The Ratio Club was a small British informal dining club from 1949 to 1958 of young psychiatrists, psychologists, physiologists, mathematicians and engineers who met to discuss issues in cybernetics. == History == The idea of the club arose from a symposium on animal behaviour held in July 1949 by the Society of Experimental Biology in Cambridge. The club was founded by the neurologist John Bates, with other notable members such as W. Ross Ashby. The name Ratio was suggested by Albert Uttley, it being the Latin root meaning "computation or the faculty of mind which calculates, plans and reasons". He pointed out that it is also the root of rationarium, meaning a statistical account, and ratiocinatius, meaning argumentative. The use was probably inspired by an earlier suggestion by Donald Mackay of the 'MR club', from Machina ratiocinatrix, a term used by Norbert Wiener in the introduction to his then recently published book Cybernetics, or Control and Communication in the Animal and the Machine. Wiener used the term in reference to calculus ratiocinator, a calculating machine constructed by Leibniz. The initial membership was W. Ross Ashby, Horace Barlow, John Bates, George Dawson, Thomas Gold, W. E. Hick, Victor Little, Donald MacKay, Turner McLardy, P. A. Merton, John Pringle, Harold Shipton, Donald Sholl, Eliot Slater, Albert Uttley, W. Grey Walter and John Hugh Westcott. Alan Turing joined after the first meeting with I. J. Good, Philip Woodward and William Rushton added soon after. Giles Brindley attended several meetings as a guest. Warren McCulloch made presentations to the club twice, the first time at its inaugural meeting (a talk which the members found disappointing), and became a correspondent with and supporter of a number of its members. Others who attended at least one Ratio Club event as guests included Walter Pitts, Claude Shannon, J.Z. Young, C.H. Waddington, Peter Elias, J. C. R. Licklider, Oliver Selfridge, Benoît Mandelbrot, Colin Cherry and Anthony Oettinger. One one occasion I.J. Good brought along the then director of the USA's National Security Agency (presumably either Ralph Canine or John Samford given the dates). Several members admired the work of psychologist and philosopher Kenneth Craik and considered him an important influence; according to Husbands and Holland "there is no doubt Craik would have been a leading member of the club" had he not died young in 1945. The club has been considered the most influential cybernetics group in the UK, and many of its members went on to become prominent scientists.
Commonsense knowledge (artificial intelligence)
In artificial intelligence research, commonsense knowledge consists of facts about the everyday world, such as "Lemons are sour" or "Cows say moo", that all humans are expected to know. It is currently an unsolved problem in artificial general intelligence. The first AI program to address common sense knowledge was Advice Taker in 1959 by John McCarthy. Commonsense knowledge can underpin a commonsense reasoning process, to attempt inferences such as "You might bake a cake because you want people to eat the cake." A natural language processing process can be attached to the commonsense knowledge base to allow the knowledge base to attempt to answer questions about the world. Common sense knowledge also helps to solve problems in the face of incomplete information. Using widely held beliefs about everyday objects, or common sense knowledge, AI systems make common sense assumptions or default assumptions about the unknown similar to the way people do. In an AI system or in English, this is expressed as "Normally P holds", "Usually P" or "Typically P so Assume P". For example, if we know the fact "Tweety is a bird", because we know the commonly held belief about birds, "typically birds fly," without knowing anything else about Tweety, we may reasonably assume the fact that "Tweety can fly." As more knowledge of the world is discovered or learned over time, the AI system can revise its assumptions about Tweety using a truth maintenance process. If we later learn that "Tweety is a penguin" then truth maintenance revises this assumption because we also know "penguins do not fly". == Commonsense reasoning == Commonsense reasoning simulates the human ability to use commonsense knowledge to make presumptions about the type and essence of ordinary situations they encounter every day, and to change their "minds" should new information come to light. This includes time, missing or incomplete information and cause and effect. The ability to explain cause and effect is an important aspect of explainable AI. Truth