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Algorithmic probability

In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. It is used in inductive inference theory and analyses of algorithms. In his general theory of inductive inference, Solomonoff uses the method together with Bayes' rule to obtain probabilities of prediction for an algorithm's future outputs. In the mathematical formalism used, the observations have the form of finite binary strings viewed as outputs of Turing machines, and the universal prior is a probability distribution over the set of finite binary strings calculated from a probability distribution over programs (that is, inputs to a universal Turing machine). The prior is universal in the Turing-computability sense, i.e. no string has zero probability. It is not computable, but it can be approximated. Formally, the probability P {\displaystyle P} is not a probability and it is not computable. It is only "lower semi-computable" and a "semi-measure". By "semi-measure", it means that 0 ≤ ∑ x P ( x ) < 1 {\displaystyle 0\leq \sum _{x}P(x)<1} . That is, the "probability" does not actually sum up to one, unlike actual probabilities. This is because some inputs to the Turing machine causes it to never halt, which means the probability mass allocated to those inputs is lost. By "lower semi-computable", it means there is a Turing machine that, given an input string x {\displaystyle x} , can print out a sequence y 1 < y 2 < ⋯ {\displaystyle y_{1} Read more →
MaPS S.A.

MaPS S.A. is a software editor founded in 2011 by Thierry Muller. The company is headquartered in Luxembourg. Its platform, called MaPS System, provides Data Management software for Multichannel Marketing. == History and funding == The first version of MaPS System was released under the agency Prem1um S.A. in 2005 in the partnership with Pingroom agency. In combination with MaPS System, Prem1um also provided various consulting services in Marketing, Publishing and Sales. This is where MaPS System takes its names (M stands for Marketing, P for Publishing and S for Sales). In 2011, after being successful, Prem1um S.A. decided to enable the software MaPS System to operate independently under MaPS S.A., as a separate company and editor of the software. The first financial supports were provided by Malta ICI, a Venture Capital firm, and the local partner Chameleon Invest, a seed-capital fund led by Business Angels, who invested €900,000. In a second investment round in 2014 led by Newion Investments, a Venture Capital firm, €1.4 Million were raised, thus amounting to total assets of €2.2 Million. In 2016, the company was taken over by three private investors. In 2018, after two years of continuous growth and European expansion in Belgium, Germany and Switzerland, MaPS S.A acquired Awevo, an e-commerce web agency. == Products == The services included in MaPS System range from the data centralization, Data Governance to an optimized Multichannel Marketing. The software currently includes more than 35 modules for Master Data Management, Product Information Management, Digital Asset Management, Business Process Management including catalogue Publishing features. == Certifications == In 2019, MaPS System and Awevo received "Made in Luxembourg" label, given to the companies whose services are entirely designed in Luxembourg, without any production or development offshoring. MaPS System is a member of ICT Cluster by Luxinnovation.
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Pseudonymization

Pseudonymization is a data management and de-identification procedure by which personally identifiable information fields within a data record are replaced by one or more artificial identifiers, or pseudonyms. A single pseudonym for each replaced field or collection of replaced fields makes the data record less identifiable while remaining suitable for data analysis and data processing. Pseudonymization (or pseudonymisation, the spelling under European guidelines) is one way to comply with the European Union's General Data Protection Regulation (GDPR) demands for secure data storage of personal information. Pseudonymized data can be restored to its original state with the addition of information which allows individuals to be re-identified. In contrast, anonymization is intended to prevent re-identification of individuals within the dataset. Clause 18, Module Four, footnote 2 of the Adoption by the European Commission of the Implementing Decisions (EU) 2021/914 "requires rendering the data anonymous in such a way that the individual is no longer identifiable by anyone ... and that this process is irreversible." == Impact of Schrems II ruling == The European Data Protection Supervisor (EDPS) on 9 December 2021 highlighted pseudonymization as the top technical supplementary measure for Schrems II compliance. Less than two weeks later, the EU Commission highlighted pseudonymization as an essential element of the equivalency decision for South Korea, which is the status that was lost by the United States under the Schrems II ruling by the Court of Justice of the European Union (CJEU). The importance of GDPR-compliant pseudonymization increased dramatically in June 2021 when the European Data Protection Board (EDPB) and the European Commission highlighted GDPR-compliant pseudonymization as the state-of-the-art technical supplementary measure for the ongoing lawful use of EU personal data when using third country (i.e., non-EU) cloud processors or remote service providers under the "Schrems II" ruling by the CJEU. Under the GDPR and final EDPB Schrems II Guidance, the term pseudonymization requires a new protected "state" of data, producing a protected outcome that: Protects direct, indirect, and quasi-identifiers, together with characteristics and behaviors; Protects at the record and data set level versus only the field level so that