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Mean Reciprocal Rank
The mean reciprocal rank is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries, ordered by probability of correctness. The reciprocal rank of a query response is the multiplicative inverse of the rank of the first correct answer: 1 for first place, for second place, for third place and so on. The mean reciprocal rank is the average of the reciprocal ranks of results for a sample of queries Q: : \text = \frac \sum_^ \frac. \! where \text_i refers to the rank position of the ''first'' relevant document for the ''i''-th query. The reciprocal value of the mean reciprocal rank corresponds to the harmonic mean of the ranks. Example For example, suppose we have the following three sample queries for a system that tries to translate English words to their plurals. In each case, the system makes three guesses, with the first one being the one it thinks is most likely correct: Given those three samples, we could calcu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an ''estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimator of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is : \left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is defined to be :H = \frac = \frac = \left(\frac\right)^. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: :H = \frac. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: :1/H(1/x_1 \ldots 1/x_n) = A(x_1 \ldots x_n) The harmonic mean is a Schur-con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evaluation Measures (information Retrieval)
Evaluation measures for an information retrieval (IR) system assess how well an index, search engine or database returns results from a collection of resources that satisfy a user's query. They are therefore fundamental to the success of information systems and digital platforms. The success of an IR system may be judged by a range of criteria including relevance, speed, user satisfaction, usability, efficiency and reliability. However the most important factor in determining a systems effectiveness for users is the overall relevance of results retrieved in response to a query. Evaluation measures may be categorised in various ways including offline or online, user-based or system-based and include methods such as observed user behaviour, test collections, precision and recall, and scores from prepared benchmark test sets. Evaluation for an information retrieval system should also include a validation of the measures used, i.e. an assessment of how well they measure what they are i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Retrieval
Information retrieval (IR) in computing and information science is the process of obtaining information system resources that are relevant to an information need from a collection of those resources. Searches can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images or sounds. Automated information retrieval systems are used to reduce what has been called information overload. An IR system is a software system that provides access to books, journals and other documents; stores and manages those documents. Web search engines are the most visible IR applications. Overview An information retrieval process begins when a user or searcher enters a query into the system. Queries are formal statements of information needs, for example search strings in web search engines. In inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Question Answering
Question answering (QA) is a computer science discipline within the fields of information retrieval and natural language processing (NLP), which is concerned with building systems that automatically answer questions posed by humans in a natural language. Overview A question answering implementation, usually a computer program, may construct its answers by querying a structured database of knowledge or information, usually a knowledge base. More commonly, question answering systems can pull answers from an unstructured collection of natural language documents. Some examples of natural language document collections used for question answering systems include: * a local collection of reference texts * internal organization documents and web pages * compiled newswire reports * a set of Wikipedia pages * a subset of World Wide Web pages Types of question answering Question answering research attempts to deal with a wide range of question types including: fact, list, definition, ''H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summary Statistics
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in * a measure of location, or central tendency, such as the arithmetic mean * a measure of statistical dispersion like the standard deviation, standard mean absolute deviation * a measure of the shape of the distribution like skewness or kurtosis * if more than one variable is measured, a measure of correlation and dependence, statistical dependence such as a Pearson product-moment correlation coefficient, correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. Examples Location Common measures of location, or central tendency, are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