maintenance algorithms automatically provide an explanation facility because they create elaborate records of presumptions. Compared with humans, all existing computer programs that attempt human-level AI perform extremely poorly on modern "commonsense reasoning" benchmark tests such as the Winograd Schema Challenge. The problem of attaining human-level competency at "commonsense knowledge" tasks is considered to probably be "AI complete" (that is, solving it would require the ability to synthesize a fully human-level intelligence), although some oppose this notion and believe compassionate intelligence is also required for human-level AI. Common sense reasoning has been applied successfully in more limited domains such as natural language processing and automated diagnosis or analysis. == Commonsense knowledge base construction == Compiling comprehensive knowledge bases of commonsense assertions (CSKBs) is a long-standing challenge in AI research. From early expert-driven efforts like CYC and WordNet, significant advances were achieved via the crowdsourced OpenMind Commonsense project, which led to the crowdsourced ConceptNet KB. Several approaches have attempted to automate CSKB construction, most notably, via text mining (WebChild, Quasimodo, TransOMCS, Ascent), as well as harvesting these directly from pre-trained language models (AutoTOMIC). These resources are significantly larger than ConceptNet, though the automated construction mostly makes them of moderately lower quality. Challenges also remain on the representation of commonsense knowledge: Most CSKB projects follow a triple data model, which is not necessarily best suited for breaking more complex natural language assertions. A notable exception here is GenericsKB, which applies no further normalization to sentences, but retains them in full. == Applications == Around 2013, MIT researchers developed BullySpace, an extension of the commonsense knowledgebase ConceptNet, to catch taunting social media comments. BullySpace included over 200 semantic assertions based around stereotypes, to help the system infer that comments like "Put on a wig and lipstick and be who you really are" are more likely to be an insult if directed at a boy than a girl. ConceptNet has also been used by chatbots and by computers that compose original fiction. At Lawrence Livermore National Laboratory, common sense knowledge was used in an intelligent software agent to detect violations of a comprehensive nuclear test ban treaty. == Data == As an example, as of 2012 ConceptNet includes these 21 language-independent relations: IsA (An "RV" is a "vehicle" | X is an instance of a Y) UsedFor (a "cake tin" is used for "making cakes" | X is used for the purpose Y) HasA (A "rabbit" has a "tail" | X possesses Y element or feature) CapableOf (a "cook" is capable of "making baked goods" | X is capable of doing Y) Desires (a "child" desires "the aroma of baking" | X has a desire for Y) CreatedBy ("cake" is created by a "baker" | X is created by Y) PartOf (a "knife" is be part of a "knife set" | X is a part of Y) Causes ("Heat" causes "cooking"| X is what causes Y) LocatedNear (the "oven" is located near the "refrigerator" | X is located near Y) AtLocation (Somewhere a "Cook" can be at a "restaurant" | X is at the location of Y) DefinedAs (a "Cupcake" is defined as a "cake" that also has the qualities of being "small", "baked within a wrapper", and "containing only one area of frosting or icing" | X is defined as Y that also has the properties A, B & C) SymbolOf (a "heart" is a symbol of "affection" | X is a symbolic representation of Y) ReceivesAction ("cake" can receive the action of being "eaten" | X is capable of receiving action Y) HasPrerequisite ("baking" has the prerequisite of obtaining the "ingredients" | X cannot do Y unless A does B) MotivatedByGoal ("baking" is motivated by the goal of "consumption"/"eating" | X has the motivation of Y goal) CausesDesire ("baking" makesYou want to "follow recipe" | X causes the desire to do Y) MadeOf ("Cake" is made of "flour"/"eggs"/"sugar"/"oil"/etc | X is made of Y) HasFirstSubevent ("baking" has first subevent "make batter" | To do X the first thing that needs to be done is Y) HasSubevent ("eat" has subevent "swallow" | Doing X will lead to Y event following) HasLastSubevent ("sleeping" has last subevent of "waking" | Doing X ends with the event Y) == Commonsense knowledge bases == Cyc Open Mind Common Sense (data source) and ConceptNet (datastore and NLP engine) Evi Graphiq
Freddy II