the protection travels wherever the data goes, including when it is in use; and Protects against unauthorized re-identification via the mosaic effect by generating high entropy (uncertainty) levels by dynamically assigning different tokens at different times for various purposes. The combination of these protections is necessary to prevent the re-identification of data subjects without the use of additional information kept separately, as required under GDPR Article 4(5) and as further underscored by paragraph 85(4) of the final EDPB Schrems II guidance: Article 4(5) "Definitions" of the GDPR defines pseudonymization as "the processing of personal data in such a manner that the personal data can no longer be attributed to a specific data subject without the use of additional information, provided that such additional information is kept separately and is subject to technical and organisational measures to ensure that the personal data are not attributed to an identified or identifiable natural person." "Use Case 2: Transfer of pseudonymised Data Paragraph 85(4)" of the final EDPB Schrems II Guidance requires that “the controller has established by means of a thorough analysis of the data in question – taking into account any information that the public authorities of the recipient country may be expected to possess and use – that the pseudonymised personal data cannot be attributed to an identified or identifiable natural person even if cross-referenced with such information." GDPR-compliant pseudonymization requires that data is "anonymous" in the strictest EU sense of the word – globally anonymous – but for the additional information held separately and made available under controlled conditions as authorized by the data controller for permitted re-identification of individual data subjects. Clause 18, Module Four, footnote 2 of the Adoption by the European Commission of the Implementing Decision (EU) 2021/914 "requires rendering the data anonymous in such a way that the individual is no longer identifiable by anyone, in line with recital 26 of Regulation (EU) 2016/679, and that this process is irreversible." Before the Schrems II ruling, pseudonymization was a technique used by security experts or government officials to hide personally identifiable information to maintain data structure and privacy of information. Some common examples of sensitive information include postal code, location of individuals, names of individuals, race and gender, etc. After the Schrems II ruling, GDPR-compliant pseudonymization must satisfy the above-noted elements as an "outcome" versus merely a technique. == Data fields == The choice of which data fields are to be pseudonymized is partly subjective. Less selective fields, such as birth date or postal code are often also included because they are usually available from other sources and therefore make a record easier to identify. Pseudonymizing these less identifying fields removes most of their analytic value and is therefore normally accompanied by the introduction of new derived and less identifying forms, such as year of birth or a larger postal code region. Data fields that are less identifying, such as date of attendance, are usually not pseudonymized. This is because too much statistical utility is lost in doing so, not because the data cannot be identified. For example, given prior knowledge of a few attendance dates it is easy to identify someone's data in a pseudonymized dataset by selecting only those people with that pattern of dates. This is an example of an inference attack. The weakness of pre-GDPR pseudonymized data to inference attacks is commonly overlooked. A famous example is the AOL search data scandal. The AOL example of unauthorized re-identification did not require access to separately kept "additional information" that was under the control of the data controller as is now required for GDPR-compliant pseudonymization, outlined below under the section "New Definition for Pseudonymization Under GDPR". Protecting statistically useful pseudonymized data from re-identification requires: a sound information security base controlling the risk that the analysts, researchers or other data workers cause a privacy breach The pseudonym allows tracking back of data to its origins, which distinguishes pseudonymization from anonymization, where all person-related data that could allow backtracking has been purged. Pseudonymization is an issue in, for example, patient-related data that has to be passed on securely between clinical centers. The application of pseudonymization to e-health intends to preserve the patient's privacy and data confidentiality. It allows primary use of medical records by authorized health care providers and privacy preserving secondary use by researchers. In the US, HIPAA provides guidelines on how health care data must be handled and data de-identification or pseudonymization is one way to simplify HIPAA compliance. However, plain pseudonymization for privacy preservation often reaches its limits when genetic data are involved (see also genetic privacy). Due to the identifying nature of genetic data, depersonalization is often not sufficient to hide the corresponding person. Potential solutions are the combination of pseudonymization with fragmentation and encryption. An example of application of pseudonymization procedure is creation of datasets for de-identification research by replacing identifying words with words from the same category (e.g. replacing a name with a random name from the names dictionary), however, in this case it is in general not possible to track data back to its origins. == New definition under GDPR == Effective as of May 25, 2018, the EU General Data Protection Regulation (GDPR) defines pseudonymization for the very first time at the EU level in Article 4(5). Under Article 4(5) definitional requirements, data is pseudonymized if it cannot be attributed to a specific data subject without the use of separately kept "additional information". Pseudonymized data embodies the state of the art in Data Protection by Design and by Default because it requires protection of both direct and indirect identifiers (not just direct). GDPR Data Protection by Design and by Default principles as embodied in pseudonymization require protection of both direct and indirect identifiers so that personal data is not cross-referenceable (or re-identifiable) via the "mosaic effect" without access to "additional information" that is kept separately by the controller. Because access to separately kept "additional information" is required
