AI Coding Benchmark Ranking

AI Coding Benchmark Ranking — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Document-oriented database

    Document-oriented database

    A document-oriented database, or document store, is a computer program and data storage system designed for storing, retrieving, and managing document-oriented information, also known as semi-structured data. Document-oriented databases are one of the main categories of NoSQL databases, and the popularity of the term "document-oriented database" has grown alongside the adoption of NoSQL itself. XML databases are a subclass of document-oriented databases optimized for XML documents. Graph databases are similar, but add another layer, the relationship, which allows them to link documents for rapid traversal. Document-oriented databases are conceptually an extension of the key–value store, another type of NoSQL database. In key-value stores, data is treated as opaque by the database, whereas document-oriented systems exploit the internal structure of documents to extract metadata and optimize storage and queries. Although in practice the distinction can be minimal due to modern tooling, document stores are designed to provide a richer programming experience with modern programming techniques. Document databases differ significantly from traditional relational databases (RDBs). Relational databases store data in predefined tables, often requiring an object to be split across multiple tables. In contrast, document databases store all information for a given object in a single document, with each document potentially having a unique structure. This design eliminates the need for object-relational mapping when loading data into the database. == Documents == The central concept of a document-oriented database is the notion of a document. Although implementations vary in their specific definitions, document-oriented databases generally treat documents as self-contained units that encapsulate and encode data in a standardized format. Common encoding formats include XML, YAML, JSON, as well as binary representations such as BSON. Documents in a document store are equivalent to the programming concept of an object. They are not required to adhere to a fixed schema, and documents within the same collection may contain different fields or structures. Fields may be optional, and documents of the same logical type may differ in composition. For example, the following illustrates a document encoded in JSON: A second document might be encoded in XML as: The two example documents share some structural elements but also contain unique fields. The structure, text, and other data within each document are collectively referred to as the document's content and can be accessed or modified using retrieval or editing operations. Unlike relational databases, in which each record contains the same fields and unused fields are left empty, document-oriented databases do not require uniform fields across documents. This design allows new information to be added to some documents without affecting the structure of others. Document databases often support the storage of additional metadata alongside the document content. Such metadata may relate to organizational features, security, indexing, or other implementation-specific features. === CRUD operations === The core operations supported by a document-oriented database for manipulating documents are similar to those in other databases. Although terminology is not perfectly standardized, these operations are generally recognized as Create, Read, Update, and Delete (CRUD). Creation (C): Adds a new document to the database. Retrieval (R): Retrieves documents or fields based on queries. Update (U): Modifies the contents of existing documents. Deletion (D): Removes documents from the database. === Keys === Documents in a document-oriented database are addressed via a unique identifier. This identifier, often a string, URI, or path, can be used to retrieve the document from the database. Most document stores maintain an index on the key to optimize retrieval, and in some implementations the key is required when creating or inserting a new document. === Retrieval === In addition to key-based access, document-oriented databases typically provide an API or query language that enables retrieval based on document content or associated metadata. For example, a query may return all documents with a specific field matching a given value. The available query features, indexing options, and performance characteristics vary across implementations. Document stores differ from key-value stores in that they exploit the internal structure and metadata of stored documents. In many key-value stores, values are treated as opaque or "black-box" data, meaning the database system does not interpret their internal structure. By contrast, document-oriented databases can classify and interpret document content. This enables queries that distinguish between types of data––for example, retrieving all phone numbers containing "555" without also matching a postal code such as "55555." === Editing === Document databases typically provide mechanisms for updating or editing the content or metadata of a document. Updates may involve replacing the entire document or modifying individual elements or fields within the document. === Organization === Document database implementations support a variety of methods for organizing documents, including: Collections: Groups of documents. Depending on the implementation, a document may be required to belong to a single collection or may be allowed in multiple collections. Tags and non-visible metadata: Additional data stored outside the main document content. Directory hierarchies: Documents organized in a tree-like structure, often based on path or URI. These organizational structures may differ between logical and physical representations (e.g. on disk or in memory). == Relationship to other databases == === Relationship to key-value stores === A document-oriented database can be viewed as a specialized form of key-value store, which is itself a category of NoSQL database. In a basic key-value store, the stored value is typically treated as opaque by the database system. By contrast, a document-oriented database provides APIs or a query and update language that allows queries and modifications based on the internal structure of the document. For users who do not require advanced query, retrieval, or update capabilities, the distinction between document-oriented databases and key-value stores may be minimal. === Relationship to search engines === Some search engine and information retrieval systems, such as Apache Solr and Elasticsearch, provide document storage and support core document operations. As a result, they may meet certain functional definitions of a document-oriented database, although their primary design goals differ. === Relationship to relational databases === In a relational database, data is organized into predefined types represented as tables. Each table contains rows (records) with a fixed set of columns (fields), so all records in a table share the same structure. Administrators typically define indexes on selected fields to improve query performance. A central principle of relational database design is database normalization, in which data that might otherwise be repeated is stored in separate tables and linked using keys. When records in different tables are related, a foreign key is used to associate them. For example, an address book application may store a contact's name, image, phone numbers, mailing addresses, and email addresses. In a normalized relational design, separate tables might be created for contacts, phone numbers, and email addresses. The phone number table would include a foreign key referencing the associated contact. To reconstruct a complete contact record, the database retrieves related information from each table using the foreign keys and combines it into a single record. In contrast, a document-oriented database stores all data related to an object within a single document, and stored in the database as a single entry. In the address book example,the contact's name, image, and contact information may be stored together in one document. The document is retrieved using a unique key, and all related information is returned together, without needing to look up multiple tables. A key difference between the document-oriented and relational models is that the data formats are not predefined in the document case. In most cases, any sort of document can be stored in a database, and documents can change in type and form over time. For example, a new field such as COUNTRY_FLAG can be added to new documents as they are inserted without affecting existing documents. To aid retrieval, document-oriented systems generally allow the administrator to provide hints to the database for locating certain types of information. These hints work in a similar fashion to indexes in relational databases. Many systems also allow additional metadata outside the content of the document itself

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  • AI Website Builders: Free vs Paid (2026)

    AI Website Builders: Free vs Paid (2026)

    Looking for the best AI website builder? An AI website builder is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI website builder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Lenhart Schubert

    Lenhart Schubert

    Lenhart Karl Otto Schubert is a professor of Computer Science at the University of Rochester, as well as a member of the Center for Language Sciences and the Center for Computation and the Brain. Schubert is a prominent researcher in the field of common sense reasoning. == Biography == Schubert received his Ph.D. from the University of Toronto in 1970. He was on the faculty of the University of Alberta between 1973 and 1988 and joined the faculty at the University of Rochester in 1988. He was elected fellow of Association for Advancement of Artificial Intelligence in 1993 for "fundamental contributions in NLP, esp. in the formalization, representation, and practical implementation of non-first order concepts".