Freddy (1969–1971) and Freddy II (1973–1976) were experimental robots built in the Department of Machine Intelligence and Perception (later Department of Artificial Intelligence, now part of the School of Informatics at the University of Edinburgh). == Technology == Technical innovations involving Freddy were at the forefront of the 70s robotics field. Freddy was one of the earliest robots to integrate vision, manipulation and intelligent systems as well as having versatility in the system and ease in retraining and reprogramming for new tasks. The idea of moving the table instead of the arm simplified the construction. Freddy also used a method of recognising the parts visually by using graph matching on the detected features. The system used an innovative collection of high level procedures for programming the arm movements which could be reused for each new task. == Lighthill controversy == In the mid 1970s there was controversy about the utility of pursuing a general purpose robotics programme in both the USA and the UK. A BBC TV programme in 1973, referred to as the "Lighthill Debate", pitched James Lighthill, who had written a critical report for the science and engineering research funding agencies in the UK, against Donald Michie from the University of Edinburgh and John McCarthy from Stanford University. The Edinburgh Freddy II and Stanford/SRI Shakey robots were used to illustrate the state-of-the-art at the time in intelligent robotics systems. == Freddy I and II == Freddy Mark I (1969–1971) was an experimental prototype, with 3 degrees-of-freedom created by a rotating platform driven by a pair of independent wheels. The other main components were a video camera and bump sensors connected to a computer. The computer moved the platform so that the camera could see and then recognise the objects. Freddy II (1973–1976) was a 5 degrees of freedom manipulator with a large vertical 'hand' that could move up and down, rotate about the vertical axis and rotate objects held in its gripper around one horizontal axis. Two remaining translational degrees of freedom were generated by a work surface that moved beneath the gripper. The gripper was a two finger pinch gripper. A video camera was added as well as later a light stripe generator. The Freddy and Freddy II projects were initiated and overseen by Donald Michie. The mechanical hardware and analogue electronics were designed and built by Stephen Salter (who also pioneered renewable energy from waves (see Salter's Duck)), and the digital electronics and computer interfacing were designed by Harry Barrow and Gregan Crawford. The software was developed by a team led by Rod Burstall, Robin Popplestone and Harry Barrow which used the POP-2 programming language, one of the world's first functional programming languages. The computing hardware was an Elliot 4130 computer with 384KB (128K 24-bit words) RAM and a hard disk linked to a small Honeywell H316 computer with 16KB of RAM which directly performed sensing and control. Freddy was a versatile system which could be trained and reprogrammed to perform a new task in a day or two. The tasks included putting rings on pegs and assembling simple model toys consisting of wooden blocks of different shapes, a boat with a mast and a car with axles and wheels. Information about part locations was obtained using the video camera, and then matched to previously stored models of the parts. It was soon realised in the Freddy project that the 'move here, do this, move there' style of robot behavior programming (actuator or joint level programming) is tedious and also did not allow for the robot to cope with variations in part position, part shape and sensor noise. Consequently, the RAPT robot programming language was developed by Pat Ambler and Robin Popplestone, in which robot behavior was specified at the object level. This meant that robot goals were specified in terms of desired position relationships between the robot, objects and the scene, leaving the details of how to achieve the goals to the underlying software system. Although developed in the 1970s RAPT is still considerably more advanced than most commercial robot programming languages. The team of people who contributed to the project were leaders in the field at the time and included Pat Ambler, Harry Barrow, Ilona Bellos, Chris Brown, Rod Burstall, Gregan Crawford, Jim Howe, Donald Michie, Robin Popplestone, Stephen Salter, Austin Tate and Ken Turner. Also of interest in the project was the use of a structured-light 3D scanner to obtain the 3D shape and position of the parts being manipulated. The Freddy II robot is currently on display at the Royal Museum in Edinburgh, Scotland, with a segment of the assembly video shown in a continuous loop.