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Materials informatics

Materials informatics is a field of study that applies the principles of informatics and data science to materials science and engineering to improve the understanding, use, selection, development, and discovery of materials. The term "materials informatics" is frequently used interchangeably with "data science", "machine learning", and "artificial intelligence" by the community. This is an emerging field, with a goal to achieve high-speed and robust acquisition, management, analysis, and dissemination of diverse materials data with the goal of greatly reducing the time and risk required to develop, produce, and deploy new materials, which generally takes longer than 20 years. This field of endeavor is not limited to some traditional understandings of the relationship between materials and information. Some more narrow interpretations include combinatorial chemistry, process modeling, materials databases, materials data management, and product life cycle management. Materials informatics is at the convergence of these concepts, but also transcends them and has the potential to achieve greater insights and deeper understanding by applying lessons learned from data gathered on one type of material to others. By gathering appropriate meta data, the value of each individual data point can be greatly expanded. == Databases == Databases are essential for any informatics research and applications. In material informatics many databases exist containing both empirical data obtained experimentally, and theoretical data obtained computationally. Big data that can be used for machine learning is particularly difficult to obtain for experimental data due to the lack of a standard for reporting data and the variability in the experimental environment. This lack of big data has led to growing effort in developing machine learning techniques that utilize data extremely data sets. On the other hand, large uniform database of theoretical density functional theory (DFT) calculations exists. These databases have proven their utility in high-throughput material screening and discovery. Some common DFT databases and high throughput tools are listed below: Databases: MaterialsProject.org, MaterialsWeb.org (University of Florida) HT software: Pymatgen, MPInterfaces, Matminer == Beyond computational methods? == The concept of materials informatics is addressed by the Materials Research Society. For example, materials informatics was the theme of the December 2006 issue of the MRS Bulletin. The issue was guest-edited by John Rodgers of Innovative Materials, Inc., and David Cebon of Cambridge University, who described the "high payoff for developing methodologies that will accelerate the insertion of materials, thereby saving millions of investment dollars." The editors focused on the limited definition of materials informatics as primarily focused on computational methods to process and interpret data. They stated that "specialized informatics tools for data capture, management, analysis, and dissemination" and "advances in computing power, coupled with computational modeling and simulation and materials properties databases" will enable such accelerated insertion of materials. A broader definition of materials informatics goes beyond the use of computational methods to carry out the same experimentation, viewing materials informatics as a framework in which a measurement or computation is one step in an information-based learning process that uses the power of a collective to achieve greater efficiency in exploration. When properly organized, this framework crosses materials boundaries to uncover fundamental knowledge of the basis of physical, mechanical, and engineering properties. == Challenges == While there are many who believe in the future of informatics in the materials development and scaling process, many challenges remain. Hill, et al., write that "Today, the materials community faces serious challenges to bringing about this data-accelerated research paradigm, including diversity of research areas within materials, lack of data standards, and missing incentives for sharing, among others. Nonetheless, the landscape is rapidly changing in ways that should benefit the entire materials research enterprise." This remaining tension between traditional materials development methodologies and the use of more computationally, machine learning, and analytics approaches will likely exist for some time as the materials industry overcomes some of the cultural barriers necessary to fully embrace such new ways of thinking. == Analogy from Biology == The overarching goals of bioinformatics and systems biology may provide a useful analogy. Andrew Murray of Harvard University expresses the hope that such an approach "will save us from the era of "one graduate student, one gene, one PhD". Similarly, the goal of materials informatics is to save us from one graduate student, one alloy, one PhD. Such goals will require more sophisticated strategies and research paradigms than applying data-science methods to the same tasks set currently undertaken by students.