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  • Best AI Blog Writers in 2026

    Best AI Blog Writers in 2026

    Trying to pick the best AI blog writer? An AI blog writer is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI blog writer slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  • Threat actor

    Threat actor

    In cybersecurity and risk assessment, a threat actor (or threat agents, attackers, or adversaries) is a person, group, organisation, state, or other entity with the ability to cause, carry, transmit, support, or exploit a threat. Threat actors are commonly analysed according to their motivations, resources, technical capability, access to systems, relationship to a target, and degree of connection to state authority. They may exploit vulnerabilities, conduct social engineering, steal or monetise data, disrupt operations, or support other actors who carry out such activity. Because the term covers a wide range of actors, researchers and security organisations use taxonomies that distinguish between groups such as cybercriminals, state-linked actors, ideologically motivated actors, thrill seekers or trolls, insiders, and competitors. Threat actor classifications are used in risk management, cyber threat intelligence, and incident response to connect observed behaviour with possible objectives and likely future activity. The categories are not always mutually exclusive: the same actor may combine criminal, ideological, commercial, or state-linked motivations, and different organisations may use different names for similar actors. == Risk assessment and security management == In risk assessment, threat actor analysis is used to identify who or what may create, carry, transmit, support, or exploit a threat, and how that actor relates to the system being assessed. Rausand and Haugen classify threat actors by their relationship to the system, distinguishing between internal and external actors, and by intent, distinguishing between intentional and unintentional actors. Threat actor classification may also support incident investigation. Rogers argued that actor categories could be inferred from observable case points, such as tools used, messages left, data targeted, forensic knowledge, and the degree of damage, allowing investigators to assess likely motivation and skill level. Later work similarly linked actor classification to operational analysis. Chng, Lu, Kumar and Yau proposed a framework connecting hacker types, motivations and typical strategies, arguing that observed behaviour before or during an attack can help analysts infer the likely type of actor involved. At the strategic level, actor analysis may consider an actor's resources, capabilities, degree of state involvement, motivations and objectives. == Landscape == The United Nations Institute for Disarmament Research has described the contemporary cyberthreat landscape as involving an increasingly diverse and interconnected set of actors, including state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, private companies and civilian volunteers. Its 2026 report argued that these actors vary in resources, technical sophistication and relationships with states, making it traditional distinctions between state, civilian combatant roles, and legitimate and illegitimate conduct harder to apply. == Academic taxonomies == Early taxonomies classified hackers by activity, skill, motivation, or criminal profile. Landreth proposed six categories based on activity: novice, student, tourist, crasher, and thief. Hollinger classified computer misuse into pirates, browsers, and crackers, describing a progression from less-skilled activity to more technically serious offences. Chantler used attributes including activity, skill, knowledge, motivation, and duration of involvement to distinguish between an elite group, neophytes, and "losers and lamers". Parker proposed seven profiles of cybercriminals: pranksters, hacksters, malicious hackers, personal problem solvers, career criminals, extreme advocates, and malcontents, addicts, and irrational or incompetent people. In 2000, Marc Rogers proposed a taxonomy of hackers with seven, non-mutually-exclusive categories: newbie/tool kit users, cyber-punks, internals, coders, old guard hackers, professional criminals, and cyber-terrorists. Rausand and Haugen distinguish between internal and external threat actors, and between intentional and unintentional threat actors. Internal actors have some relationship with, access to, or position inside the system or organisation, while external actors operate from outside it. Intentional actors seek to create, exploit, or support a threat event, whereas unintentional actors may cause or enable a threat event through error, negligence, accident, or lack of awareness. Rogers later revised his hacker taxonomy into Novices, Cyber-punks, Internals, Petty Thieves, Virus Writers, Old Guard hackers, Professional Criminals, Information Warriors, and, more tentatively, Political Activists. In the model, motivation is grouped into four broad domains: curiosity, notoriety, revenge, and financial gain. A 2022 review by Chng, Lu, Kumar and Yau examined 11 hacker typologies published over three decades and proposed a unified framework linking hacker types, motivations, and strategies. The framework identified 13 hacker types and seven motivations, and argued that observed strategies during an attack can help analysts infer the likely type of actor involved. == Government taxonomies == Taxonomies of threat actors by governments are much more likely to include state-level threat actors. In the United States the National Institute of Standards and Technology (NIST) uses the term threat source in its risk-assessment guidance: organisations are directed to identify and characterise threat sources of concern, including capability, intent and targeting for adversarial threat sources, and the range of effects for non-adversarial threat sources. NIST treats threat-source identification as part of the risk-assessment process, alongside identifying threat events, vulnerabilities, likelihood and impact. In the EU, European Union Agency for Cybersecurity publishes the annual ENISA Threat Landscape, which analyses cyber incidents and adversary behaviour affecting the European Union. The 2025 report analysed selected incidents from the previous year and grouped activity around cybercrime, state-aligned activity, foreign information manipulation and interference, and hacktivism. In ENISA's 2025 analysis, hacktivist activity dominated reporting, representing almost 80% of recorded incidents and consisting mainly of low-level distributed denial-of-service operations. ENISA also reported increasing convergence between hacktivism, cybercrime and state-nexus activity, including state-aligned use of hacktivist personas, hacktivist adoption of ransomware, and false-flag or impersonation activity. At the UN level, A 2026 report by the United Nations Institute for Disarmament Research described the cyberthreat landscape as involving state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, and civilian volunteers, with actors varying in resources, technical sophistication, and links to states. Canada defines threat actors as states, groups, or individuals who aim to cause harm by exploiting a vulnerability with malicious intent. A threat actor must be trying to gain access to information systems to access or alter data, devices, systems, or networks. The Japanese government's National Centre of Incident Readiness and Strategy (NISC) was established in 2015 to create a "free, fair and secure cyberspace" in Japan. The NICS created a cybersecurity strategy in 2018 that outlines nation-states and cybercrime to be some of the most key threats. It also indicates that terrorist usage of the cyberspace needs to be monitored and understood. The Security Council of the Russian Federation published the cyber security strategy doctrine in 2016. This strategy highlights the following threat actors as a risk to cyber security measures: nation-state actors, cyber criminals, and terrorists. == Techniques == Threat actors use techniques like Social engineering (security), and Phishing, alongside technical exploits like Cross-site scripting, SQL injection, and denial-of-service attacks. == Limitations == In practice, actor categories may overlap (Edward Snowden for example), and the same activity may combine features associated with hacktivism, cybercrime and state-linked operations. The lines between hacktivism, cybercrime and state-nexus activity had continued to blur, with shared toolsets, overlapping methods, fake personas, hacktivist adoption of ransomware, and cybercriminal or state-linked actors masquerading as other groups. Threat actor analysis also has limits as a risk-management method. NIST notes that risk assessments depend on their purpose, scope, assumptions, constraints, information sources, risk model and analytic approach, and that assessments are tied to particular time frames and organisational contexts. NIST also warns that simple threat-vulnerability pairing may be undesirable or problematic where there are many threats and vulnerabilities, and recom

