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Grammatical Inference
Grammar induction (or grammatical inference) is the process in machine learning of learning a formal grammar (usually as a collection of ''re-write rules'' or '' productions'' or alternatively as a finite-state machine or automaton of some kind) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. Grammar classes Grammatical inference has often been very focused on the problem of learning finite-state machines of various types (see the article Induction of regular languages for details on these approaches), since there have been efficient algorithms for this problem since the 1980s. Since the beginning of the century, these approaches have been extended to the problem of inference of context-free grammars and richer formalisms, such as mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Koza
John R. Koza is a computer scientist and a former adjunct professor at Stanford University, most notable for his work in pioneering the use of genetic programming for the optimization of complex problems. Koza co-founded Scientific Games Corporation, a company which builds computer systems to run state lotteries in the United States. John Koza is also credited with being the creator of the ' scratch card' with the help of retail promotions specialist Daniel Bower. Koza was born in 1944 and earned a bachelor's degree in computer science from the University of Michigan, being the second person to ever earn a bachelor's degree in computer science. He earned a doctoral degree in computer science from the University of Michigan in 1972. Koza was featured in Popular Science for his work on evolutionary programming that alters its own code to find far more complex solutions. The machine, which he calls the "invention machine", has created antennae, circuits, and lenses, and has recei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pumping Lemma For Regular Languages
In the theory of formal languages, the pumping lemma for regular languages is a Lemma (mathematics), lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long string (computer science), strings in a regular language may be ''pumped''—that is, have a middle section of the string repeated an arbitrary number of times—to produce a new string that is also part of the language. The pumping lemma is useful for proving that a specific language is not a regular language, by showing that the language does not have the property. Specifically, the pumping lemma says that for any regular language L, there exists a constant p such that any string w in L with length at least p can be split into three substrings x, y and z (w = xyz, with y being non-empty), such that the strings xz, xyz, xyyz, xyyyz, ... are also in L. The process of repeating y zero or more times is known as "pumping". Moreover, the pumping lemma guarantees that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Language (formal Languages)
In theoretical computer science, a pattern language is a formal language that can be defined as the set of all particular instances of a string of constants and variables. Pattern Languages were introduced by Dana Angluin in the context of machine learning. Definition Given a finite set Σ of constant symbols and a countable set ''X'' of variable symbols disjoint from Σ, a pattern is a finite non-empty string of symbols from Σ∪''X''. The length of a pattern ''p'', denoted by , ''p'', , is just the number of its symbols. The set of all patterns containing exactly ''n'' distinct variables (each of which may occur several times) is denoted by ''P''''n'', the set of all patterns at all by ''P''*. A substitution is a mapping ''f'': ''P''* → ''P''* such thatAngluin's notion of substitution differs from the usual notion of string substitution. * ''f'' is a homomorphism with respect to string concatenation (⋅), formally: ∀''p'',''q''∈''P''*. ''f''(''p''⋅''q'') = ''f''(''p' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mildly Context-sensitive Language
In computational linguistics, the term mildly context-sensitive grammar formalisms refers to several grammar formalisms that have been developed in an effort to provide adequate descriptions of the syntactic structure of natural language. Every mildly context-sensitive grammar formalism defines a class of mildly context-sensitive grammars (the grammars that can be specified in the formalism), and therefore also a class of mildly context-sensitive languages (the formal languages generated by the grammars). Background By 1985, several researchers in descriptive and mathematical linguistics had provided evidence against the hypothesis that the syntactic structure of natural language can be adequately described by context-free grammars.Riny Huybregts. "The Weak Inadequacy of Context-Free Phrase Structure Grammars". In Ger de Haan, Mieke Trommelen, and Wim Zonneveld, editors, ''Van periferie naar kern'', pages 81–99. Foris, Dordrecht, The Netherlands, 1984.Stuart M. Shieber.Evide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Byte Pair Encoding