Komodo (chess)
Komodo and Dragon by Komodo Chess (also known as Dragon or Komodo Dragon) are UCI chess engines developed by Komodo Chess, which is a part of Chess.com. The engines were originally authored by Don Dailey and GM Larry Kaufman. Dragon is a commercial chess engine, but Komodo is free for non-commercial use. Dragon is consistently ranked near the top of most major chess engine rating lists, along with Stockfish and Leela Chess Zero. == History == === Komodo === Komodo was derived from Don Dailey's former engine Doch in January 2010. The first multiprocessor version of Komodo was released in June 2013 as Komodo 5.1 MP. This version was a major rewrite and a port of Komodo to C++11. A single-processor version of Komodo (which won the CCT15 tournament in February earlier that year) was released as a stand-alone product shortly before the 5.1 MP release. This version, named Komodo CCT, was still based on the older C code, and was approximately 30 Elo stronger than the 5.1 MP version, as the latter was still undergoing massive code-cleanup work. With the release of Komodo 6 on October 4, 2013, Don Dailey announced that he was suffering from an acute form of leukaemia, and would no longer contribute to the future development of Komodo. On October 8, Don made an announcement on the Talkchess forum that Mark Lefler would be joining the Komodo team and would continue its development. Komodo TCEC was released on December 4, 2013. This was the same version that had won TCEC Season 5, and was the last with input from Don Dailey, to whom it was dedicated. Komodo 7 was released on May 21, 2014, adding Syzygy tablebase support. On May 24, 2018, Chess.com announced that it has acquired Komodo and that the Komodo team have joined Chess.com. The Komodo team is now called Komodo Chess. On December 17, 2018, Komodo Chess released Komodo 12.3 MCTS, a version of the Komodo 12.3 engine that uses Monte Carlo tree search instead of alpha–beta pruning/minimax. The last version, Komodo 14.3, was released on October 4, 2023. === Dragon === On November 9, 2020, Komodo Chess released Dragon by Komodo Chess 1.0, which features the use of efficiently updatable neural networks in its evaluation function. Dragon is derived from Komodo in the same way that Komodo was derived from Doch. Dragon is also called Komodo Dragon in certain tournaments such as the Top Chess Engine Championship and the World Computer Chess Championship (WCCC) but not in the Chess.com Computer Chess Championship (CCC). A Chess.com staff member named Dmitry Pervov joined the Dragon development team to write the NNUE code for Dragon, and Dietrich Kappe joined the Dragon development team to help Larry Kaufman and Mark Lefter train Dragon's neural networks. On March 17, 2023, Larry Kaufman announced that he and Mark Lefter have stepped down from Dragon development and from ownership of Komodo Chess, and that Chess.com have taken full control of Komodo Chess. As of March 17, 2023, Dietrich Kappe is the only person responsible for the development of Dragon, but Chess.com are looking for more programmers to help with Dragon development. The final version, Dragon 3.3, was released on October 4, 2023. == Competition results == === Komodo === Komodo has played in the ICT 2010 in Leiden, and further in the CCT12 and CCT14. Komodo had its first tournament success in 1999, when it won the CCT15 with a score of 6½/7. Komodo won both the World Computer Chess Championship and World Computer Software Championship in 2016. Komodo once again won the World Computer Chess Championship and World Blitz in 2017. In TCEC competition, Komodo was historically one of the strongest engines. In Season 4, it lost only eight out of its 53 games and managed to reach Stage 4 (Quarterfinals), against very strong competition which were running on eight cores (Komodo was running on a single processor). The next season, Komodo won the superfinal against Stockfish. The two engines jockeyed for the championship over the next few seasons: Stockfish won in Season 6, while Komodo won Seasons 7 and 8. Komodo failed to make the superfinal in Season 9, losing out to Houdini; but after Houdini was later disqualified for containing code plagiarized from Stockfish, Komodo was promoted to the runner-up. Komodo retrospectively won Season 10 in the same way. Starting from Season 11 however, Stockfish improved at a rate that left its rivals behind, crushing Komodo in Season 12 and 13. The advent of the neural network engine Leela Chess Zero meant Komodo has largely failed to qualify for the superfinal since, with a single exception in Season 22, when it lost to Stockfish. Although Komodo has not qualified for the superfinal, it has cemented itself as the third-strongest engine in the competition, finishing in that position for five of the last six seasons. ==== Chess.com Computer Chess Championship ==== === Dragon === ==== Chess.com Computer Chess Championship ==== ==== Top Chess Engine Championship ==== == Notable games == Komodo vs Hannibal, nTCEC - Stage 2b - Season 1, Round 4.1, ECO: A10, 1–0 Archived 2016-03-04 at the Wayback Machine Komodo sacrifices an exchange for positional gain. Gull vs Komodo, nTCEC - Stage 3 - Season 2, Round 2.2, ECO: E10, 0–1 Archived March 4, 2016, at the Wayback Machine Archived 2016-03-04 at the Wayback Machine
Historical Thesaurus of English