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  • Corpus-assisted discourse studies

    Corpus-assisted discourse studies

    Corpus-assisted discourse studies (abbr.: CADS) is related historically and methodologically to the discipline of corpus linguistics. The principal endeavor of corpus-assisted discourse studies is the investigation, and comparison of features of particular discourse types, integrating into the analysis the techniques and tools developed within corpus linguistics. These include the compilation of specialised corpora and analyses of word and word-cluster frequency lists, comparative keyword lists and, above all, concordances. A broader conceptualisation of corpus-assisted discourse studies would include any study that aims to bring together corpus linguistics and discourse analysis. Such research is often labelled as corpus-based or corpus-assisted discourse analysis, with the term CADS coined by a research group in Italy (Partington 2004) for a specific type of corpus-assisted discourse analysis (see the section 'in different countries' below). == Aims == Corpus-assisted discourse studies aim to uncover non-obvious meaning, that is, meaning which might not be readily available to naked-eye perusal. Much of what carries meaning in texts is not open to direct observation: “you cannot understand the world just by looking at it” (Stubbs [after Gellner 1959] 1996: 92). We use language “semi-automatically”, in the sense that speakers and writers make semi-conscious choices within the various complex overlapping systems of which language is composed, including those of transitivity, modality (Michael Halliday 1994), lexical sets (e.g. freedom, liberty, deliverance), modification, and so on. Authors themselves are, famously, generally unaware of all the meanings their texts convey. By combining the quantitative research approach, that is, statistical analysis of large amounts of the discourse in question - more precisely, large numbers of tokens of the discourse type under study contained in a corpus - with the more qualitative research approach typical of discourse analysis, that is, the close, detailed examination of particular stretches of discourse it may be possible to better understand the processes at play in the discourse type and to gain access to non-obvious meanings. Aims can differ in other types of corpus-based or corpus-assisted discourse analysis; but in general such studies combine quantitative and qualitative research and aim to shed light on discourses, registers, discourse patterns, etc., with the help of a corpus linguistic approach. Specific aims and techniques depend on the relevant project. == In different countries == In German-speaking countries: Pioneering work in corpus-based discourse analysis was conducted in Europe, in particular by Hardt-Mautner/Mautner (1995, 2000) and Stubbs (1996, 2001). CADS and other types of corpus-based discourse analysis are inspired by this important early work. In Italy: A considerable body of research has been conducted in Italy either by individual researchers or under the aegis of combined inter-university projects such as Newspool (Partington et al. 2004) and CorDis (Morley and Bayley eds, 2009). It has concentrated on political and media language, mainly because a nucleus of linguists in Italian universities work in Political Science faculties and are increasingly interested in the use of corpus techniques to conduct a particular type of sociopolitical discourse analysis, including the unearthing of noteworthy ideological metaphors and motifs in the language of political figures and institutions. Italian researchers also developed Modern diachronic corpus-assisted discourse studies (MD-CADS). This approach contrasts the language contained in comparable corpora from different but recent points in time in order to track changes in modern language usage but also social, cultural and political changes over modern times, as reflected - and shared among people - in language. It is this Italian body of research that makes most use of the label CADS. In the UK: Linguists in the UK tend to undertake corpus-based critical discourse analysis (CDA). CDA generally adopts a leftist political stance, focusing on the ways that social and political domination is reproduced by text and talk. This type of corpus-based research was originally associated with Lancaster University (Baker et al. 2008), but has spread more widely since. Such work typically studies the discourses around particular groups of people (e.g. Muslims, people with disabilities) or concepts/events (e.g. feminism, same-sex marriage). In Australia: Corpus-based discourse analysis is undertaken by a growing number of Australian researchers, most often on media texts. Some of this work aims to elucidate specific features of discourse types (news, social media, television series, etc.), while other work is rooted in the tradition of corpus-based critical discourse analysis. == Comparison with traditional corpus linguistics == Traditional corpus linguistics has, quite naturally, tended to privilege the quantitative approach. In the drive to produce more authentic dictionaries and grammars of a language, it has been characterised by the compilation of some very large corpora of heterogeneric discourse types in the desire to obtain an overview of the greatest quantity and variety of discourse types possible, in other words, of the chimerical but useful fiction called the “general language” (“general English”, “general Italian”, and so on). This has led to the construction of immensely valuable research tools such as the Bank of English and the British National Corpus. Some branches of corpus linguistics have also promoted an approach that is "corpus-driven", in which we need, grammatically speaking, a mental tabula rasa to free ourselves of the baleful prejudice exerted by traditional models and allow the data to speak entirely for itself. The aim of corpus-assisted discourse studies and related approaches is radically different. Here the aim of the exercise is to acquaint oneself as much as possible with the discourse type(s) in hand. Researchers typically engage with their corpus in a variety of ways. As well as via wordlists and concordancing, intuitions for further research can also arise from reading or watching or listening to parts of the data-set, a process which can help provide a feel for how things are done linguistically in the discourse-type being studied. Corpus-assisted discourse analysis is also typically characterised by the compilation of ad hoc specialised corpora, since very frequently there exists no previously available collection of the discourse type in question. Often, other corpora are utilized in the course of a study for purposes of comparison. These may include pre-existing corpora or may themselves need to be compiled by the researcher. In some sense, all work with corpora – just as all work with discourse - is properly comparative. Even when a single corpus is employed, it is used to test the data it contains against another body of data. This may consist of the researcher's intuitions, or the data found in reference works such as dictionaries and grammars, or it may be statements made by previous authors in the field. == CADS as a specific type of corpus-based discourse analysis == Researchers in Italy have developed CADS as a specific type of corpus-based discourse analysis, creating a standard set of methods: 'A basic, standard methodology in CADS may resemble the following:' Step 1: Decide upon the research question; Step 2: Choose, compile or edit an appropriate corpus; Step 3: Choose, compile or edit an appropriate reference corpus / corpora; Step 4: Make frequency lists and run a keywords comparison of the corpora; Step 5: Determine the existence of sets of key items; Step 6: Concordance interesting key items (with differing quantities of co-text); Step 7: (Possibly) refine the research question and return to Step 2. This basic procedure can of course vary according to individual research circumstances and requirements. A particular way of conceptualising research questions has also been proposed in such CADS projects: Given that P is a discourse participant (or possibly an institution) and G is a goal, often a political goal: How does P achieve G with language? What does this tell us about P? Comparative studies: how do P1 and P2 differ in their use of language? Does this tell us anything about their different principles and objectives? A second general type of CADS research question, which might be asked of interactive discourse data, has been conceptualised as follows: Given that P(x) is a particular participant or set of participants, DT is the discourse type, and R is an observed relationship between or among participants: How do {P(a), P(b)...P(n)} achieve / maintain R in DT [using language]? Another common type of research question has been conceptualised thus: Given that A is an author, Ph(x) is a phenomenon or practice or behaviour, and DT(x) is a particular discourse type. A has said P

