-processor, which shipped in 2016. In conventional processors, AVX-512 was introduced with Skylak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incremental Computing
Incremental computing, also known as incremental computation, is a software feature which, whenever a piece of data changes, attempts to save time by only recomputing those outputs which depend on the changed data. When incremental computing is successful, it can be significantly faster than computing new outputs naively. For example, a spreadsheet software package might use incremental computation in its recalculation features, to update only those cells containing formulas which depend (directly or indirectly) on the changed cells. When incremental computing is implemented by a tool that can implement it for a variety of different pieces of code automatically, that tool is an example of a program analysis tool for optimization. Static versus dynamic Incremental computing techniques can be broadly separated into two types of approaches: '' Static approaches'' attempt to derive an incremental program from a conventional program P using, e.g., either manual design and refactori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications Of The ACM
''Communications of the ACM'' (''CACM'') is the monthly journal of the Association for Computing Machinery (ACM). History It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with backgrounds in all areas of computer science and information systems. The focus is on the practical implications of advances in information technology and associated management issues; ACM also publishes a variety of more theoretical journals. The magazine straddles the boundary of a science magazine, trade magazine, and a scientific journal. While the content is subject to peer review, the articles published are often summaries of research that may also be published elsewhere. Material published must be accessible and relevant to a broad readership. From 1960 onward, ''CACM'' also published algorithms, expressed in ALGOL. The collection of algorithms later became known as the Collected Algorithms of the ACM. CA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Algorithm
In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can do multiple operations in a given time. It has been a tradition of computer science to describe serial algorithms in abstract machine models, often the one known as random-access machine. Similarly, many computer science researchers have used a so-called parallel random-access machine (PRAM) as a parallel abstract machine (shared-memory). Many parallel algorithms are executed concurrently – though in general concurrent algorithms are a distinct concept – and thus these concepts are often conflated, with which aspect of an algorithm is parallel and which is concurrent not being clearly distinguished. Further, non-parallel, non-concurrent algorithms are often referred to as " sequential algorithms", by contrast with concurrent algorithms. Parallelizability Algorithms vary significantly in how parallelizable they are, ranging from easily parallelizable to compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catastrophic Cancellation
In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one L_1 = 253.51\,\text long and the other L_2 = 252.49\,\text long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be \tilde L_1 = 254\,\text and \tilde L_2 = 252\,\text. These may be good approximations, in relative error, to the true lengths: the approximations are in error by less than 0.2% of the true lengths, , L_1 - \tilde L_1, /, L_1, < 0.2\%. However, if the ''approximate'' lengths are subtracted, the difference will be , even though the true difference between the lengths is . The difference of the approximations, |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive multi-volume monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. it consists of published volumes 1, 2, 3, 4A, and 4B, with more expected to be released in the future. The Volumes 1–5 are intended to represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald E
Donald is a Scottish masculine given name. It is derived from the Goidelic languages, Gaelic name ''Dòmhnall''.. This comes from the Proto-Celtic language, Proto-Celtic *''Dumno-ualos'' ("world-ruler" or "world-wielder"). The final -''d'' in ''Donald'' is partly derived from a misinterpretation of the Gaelic pronunciation by English speakers. A short form of Donald is Don (given name), Don, and pet forms of Donald include Donnie and Donny. The feminine given name Donella (other) , Donella is derived from Donald. ''Donald'' has cognates in other Celtic languages: Irish language, Modern Irish ''Dónal'' (anglicised as ''Donal'' and ''Donall'');. Scottish Gaelic ''Dòmhnall'', ''Domhnull'' and ''Dòmhnull''; Welsh language, Welsh ''Dyfnwal (other), Dyfnwal'' and Cumbric ''Dumnagual''. Although the feminine given name ''Donna (given name), Donna'' is sometimes used as a feminine form of ''Donald'', the names are not etymologically related. Variations King ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technometrics
''Technometrics'' is a journal of statistics for the physical, chemical, and engineering sciences, published quarterly since 1959 by the American Society for Quality The American Society for Quality (ASQ), formerly the American Society for Quality Control (ASQC), is a society of quality professionals, with more than 30,000 members, in more than 140 countries. History ASQC was established on 16 February ... and the American Statistical Association. Statement of purpose The journal describes itself this way: "The purpose of ''Technometrics'' is to contribute to the development and use of statistical methods in physical, chemical, and engineering sciences as well as information sciences and technology. This vision includes developments on the interface of statistics and computer science such as data mining, machine learning, large databases, and so on. The journal places a premium on clear communication among statisticians and practitioners of these sciences and an emph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