The Historical Thesaurus of English (HTE) is the largest thesaurus in the world. It is called a historical thesaurus as it arranges the whole vocabulary of English, from the earliest written records in Old English to the present, according to the first documented occurrence of a word in the entire history of the English language. The HTE was conceived and begun in 1965 by the English Language & Linguistics department of the University of Glasgow, who have ever since continued to compile the thesaurus. From the 1980s onwards the project was moved from paper-based records to a computer database. Today, the HTE is available to the public online, but a print version, the Historical Thesaurus of the Oxford English Dictionary (HTOED), was published in 2009. == Main project: The Historical Thesaurus of English (HTE) == The Historical Thesaurus of English (HTE) is a complete database of all the words in the Oxford English Dictionary and other dictionaries (including Old English), arranged by semantic field and date. In this way, the HTE arranges the whole vocabulary of English, from the earliest written records in Old English to the present, alongside dates of use. It is the first historical thesaurus to be compiled for any of the world's languages and contains 800,000 meanings for 600,000 words, within 230,000 categories. As the HTE website states, "in addition to providing hitherto unavailable information for linguistic and textual scholars, the Historical Thesaurus online is a rich resource for students of social and cultural history, showing how concepts developed through the words that refer to them." === Structure === The work is divided into three main sections: the External World, the Mind, and Society. These are broken down into successively narrower domains. The text eventually discriminates more than 236,000 categories. The second order categories are: === History === The ambitious project was announced at a 1965 meeting of the Philological Society by its originator, Michael Samuels. Work on the HTE started in the same year. In 2017, the University of Glasgow was awarded the Queen's Anniversary Prize for Higher Education for the HTE. A second edition of the online HTE is currently in progress and is expected to be launched in late 2020. Work is released on the freely-available HTE website when available. == Print edition: Historical Thesaurus of the Oxford English Dictionary (HTOED) == On 22 October 2009, after 44 years of work, version 1.0 of the HTE was published by Oxford University Press in a two-volume slipcased set as the Historical Thesaurus of the Oxford English Dictionary (HTOED). The two hardcover volumes together total nearly 4,500 pages.
Kernel density estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ( h ) = AMISE ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the
Reification (computer science)
In computer science, reification is the process by which an abstract idea about a program is turned into an explicit data model or other object created in a programming language. A computable/addressable object—a resource—is created in a system as a proxy for a non computable/addressable object. By means of reification, something that was previously implicit, unexpressed, and possibly inexpressible is explicitly formulated and made available to conceptual (logical or computational) manipulation. Informally, reification is often referred to as "making something a first-class citizen" within the scope of a particular system. Some aspect of a system can be reified at language design time, which is related to reflection in programming languages. It can be applied as a stepwise refinement at system design time. Reification is one of the most frequently used techniques of conceptual analysis and knowledge representation. == Reflective programming languages == In the context of programming languages, reification is the process by which a user program or any aspect of a programming language that was implicit in the translated program and the run-time system, are expressed in the language itself. This process makes it available to the program, which can inspect all these aspects as ordinary data. In reflective languages, reification data is causally connected to the related reified aspect such that a modification to one of them affects the other. Therefore, the reification data is always a faithful representation of the related reified aspect . Reification data is often said to be made a first class object. Reification, at least partially, has been experienced in many languages to date: in early Lisp dialects and in current Prolog dialects, programs have been treated as data, although the causal connection has often been left to the responsibility of the programmer. In Smalltalk-80, the compiler from the source text to bytecode has been part of the run-time system since the very first implementations of the language. The C programming language reifies the low-level detail of memory addresses.Many programming language designs encapsulate the details of memory allocation in the compiler and the run-time system. In the design of the C programming language, the memory address is reified and is available for direct manipulation by other language constructs. For example, the following code may be used when implementing a memory-mapped device driver. The buffer pointer is a proxy for the memory address 0xB8000000. Functional programming languages based on lambda-calculus reify the concept of a procedure abstraction and procedure application in the form of the Lambda expression. The Scheme programming language reifies continuations (approximately, the call stack). In C#, reification is used to make parametric polymorphism implemented in the form of generics as a first-class feature of the language. In the Java programming language, there exist "reifiable types" that are "completely available at run time" (i.e. their information is not erased during compilation). REBOL reifies code as data and vice versa. Many languages, such as Lisp, JavaScript, and Curl, provide an eval or evaluate procedure that effectively