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  • AI Marketing Tools: Free vs Paid (2026)

    AI Marketing Tools: Free vs Paid (2026)

    Shopping for the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Dilek Hakkani-Tür

    Dilek Hakkani-Tür

    Dilek Z. Hakkani-Tür is a Turkish-American computer scientist focusing on speech processing, speech recognition, and dialogue systems. She is a professor of computer science at the University of Illinois Urbana-Champaign. == Education and career == Hakkani-Tür is a 1994 graduate of Middle East Technical University in Ankara, Turkey. She continued her studies at Bilkent University, also in Ankara, where she earned a master's degree in 1996 and completed her Ph.D. in 2000. She worked as a researcher at AT&T Labs from 2001 to 2005, at the International Computer Science Institute from 2006 to 2010, at Microsoft Research from 2010 to 2016, at Google Research from 2016 to 2018, and at Amazon Alexa from 2018 to 2023. At Microsoft, she was in the team of scientists that built the first prototype of the Cortana virtual assistant. While working for Amazon Alexa, she also taught at the University of California, Santa Cruz as a distinguished visiting instructor. She joined the University of Illinois Urbana-Champaign faculty in 2023. She was editor-in-chief of IEEE/ACM Transactions on Audio, Speech and Language Processing from 2019 to 2021, and is president of the Special Interest Group on Discourse and Dialogue of the Association for Computational Linguistics for the 2023–2025 term. She has served as co-editor-in-chief of Transactions of the Association for Computational Linguistics since 2024. == Recognition == In 2014, Hakkani-Tür was elected as an IEEE Fellow "for contributions to spoken language processing", and as a Fellow of the International Speech Communication Association "for contributions to advancing the state-of-the-art in spoken language processing, especially for human/human and human/machine conversational understanding". In 2024, she was elected as a Fellow of the Association for Computational Linguistics for her contributions to spoken dialogue systems.