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SWIG

The Simplified Wrapper and Interface Generator (SWIG) is an open-source software tool used to connect computer programs or libraries written in C or C++ with scripting languages such as Lua, Perl, PHP, Python, R, Ruby, Tcl, and other language implementations like C#, Java, JavaScript, Go, D, OCaml, Octave, Scilab and Scheme. Output can also be in the form of XML. == Function == The aim is to allow the calling of native functions (that were written in C or C++) by other programming languages, passing complex data types to those functions, keeping memory from being inappropriately freed, inheriting object classes across languages, etc. The programmer writes an interface file containing a list of C/C++ functions to be made visible to an interpreter. SWIG will compile the interface file and generate code in regular C/C++ and the target programming language. SWIG will generate conversion code for functions with simple arguments; conversion code for complex types of arguments must be written by the programmer. The SWIG tool creates source code that provides the glue between C/C++ and the target language. Depending on the language, this glue comes in three forms: a shared library that an extant interpreter can link to as some form of extension module, or a shared library that can be linked to other programs compiled in the target language (for example, using Java Native Interface (JNI) in Java). a shared dynamic library source code that should be compiled and dynamically loaded (e.g. Node.js native extensions) SWIG is not used for calling interpreted functions by native code; this must be done by the programmer manually. == Example == SWIG wraps simple C declarations by creating an interface that closely matches the way in which the declarations would be used in a C program. For example, consider the following interface file: In this file, there are two functions sin() and strcmp(), a global variable Foo, and two constants STATUS and VERSION. When SWIG creates an extension module, these declarations are accessible as scripting language functions, variables, and constants respectively. In Python: == Purpose == There are two main reasons to embed a scripting engine in an existing C/C++ program: The program can then be customized far faster, via a scripting language instead of C/C++. The scripting engine may even be exposed to the end-user, so that they can automate common tasks by writing scripts. Even if the final product is not to contain the scripting engine, it may nevertheless be very useful for writing test scripts. There are several reasons to create dynamic libraries that can be loaded into extant interpreters, including: Provide access to a C/C++ library which has no equivalent in the scripting language. Write the whole program in the scripting language first, and after profiling, rewrite performance-critical code in C or C++. == History == SWIG is written in C and C++ and has been publicly available since February 1996. The initial author and main developer was David M. Beazley who developed SWIG while working as a graduate student at Los Alamos National Laboratory and the University of Utah and while on the faculty at the University of Chicago. Development is currently supported by an active group of volunteers led by William Fulton. SWIG has been released under a GNU General Public License. == Google Summer of Code == SWIG was a successful participant of Google Summer of Code in 2008, 2009, 2012. In 2008, SWIG got four slots. Haoyu Bai spent his summers on SWIG's Python 3.0 Backend, Jan Jezabek worked on Support for generating COM wrappers, Cheryl Foil spent her time on Comment 'Translator' for SWIG, and Maciej Drwal worked on a C backend. In 2009, SWIG again participated in Google Summer of Code. This time four students participated. Baozeng Ding worked on a Scilab module. Matevz Jekovec spent time on C++0x features. Ashish Sharma spent his summer on an Objective-C module, Miklos Vajna spent his time on PHP directors. In 2012, SWIG participated in Google Summer of Code. This time four out of five students successfully completed the project. Leif Middelschulte worked on a C target language module. Swati Sharma enhanced the Objective-C module. Neha Narang added the new module on JavaScript. Dmitry Kabak worked on source code documentation and Doxygen comments. == Alternatives == For Python, similar functionality is offered by SIP, Pybind11, and Boost's Boost.python library. == Projects using SWIG == ZXID (Apache License, Version 2.0) Symlabs SFIS (commercial) LLDB GNU Radio up to (including) version 3.8.x.x; later versions use Pybind11 Xapian TensorFlow Apache SINGA QuantLib Babeltrace
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Artificial empathy