Byte-pair encoding (also known as BPE, or digram coding) is an algorithm, first described in 1994 by Philip Gage, for encoding strings of text into smaller strings by creating and using a translation table. A slightly modified version of the algorithm is used in large language model tokenizers. The original version of the algorithm focused on compression. It replaces the highest-frequency pair of bytes with a new byte that was not contained in the initial dataset. A lookup table of the replacements is required to rebuild the initial dataset. The modified version builds "tokens" (units of recognition) that match varying amounts of source text, from single characters (including single digits or single punctuation marks) to whole words (even long compound words). Original algorithm The original BPE algorithm operates by iteratively replacing the most common contiguous sequences of characters in a target text with unused 'placeholder' bytes. The iteration ends when no sequences can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequitur Algorithm
Sequitur (or Nevill-Manning–Witten algorithm) is a recursive algorithm developed by Craig Nevill-Manning and Ian H. Witten in 1997 that infers a hierarchical structure (context-free grammar) from a sequence of discrete symbols. The algorithm operates in linear space and time. It can be used in data compression software applications. Constraints The sequitur algorithm constructs a grammar by substituting repeating phrases in the given sequence with new rules and therefore produces a concise representation of the sequence. For example, if the sequence is : S→abcab, the algorithm will produce : S→AcA, A→ab. While scanning the input sequence, the algorithm follows two constraints for generating its grammar efficiently: digram uniqueness and rule utility. Digram uniqueness Whenever a new symbol is scanned from the sequence, it is appended with the last scanned symbol to form a new digram. If this digram has been formed earlier then a new rule is made to replace both occurr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form : A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). Regardless of which symbols surround it, the single nonterminal A on the left hand side can always be replaced by \alpha on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form \alpha A \beta \rightarrow \alpha \gamma \beta with A a nonterminal symbol and \alpha, \beta, and \gamma strings of terminal and/or nonterminal symbols. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, : \lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. Specifics Greedy algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Verb Phrase
In linguistics, a verb phrase (VP) is a syntax, syntactic unit composed of a verb and its argument (linguistics), arguments except the subject (grammar), subject of an independent clause or coordinate clause. Thus, in the sentence ''A fat man quickly put the money into the box'', the words ''quickly put the money into the box'' constitute a verb phrase; it consists of the verb ''put'' and its arguments, but not the subject ''a fat man''. A verb phrase is similar to what is considered a ''predicate (grammar), predicate'' in traditional grammars. Verb phrases generally are divided among two types: finite, of which the Head (linguistics), head of the phrase is a finite verb; and nonfinite, where the head is a nonfinite verb, such as an infinitive, participle or gerund. Phrase structure grammars acknowledge both types, but dependency grammars treat the subject as just another verbal dependent, and they do not recognize the finite verbal phrase constituent (linguistics), constituent. Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noun Phrase
A noun phrase – or NP or nominal (phrase) – is a phrase that usually has a noun or pronoun as its head, and has the same grammatical functions as a noun. Noun phrases are very common cross-linguistically, and they may be the most frequently occurring phrase type. Noun phrases often function as verb subjects and objects, as predicative expressions, and as complements of prepositions. One NP can be embedded inside another NP; for instance, ''some of his constituents'' has as a constituent the shorter NP ''his constituents''. In some theories of grammar, noun phrases with determiners are analyzed as having the determiner as the head of the phrase, see for instance Chomsky (1995) and Hudson (1990) . Identification Some examples of noun phrases are underlined in the sentences below. The head noun appears in bold. ::This election-year's politics are annoying for many people. ::Almost every sentence contains at least one noun phrase. ::Current economic weakness may be a re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminal Symbol
In formal languages, terminal and nonterminal symbols are parts of the ''vocabulary'' under a formal grammar. ''Vocabulary'' is a finite, nonempty set of symbols. ''Terminal symbols'' are symbols that cannot be replaced by other symbols of the vocabulary. ''Nonterminal symbols'' are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar. A formal grammar defines a formal language over the vocabulary of the grammar. In the context of formal language, the term ''vocabulary'' is more commonly known as ''alphabet''. Nonterminal symbols are also called ''syntactic variables''. Terminal symbols Terminal symbols are those symbols that can appear in the formal language defined by a formal grammar. The process of applying the production rules successively to a start symbol might not terminate, but if it terminates when there is no more production rule can be applied, the output string will consist only of terminal symb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