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  • Autonomic networking

    Autonomic networking

    Autonomic networking follows the concept of Autonomic Computing, an initiative started by IBM in 2001. Its ultimate aim is to create self-managing networks to overcome the rapidly growing complexity of the Internet and other networks and to enable their further growth, far beyond the size of today. == Increasing size and complexity == The ever-growing management complexity of the Internet caused by its rapid growth is seen by some experts as a major problem that limits its usability in the future. What's more, increasingly popular smartphones, PDAs, networked audio and video equipment, and game consoles need to be interconnected. Pervasive Computing not only adds features, but also burdens existing networking infrastructure with more and more tasks that sooner or later will not be manageable by human intervention alone. Another important aspect is the price of manually controlling huge numbers of vitally important devices of current network infrastructures. == Autonomic nervous system == The autonomic nervous system (ANS) is the part of complex biological nervous systems that is not consciously controlled. It regulates bodily functions and the activity of specific organs. As proposed by IBM, future communication systems might be designed in a similar way to the ANS. == Components of autonomic networking == As autonomics conceptually derives from biological entities such as the human autonomic nervous system, each of the areas can be metaphorically related to functional and structural aspects of a living being. In the human body, the autonomic system facilitates and regulates a variety of functions including respiration, blood pressure and circulation, and emotive response. The autonomic nervous system is the interconnecting fabric that supports feedback loops between internal states and various sources by which internal and external conditions are monitored. === Autognostics === Autognostics includes a range of self-discovery, awareness, and analysis capabilities that provide the autonomic system with a view on high-level state. In metaphor, this represents the perceptual sub-systems that gather, analyze, and report on internal and external states and conditions – for example, this might be viewed as the eyes, visual cortex and perceptual organs of the system. Autognostics, or literally "self-knowledge", provides the autonomic system with a basis for response and validation. A rich autognostic capability may include many different "perceptual senses". For example, the human body gathers information via the usual five senses, the so-called sixth sense of proprioception (sense of body position and orientation), and through emotive states that represent the gross wellness of the body. As conditions and states change, they are detected by the sensory monitors and provide the basis for adaptation of related systems. Implicit in such a system are imbedded models of both internal and external environments such that relative value can be assigned to any perceived state - perceived physical threat (e.g. a snake) can result in rapid shallow breathing related to fight-flight response, a phylogenetically effective model of interaction with recognizable threats. In the case of autonomic networking, the state of the network may be defined by inputs from: individual network elements such as switches and network interfaces including specification and configuration historical records and current state traffic flows end-hosts application performance data logical diagrams and design specifications Most of these sources represent relatively raw and unprocessed views that have limited relevance. Post-processing and various forms of analysis must be applied to generate meaningful measurements and assessments against which current state can be derived. The autognostic system interoperates with: configuration management - to control network elements and interfaces policy management - to define performance objectives and constraints autodefense - to identify attacks and accommodate the impact of defensive responses === Configuration management === Configuration management is responsible for the interaction with network elements and interfaces. It includes an accounting capability with historical perspective that provides for the tracking of configurations over time, with respect to various circumstances. In the biological metaphor, these are the hands and, to some degree, the memory of the autonomic system. On a network, remediation and provisioning are applied via configuration setting of specific devices. Implementation affecting access and selective performance with respect to role and relationship are also applied. Almost all the "actions" that are currently taken by human engineers fall under this area. With only a few exceptions, interfaces are set by hand, or by extension of the hand, through automated scripts. Implicit in the configuration process is the maintenance of a dynamic population of devices under management, a historical record of changes and the directives which invoked change. Typical to many accounting functions, configuration management should be capable of operating on devices and then rolling back changes to recover previous configurations. Where change may lead to unrecoverable states, the sub-system should be able to qualify the consequences of changes prior to issuing them. As directives for change must originate from other sub-systems, the shared language for such directives must be abstracted from the details of the devices involved. The configuration management sub-system must be able to translate unambiguously between directives and hard actions or to be able to signal the need for further detail on a directive. An inferential capacity may be appropriate to support sufficient flexibility (i.e. configuration never takes place because there is no unique one-to-one mapping between directive and configuration settings). Where standards are not sufficient, a learning capacity may also be required to acquire new knowledge of devices and their configuration. Configuration management interoperates with all of the other sub-systems including: autognostics - receives direction for and validation of changes policy management - implements policy models through mapping to underlying resources security - applies access and authorization constraints for particular policy targets autodefense - receives direction for changes === Policy management === Policy management includes policy specification, deployment, reasoning over policies, updating and maintaining policies, and enforcement. Policy-based management is required for: constraining different kinds of behavior including security, privacy, resource access, and collaboration configuration management describing business processes and defining performance defining role and relationship, and establishing trust and reputation It provides the models of environment and behavior that represent effective interaction according to specific goals. In the human nervous system metaphor, these models are implicit in the evolutionary "design" of biological entities and specific to the goals of survival and procreation. Definition of what constitutes a policy is necessary to consider what is involved in managing it. A relatively flexible and abstract framework of values, relationships, roles, interactions, resources, and other components of the network environment is required. This sub-system extends far beyond the physical network to the applications in use and the processes and end-users that employ the network to achieve specific goals. It must express the relative values of various resources, outcomes, and processes and include a basis for assessing states and conditions. Unless embodied in some system outside the autonomic network or implicit to the specific policy implementation, the framework must also accommodate the definition of process, objectives and goals. Business process definitions and descriptions are then an integral part of the policy implementation. Further, as policy management represents the ultimate basis for the operation of the autonomic system, it must be able to report on its operation with respect to the details of its implementation. The policy management sub-system interoperates (at least) indirectly with all other sub-systems but primarily interacts with: autognostics - providing the definition of performance and accepting reports on conditions configuration management - providing constraints on device configuration security - providing definitions of roles, access and permissions === Autodefense === Autodefense represents a dynamic and adaptive mechanism that responds to malicious and intentional attacks on the network infrastructure, or use of the network infrastructure to attack IT resources. As defensive measures tend to impede the operation of IT, it is optimally capable of balancing performance objectives with typically over-riding threat management actions. In the

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  • Regularization perspectives on support vector machines