Artificial empathy or computational empathy is the development of AI systems—such as companion robots or virtual agents—that can detect emotions and respond to them in an empathic way. Although such technology can be perceived as scary or threatening, it could also have a significant advantage over humans for roles in which emotional expression can be important, such as in the health care sector. An October 2025 review and meta-analysis in the British Medical Bulletin found that AI chatbots were rated as showing more empathy than human healthcare professionals in 13 of 15 studies that compared them. Care-givers who perform emotional labor above and beyond the requirements of paid labor can experience chronic stress or burnout, and can become desensitized to patients. Artificial empathy could also help the socialization of care-givers, or serve as role model for emotional detachment. A broader definition of artificial empathy is "the ability of nonhuman models to predict a person's internal state (e.g., cognitive, affective, physical) given the signals (s)he emits (e.g., facial expression, voice, gesture) or to predict a person's reaction (including, but not limited to internal states) when he or she is exposed to a given set of stimuli (e.g., facial expression, voice, gesture, graphics, music, etc.)". A 2025 study reported that some multimodal large language models can recognize basic facial expressions with human-level accuracy on a commonly used research dataset of posed facial expressions. == Areas of research == There are a variety of philosophical, theoretical, and applicative questions related to artificial empathy. For example: Which conditions would have to be met for a robot to respond competently to a human emotion? What models of empathy can or should be applied to Social and Assistive Robotics? Must the interaction of humans with robots imitate affective interaction between humans? Can a robot help science learn about affective development of humans? Would robots create unforeseen categories of inauthentic relations? What relations with robots can be considered authentic? How can we assess artificial empathy in AI systems? == Examples of artificial empathy research and practice == People often communicate and make decisions based on inferences about each other's internal states (e.g., emotional, cognitive, and physical states) that are in turn based on signals emitted by the person such as facial expression, body gesture, voice, and words. Broadly speaking, artificial empathy focuses on developing non-human models that achieve similar objectives using similar data. === Streams of artificial empathy research === Artificial empathy has been applied in various research disciplines, including artificial intelligence and business. Two main streams of research in this domain are: the use of nonhuman models to predict a person's internal state (e.g., cognitive, affective, physical) given the signals he or she emits (e.g., facial expression, voice, gesture) the use of nonhuman models to predict a person's reaction when he or she is exposed to a given set of stimuli (e.g., facial expression, voice, gesture, graphics, music, etc.). Research on affective computing, such as emotional speech recognition and facial expression detection, falls within the first stream of artificial empathy. Contexts that have been studied include oral interviews, call centers, human-computer interaction, sales pitches, and financial reporting. The second stream of artificial empathy has been researched more in marketing contexts, such as advertising, branding, customer reviews, in-store recommendation systems, movies, and online dating. === Artificial empathy applications in practice === With the increasing volume of visual, audio, and text data in commerce, many business applications for artificial empathy have followed. For example, Affectiva analyses viewers' facial expressions from video recordings while they are watching video advertisements in order to optimize the content design of video ads. Software like HireVue, BarRaiser, a hiring intelligence firm, helps firms make recruitment decisions by analyzing audio and video information from candidates' video interviews. Lapetus Solutions develops a model to estimate an individual's longevity, health status, and disease susceptibility from a face photo. Their technology has been applied in the insurance industry. == Artificial empathy and human services == Although artificial intelligence cannot yet replace social workers themselves, the technology has been deployed in that field. Florida State University published a study about Artificial Intelligence being used in the human services field. The research used computer algorithms to analyze health records for combinations of risk factors that could predict a future suicide attempt. The article reports, "machine learning—a future frontier for artificial intelligence—can predict with 80% to 90% accuracy whether someone will attempt suicide as far off as two years into the future. The algorithms become even more accurate as a person's suicide attempt gets closer. For example, the accuracy climbs to 92% one week before a suicide attempt when artificial intelligence focuses on general hospital patients". Such algorithmic machines can help social workers. Social work operates on a cycle of engagement, assessment, intervention, and evaluation with clients. Earlier assessment for risk of suicide can lead to earlier interventions and prevention, therefore saving lives. The system would learn, analyze, and detect risk factors, alerting the clinician of a patient's suicide risk score (analogous to a patient's cardiovascular risk score). Then, social workers could step in for further assessment and preventive intervention.