reifies the language interpreter. Smalltalk and Actor languages permit the reification of blocks and messages, which are equivalent of lambda expressions in Lisp, and thisContext in Smalltalk, which is a reification of the current executing block. Homoiconic languages reify the syntax of the language as data that is understood by the language itself. This allows the user to write programs whose inputs and outputs are code (see macros, eval). Common representations of code include S-expressions (e.g. Clojure, Lisp), and abstract syntax trees (e.g. Rust). == Data reification vs. data refinement == Data reification (stepwise refinement) involves finding a more concrete representation of the abstract data types used in a formal specification. Data reification is the terminology of the Vienna Development Method (VDM) that most other people would call data refinement. An example is taking a step towards an implementation by replacing a data representation without a counterpart in the intended implementation language, such as sets, by one that does have a counterpart (such as maps with fixed domains that can be implemented by arrays), or at least one that is closer to having a counterpart, such as sequences. The VDM community prefers the word "reification" over "refinement", as the process has more to do with concretising an idea than with refining it. For similar usages, see Reification (linguistics). == In conceptual modeling == Reification is widely used in conceptual modeling. Reifying a relationship means viewing it as an entity. The purpose of reifying a relationship is to make it explicit, when additional information needs to be added to it. Consider the relationship type IsMemberOf(member:Person, Committee). An instance of IsMemberOf is a relationship that represents the fact that a person is a member of a committee. The figure below shows an example population of IsMemberOf relationship in tabular form. Person P1 is a member of committees C1 and C2. Person P2 is a member of committee C1 only. The same fact, however, could also be viewed as an entity. Viewing a relationship as an entity, one can say that the entity reifies the relationship. This is called reification of a relationship. Like any other entity, it must be an instance of an entity type. In the present example, the entity type has been named Membership. For each instance of IsMemberOf, there is one and only one instance of Membership, and vice versa. Now, it becomes possible to add more information to the original relationship. As an example, we can express the fact that "person p1 was nominated to be the member of committee c1 by person p2". Reified relationship Membership can be used as the source of a new relationship IsNominatedBy(Membership, Person). For related usages see Reification (knowledge representation). == In Unified Modeling Language (UML) == UML provides an association class construct for defining reified relationship types. The association class is a single model element that is both a kind of association and a kind of class. The association and the entity type that reifies are both the same model element. Note that attributes cannot be reified. == On Semantic Web == === RDF and OWL === In Semantic Web languages, such as Resource Description Framework (RDF) and Web Ontology Language (OWL), a statement is a binary relation. It is used to link two individuals or an individual and a value. Applications sometimes need to describe other RDF statements, for instance, to record information like when statements were made, or who made them, which is sometimes called "provenance" information. As an example, we may want to represent properties of a relation, such as our certainty about it, severity or strength of a relation, relevance of a relation, and so on. The example from the conceptual modeling section describes a particular person with URIref person:p1, who is a member of the committee:c1. The RDF triple from that description is Consider to store two further facts: (i) to record who nominated this particular person to this committee (a statement about the membership itself), and (ii) to record who added the fact to the database (a statement about the statement). The first case is a case of classical reification like above in UML: reify the membership and store its attributes and roles etc.: Additionally, RDF provides a built-in vocabulary intended for describing RDF statements. A description of a statement using this vocabulary is called a reification of the statement. The RDF reification vocabulary consists of the type rdf:Statement, and the properties rdf:subject, rdf:predicate, and rdf:object. Using the reification vocabulary, a reification of the statement about the person's membership would be given by assigning the statement a URIref such as committee:membership12345 so that describing statements can be written as follows: These statements say that the resource identified by the URIref committee:membership12345Stat is an RDF statement, that the subject of the statement refers to the resource identified by person:p1, the predicate of the statement refers to the resource identified by committee:isMemberOf, and the object of the statement refers to the resource committee:c1. Assuming that the original statement is actually identified by committee:membership12345, it should be clear by comparing the original statement with the reification that the reification actually does describe it. The conventional use of the RDF reification vocabulary always involves describing a statement using four statements in this pattern. Therefore, they are sometimes referred to as the "reification quad". Using reification according to this convention, we could record the fact that pe