    Regularization perspectives on support vector machines

    Within mathematical analysis, Regularization perspectives on support-vector machines provide a way of interpreting support-vector machines (SVMs) in the context of other regularization-based machine-learning algorithms. SVM algorithms categorize binary data, with the goal of fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting via Tikhonov regularization and in the L2 norm sense and also corresponds to minimizing the bias and variance of our estimator of the weights. Estimators with lower Mean squared error predict better or generalize better when given unseen data. Specifically, Tikhonov regularization algorithms produce a decision boundary that minimizes the average training-set error and constrain the Decision boundary not to be excessively complicated or overfit the training data via a L2 norm of the weights term. The training and test-set errors can be measured without bias and in a fair way using accuracy, precision, Auc-Roc, precision-recall, and other metrics. Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize without overfitting. SVM was first proposed in 1995 by Corinna Cortes and Vladimir Vapnik, and framed geometrically as a method for finding hyperplanes that can separate multidimensional data into two categories. This traditional geometric interpretation of SVMs provides useful intuition about how SVMs work, but is difficult to relate to other machine-learning techniques for avoiding overfitting, like regularization, early stopping, sparsity and Bayesian inference. However, once it was discovered that SVM is also a special case of Tikhonov regularization, regularization perspectives on SVM provided the theory necessary to fit SVM within a broader class of algorithms. This has enabled detailed comparisons between SVM and other forms of Tikhonov regularization, and theoretical grounding for why it is beneficial to use SVM's loss function, the hinge loss. == Theoretical background == In the statistical learning theory framework, an algorithm is a strategy for choosing a function f : X → Y {\displaystyle f\colon \mathbf {X} \to \mathbf {Y} } given a training set S = { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle S=\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\}} of inputs x i {\displaystyle x_{i}} and their labels y i {\displaystyle y_{i}} (the labels are usually ± 1 {\displaystyle \pm 1} ). Regularization strategies avoid overfitting by choosing a function that fits the data, but is not too complex. Specifically: f = argmin f ∈ H { 1 n ∑ i = 1 n V ( y i , f ( x i ) ) + λ ‖ f ‖ H 2 } , {\displaystyle f={\underset {f\in {\mathcal {H}}}{\operatorname {argmin} }}\left\{{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},f(x_{i}))+\lambda \|f\|_{\mathcal {H}}^{2}\right\},} where H {\displaystyle {\mathcal {H}}} is a hypothesis space of functions, V : Y × Y → R {\displaystyle V\colon \mathbf {Y} \times \mathbf {Y} \to \mathbb {R} } is the loss function, ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} is a norm on the hypothesis space of functions, and λ ∈ R {\displaystyle \lambda \in \mathbb {R} } is the regularization parameter. When H {\displaystyle {\mathcal {H}}} is a reproducing kernel Hilbert space, there exists a kernel function K : X × X → R {\displaystyle K\colon \mathbf {X} \times \mathbf {X} \to \mathbb {R} } that can be written as an n × n {\displaystyle n\times n} symmetric positive-definite matrix K {\displaystyle \mathbf {K} } . By the representer theorem, f ( x i ) = ∑ j = 1 n c j K i j , and ‖ f ‖ H 2 = ⟨ f , f ⟩ H = ∑ i = 1 n ∑ j = 1 n c i c j K ( x i , x j ) = c T K c . {\displaystyle f(x_{i})=\sum _{j=1}^{n}c_{j}\mathbf {K} _{ij},{\text{ and }}\|f\|_{\mathcal {H}}^{2}=\langle f,f\rangle _{\mathcal {H}}=\sum _{i=1}^{n}\sum _{j=1}^{n}c_{i}c_{j}K(x_{i},x_{j})=c^{T}\mathbf {K} c.} == Special properties of the hinge loss == The simplest and most intuitive loss function for categorization is the misclassification loss, or 0–1 loss, which is 0 if f ( x i ) = y i {\displaystyle f(x_{i})=y_{i}} and 1 if f ( x i ) ≠ y i {\displaystyle f(x_{i})\neq y_{i}} , i.e. the Heaviside step function on − y i f ( x i ) {\displaystyle -y_{i}f(x_{i})} . However, this loss function is not convex, which makes the regularization problem very difficult to minimize computationally. Therefore, we look for convex substitutes for the 0–1 loss. The hinge loss, V ( y i , f ( x i ) ) = ( 1 − y f ( x ) ) + {\displaystyle V{\big (}y_{i},f(x_{i}){\big )}={\big (}1-yf(x){\big )}_{+}} , where ( s ) + = max ( s , 0 ) {\displaystyle (s)_{+}=\max(s,0)} , provides such a convex relaxation. In fact, the hinge loss is the tightest convex upper bound to the 0–1 misclassification loss function, and with infinite data returns the Bayes-optimal solution: f b ( x ) = { 1 , p ( 1 ∣ x ) > p ( − 1 ∣ x ) , − 1 , p ( 1 ∣ x ) < p ( − 1 ∣ x ) . {\displaystyle f_{b}(x)={\begin{cases}1,&p(1\mid x)>p(-1\mid x),\\-1,&p(1\mid x) Read more →

  • Pedro Domingos

    Pedro Domingos

    Pedro Domingos (born 1965) is a Professor Emeritus of computer science and engineering at the University of Washington. He is a researcher in machine learning known for Markov logic network enabling uncertain inference. == Education == Domingos received an undergraduate degree and Master of Science degree from Instituto Superior Técnico (IST). He moved to the University of California, Irvine, where he received a Master of Science degree followed by his PhD. == Research and career == After spending two years as an assistant professor at IST, he joined the University of Washington as an assistant professor of Computer Science and Engineering in 1999 and became a full professor in 2012. He started a machine learning research group at the hedge fund D. E. Shaw & Co. in 2018, but left in 2019. He co-founded the International Machine Learning Society. As of 2018, he was on the editorial board of Machine Learning journal. === Publications === Pedro Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World, New York, Basic Books, 2015, ISBN 978-0-465-06570-7. Pedro Domingos, "Our Digital Doubles: AI will serve our species, not control it", Scientific American, vol. 319, no. 3 (September 2018), pp. 88–93. "AIs are like autistic savants and will remain so for the foreseeable future.... AIs lack common sense and can easily make errors that a human never would... They are also liable to take our instructions too literally, giving us precisely what we asked for instead of what we actually wanted." (p. 93.) Pedro Domingos, 2040: A Silicon Valley Satire, BookBaby, 2024, ISBN 979-8-350-96334-2. === Awards and honors === 2014: ACM SIGKDD Innovation Award. for his foundational research in data stream analysis, cost-sensitive classification, adversarial learning, and Markov logic networks, as well as applications in viral marketing and information integration. 2010: Elected an Association for the Advancement of Artificial Intelligence (AAAI) Fellow. For significant contributions to the field of machine learning and to the unification of first-order logic and probability. 2003: Sloan Fellowship 1992–1997: Fulbright Scholarship

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  • How to Choose an AI Photo Editor

    How to Choose an AI Photo Editor

    In search of the best AI photo editor? An AI photo editor is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI photo editor slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  • Orleans (software framework)

    Orleans (software framework)

    Orleans is a cross-platform software framework for building scalable and robust distributed interactive applications based on the .NET Framework or on the more recent .NET. == Overview == Orleans was originally created by the eXtreme Computing Group at Microsoft Research and introduced the virtual actor model as a new approach to building distributed systems for the cloud. Orleans scales from a single on-premises server to highly-available and globally distributed applications in the cloud. The virtual actor model is based on the actor model but has several differences: A virtual actor always exists, it cannot be explicitly created or destroyed. Virtual actors are automatically instantiated. If a server hosting an actor crashes, the next message sent to the actor causes it to be reinstantiated automatically. The server that an actor is on is transparent to the application code. Orleans can automatically create multiple instances of the same stateless actor. Starting with cloud services for the Halo franchise, the framework has been used by a number of cloud services at Microsoft and other companies since 2011. The core Orleans technology was transferred to 343 Industries and is available as open source since January 2015. The source code is licensed under MIT License and hosted on GitHub. Orleans runs on Microsoft Windows, Linux, and macOS and is compatible with .NET Standard 2.0 and above. == Features == Some Orleans features include: Persistence Distributed ACID transactions Streams Timers & Reminders Fault tolerance == Related implementations == The Electronic Arts BioWare division created Project Orbit. It is a Java implementation of virtual actors that was heavily inspired by the Orleans project.

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  • Unsupervised learning

    Unsupervised learning

    Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, where a small portion of the data is tagged, and self-supervision. Some researchers consider self-supervised learning a form of unsupervised learning. Conceptually, unsupervised learning divides into the aspects of data, training, algorithm, and downstream applications. Typically, the dataset is harvested cheaply "in the wild", such as massive text corpus obtained by web crawling, with only minor filtering (such as Common Crawl). This compares favorably to supervised learning, where the dataset (such as the ImageNet1000) is typically constructed manually, which is much more expensive. There are algorithms designed specifically for unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques like principal component analysis (PCA), Boltzmann machine learning, and autoencoders. After the rise of deep learning, most large-scale unsupervised learning has been done by training general-purpose neural network architectures by gradient descent, adapted to performing unsupervised learning by designing an appropriate training procedure. Sometimes a trained model can be used as-is, but more often they are modified for downstream applications. For example, the generative pretraining method trains a model to generate a textual dataset, before finetuning it for other applications, such as text classification. As another example, autoencoders are trained to produce good features, which can then be used as a module for other models, such as in a latent diffusion model. == Tasks == Tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see Venn diagram); however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups. Furthermore, as progress marches onward, some tasks employ both methods, and some tasks swing from one to another. For example, image recognition started off as heavily supervised, but became hybrid by employing unsupervised pre-training, and then moved towards supervision again with the advent of dropout, ReLU, and adaptive learning rates. A typical generative task is as follows. At each step, a datapoint is sampled from the dataset, and part of the data is removed, and the model must infer the removed part. This is particularly clear for the denoising autoencoders and BERT. == Neural network architectures == === Training === During the learning phase, an unsupervised network tries to mimic the data it is given and uses the error in its mimicked output to correct itself (i.e. correct its weights and biases). Sometimes the error is expressed as a low probability that the erroneous output occurs, or it might be expressed as an unstable high energy state in the network. In contrast to supervised methods' dominant use of backpropagation, unsupervised learning also employs other methods including: Hopfield learning rule, Boltzmann learning rule, Contrastive Divergence, Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling, and backpropagating reconstruction errors or hidden state reparameterizations. See the table below for more details. === Energy === An energy function is a macroscopic measure of a network's activation state. In Boltzmann machines, it plays the role of the Cost function. This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion p ∝ e − E / k T {\displaystyle p\propto e^{-E/kT}} , where k is the Boltzmann constant and T is temperature. In the RBM network the relation is p = e − E / Z {\displaystyle p=e^{-E}/Z} , where p {\displaystyle p} and E {\displaystyle E} vary over every possible activation pattern and Z = ∑ All Patterns e − E ( pattern ) {\displaystyle \textstyle {Z=\sum _{\scriptscriptstyle {\text{All Patterns}}}e^{-E({\text{pattern}})}}} . To be more precise, p ( a ) = e − E ( a ) / Z {\displaystyle p(a)=e^{-E(a)}/Z} , where a {\displaystyle a} is an activation pattern of all neurons (visible and hidden). Hence, some early neural networks bear the name Boltzmann Machine. Paul Smolensky calls − E {\displaystyle -E\,} the Harmony. A network seeks low energy which is high Harmony. === Networks === This table shows connection diagrams of various unsupervised networks, the details of which will be given in the section Comparison of Networks. Circles are neurons and edges between them are connection weights. As network design changes, features are added on to enable new capabilities or removed to make learning faster. For instance, neurons change between deterministic (Hopfield) and stochastic (Boltzmann) to allow robust output, weights are removed within a layer (RBM) to hasten learning, or connections are allowed to become asymmetric (Helmholtz). Of the networks bearing people's names, only Hopfield worked directly with neural networks. Boltzmann and Helmholtz came before artificial neural networks, but their work in physics and physiology inspired the analytical methods that were used. === History === === Specific Networks === Here, we highlight some characteristics of select networks. The details of each are given in the comparison table below. Hopfield Network Ferromagnetism inspired Hopfield networks. A neuron corresponds to an iron domain with binary magnetic moments Up and Down, and neural connections correspond to the domain's influence on each other. Symmetric connections enable a global energy formulation. During inference the network updates each state using the standard activation step function. Symmetric weights and the right energy functions guarantees convergence to a stable activation pattern. Asymmetric weights are difficult to analyze. Hopfield nets are used as Content Addressable Memories (CAM). Boltzmann Machine These are stochastic Hopfield nets. Their state value is sampled from this pdf as follows: suppose a binary neuron fires with the Bernoulli probability p(1) = 1/3 and rests with p(0) = 2/3. One samples from it by taking a uniformly distributed random number y, and plugging it into the inverted cumulative distribution function, which in this case is the step function thresholded at 2/3. The inverse function = { 0 if x <= 2/3, 1 if x > 2/3 }. Sigmoid Belief Net Introduced by Radford Neal in 1992, this network applies ideas from probabilistic graphical models to neural networks. A key difference is that nodes in graphical models have pre-assigned meanings, whereas Belief Net neurons' features are determined after training. The network is a sparsely connected directed acyclic graph composed of binary stochastic neurons. The learning rule comes from Maximum Likelihood on p(X): Δwij ∝ {\displaystyle \propto } sj (si - pi), where pi = 1 / ( 1 + eweighted inputs into neuron i ). sj's are activations from an unbiased sample of the posterior distribution and this is problematic due to the Explaining Away problem raised by Judea Perl. Variational Bayesian methods uses a surrogate posterior and blatantly disregard this complexity. Deep Belief Network Introduced by Hinton, this network is a hybrid of RBM and Sigmoid Belief Network. The top 2 layers is an RBM and the second layer downwards form a sigmoid belief network. One trains it by the stacked RBM method and then throw away the recognition weights below the top RBM. As of 2009, 3-4 layers seems to be the optimal depth. Helmholtz machine These are early inspirations for the Variational Auto Encoders. Its 2 networks combined into one—forward weights operates recognition and backward weights implements imagination. It is perhaps the first network to do both. Helmholtz did not work in machine learning but he inspired the view of "statistical inference engine whose function is to infer probable causes of sensory input". the stochastic binary neuron outputs a probability that its state is 0 or 1. The data input is normally not considered a layer, but in the Helmholtz machine generation mode, the data layer receives input from the middle layer and has separate weights for this purpose, so it is considered a layer. Hence this network has 3 layers. Variational autoencoder These are inspired by Helmholtz machines and combines probability network with neural networks. An Autoencoder is a 3-layer CAM network, where the middle layer is supposed to be some internal representation of input patterns. The encoder neural network is a probability distribution qφ(z given x) and the decoder network is pθ(x given z). The weights are named phi & theta rather than W and V as in Helmholtz—a cosmetic difference. These 2 networks h

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  • Katz's back-off model

    Katz's back-off model

    Katz back-off is a generative n-gram language model that estimates the conditional probability of a word given its history in the n-gram. It accomplishes this estimation by backing off through progressively shorter history models under certain conditions. By doing so, the model with the most reliable information about a given history is used to provide the better results. The model was introduced in 1987 by Slava M. Katz. Prior to that, n-gram language models were constructed by training individual models for different n-gram orders using maximum likelihood estimation and then interpolating them together. == Method == The equation for Katz's back-off model is: P b o ( w i ∣ w i − n + 1 ⋯ w i − 1 ) = { d w i − n + 1 ⋯ w i C ( w i − n + 1 ⋯ w i − 1 w i ) C ( w i − n + 1 ⋯ w i − 1 ) if C ( w i − n + 1 ⋯ w i ) > k α w i − n + 1 ⋯ w i − 1 P b o ( w i ∣ w i − n + 2 ⋯ w i − 1 ) otherwise {\displaystyle {\begin{aligned}&P_{bo}(w_{i}\mid w_{i-n+1}\cdots w_{i-1})\\[4pt]={}&{\begin{cases}d_{w_{i-n+1}\cdots w_{i}}{\dfrac {C(w_{i-n+1}\cdots w_{i-1}w_{i})}{C(w_{i-n+1}\cdots w_{i-1})}}&{\text{if }}C(w_{i-n+1}\cdots w_{i})>k\\[10pt]\alpha _{w_{i-n+1}\cdots w_{i-1}}P_{bo}(w_{i}\mid w_{i-n+2}\cdots w_{i-1})&{\text{otherwise}}\end{cases}}\end{aligned}}} where C(x) = number of times x appears in training wi = ith word in the given context Essentially, this means that if the n-gram has been seen more than k times in training, the conditional probability of a word given its history is proportional to the maximum likelihood estimate of that n-gram. Otherwise, the conditional probability is equal to the back-off conditional probability of the (n − 1)-gram. The more difficult part is determining the values for k, d and α. k {\displaystyle k} is the least important of the parameters. It is usually chosen to be 0. However, empirical testing may find better values for k. d {\displaystyle d} is typically the amount of discounting found by Good–Turing estimation. In other words, if Good–Turing estimates C {\displaystyle C} as C ∗ {\displaystyle C^{}} , then d = C ∗ C {\displaystyle d={\frac {C^{}}{C}}} To compute α {\displaystyle \alpha } , it is useful to first define a quantity β, which is the left-over probability mass for the (n − 1)-gram: β w i − n + 1 ⋯ w i − 1 = 1 − ∑ { w i : C ( w i − n + 1 ⋯ w i ) > k } d w i − n + 1 ⋯ w i C ( w i − n + 1 ⋯ w i − 1 w i ) C ( w i − n + 1 ⋯ w i − 1 ) {\displaystyle \beta _{w_{i-n+1}\cdots w_{i-1}}=1-\sum _{\{w_{i}:C(w_{i-n+1}\cdots w_{i})>k\}}d_{w_{i-n+1}\cdots w_{i}}{\frac {C(w_{i-n+1}\cdots w_{i-1}w_{i})}{C(w_{i-n+1}\cdots w_{i-1})}}} Then the back-off weight, α, is computed as follows: α w i − n + 1 ⋯ w i − 1 = β w i − n + 1 ⋯ w i − 1 ∑ { w i : C ( w i − n + 1 ⋯ w i ) ≤ k } P b o ( w i ∣ w i − n + 2 ⋯ w i − 1 ) {\displaystyle \alpha _{w_{i-n+1}\cdots w_{i-1}}={\frac {\beta _{w_{i-n+1}\cdots w_{i-1}}}{\sum _{\{w_{i}:C(w_{i-n+1}\cdots w_{i})\leq k\}}P_{bo}(w_{i}\mid w_{i-n+2}\cdots w_{i-1})}}} The above formula only applies if there is data for the "(n − 1)-gram". If not, the algorithm skips n-1 entirely and uses the Katz estimate for n-2. (and so on until an n-gram with data is found) == Discussion == This model generally works well in practice, but fails in some circumstances. For example, suppose that the bigram "a b" and the unigram "c" are very common, but the trigram "a b c" is never seen. Since "a b" and "c" are very common, it may be significant (that is, not due to chance) that "a b c" is never seen. Perhaps it's not allowed by the rules of the grammar. Instead of assigning a more appropriate value of 0, the method will back off to the bigram and estimate P(c | b), which may be too high.

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