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Regulation of algorithms

Regulation of algorithms, or algorithmic regulation, is the creation of laws, rules and public sector policies for promotion and regulation of algorithms, particularly in artificial intelligence and machine learning. For the subset of AI algorithms, the term regulation of artificial intelligence is used. The regulatory and policy landscape for artificial intelligence (AI) is an emerging issue in jurisdictions globally, including in the European Union. Regulation of AI is considered necessary to both encourage AI and manage associated risks, but challenging. Another emerging topic is the regulation of blockchain algorithms (Use of the smart contracts must be regulated) and is mentioned along with regulation of AI algorithms. Many countries have enacted regulations of high frequency trades, which is shifting due to technological progress into the realm of AI algorithms. The motivation for regulation of algorithms is the apprehension of losing control over the algorithms, whose impact on human life increases. Multiple countries have already introduced regulations in case of automated credit score calculation—right to explanation is mandatory for those algorithms. For example, The IEEE has begun developing a new standard to explicitly address ethical issues and the values of potential future users. Bias, transparency, and ethics concerns have emerged with respect to the use of algorithms in diverse domains ranging from criminal justice to healthcare—many fear that artificial intelligence could replicate existing social inequalities along race, class, gender, and sexuality lines. == Regulation of artificial intelligence == === Public discussion === In 2016, Joy Buolamwini founded Algorithmic Justice League after a personal experience with biased facial detection software in order to raise awareness of the social implications of artificial intelligence through art and research. In 2017 Elon Musk advocated regulation of algorithms in the context of the existential risk from artificial general intelligence. According to NPR, the Tesla CEO was "clearly not thrilled" to be advocating for government scrutiny that could impact his own industry, but believed the risks of going completely without oversight are too high: "Normally the way regulations are set up is when a bunch of bad things happen, there's a public outcry, and after many years a regulatory agency is set up to regulate that industry. It takes forever. That, in the past, has been bad but not something which represented a fundamental risk to the existence of civilisation." In response, some politicians expressed skepticism about the wisdom of regulating a technology that is still in development. Responding both to Musk and to February 2017 proposals by European Union lawmakers to regulate AI and robotics, Intel CEO Brian Krzanich has argued that artificial intelligence is in its infancy and that it is too early to regulate the technology. Instead of trying to regulate the technology itself, some scholars suggest to rather develop common norms including requirements for the testing and transparency of algorithms, possibly in combination with some form of warranty. One suggestion has been for the development of a global governance board to regulate AI development. In 2020, the European Union published its draft strategy paper for promoting and regulating AI. Algorithmic tacit collusion is a legally dubious antitrust practise committed by means of algorithms, which the courts are not able to prosecute. This danger concerns scientists and regulators in EU, US and beyond. European Commissioner Margrethe Vestager mentioned an early example of algorithmic tacit collusion in her speech on "Algorithms and Collusion" on March 16, 2017, described as follows: "A few years ago, two companies were selling a textbook called The Making of a Fly. One of those sellers used an algorithm which essentially matched its rival’s price. That rival had an algorithm which always set a price 27% higher than the first. The result was that prices kept spiralling upwards, until finally someone noticed what was going on, and adjusted the price manually. By that time, the book was selling – or rather, not selling – for 23 million dollars a copy." In 2018, the Netherlands employed an algorithmic system SyRI (Systeem Risico Indicatie) to detect citizens perceived being high risk for committing welfare fraud, which quietly flagged thousands of people to investigators. This caused a public protest. The district court of Hague shut down SyRI referencing Article 8 of the European Convention on Human Rights (ECHR). In 2020, algorithms assigning exam grades to students in the UK sparked open protest under the banner "Fuck the algorithm." This protest was successful and the grades were taken back. In 2024, the Munich Convention on AI, Data and Human Rights was introduced as part of growing international efforts to regulate artificial intelligence through a human rights lens. Developed through a collaborative drafting process involving scholars from the Technical University of Munich, Stellenbosch University, Ulster University, and KNUST, the initiative calls for an international conversation on a binding treaty to safeguard human rights and the principles enshrined in the UN Charter in the age of AI. === Implementation === AI law and regulations can be divided into three main topics, namely governance of autonomous intelligence systems, responsibility and accountability for the systems, and privacy and safety issues. The development of public sector strategies for management and regulation of AI has been increasingly deemed necessary at the local, national, and international levels and in fields from public service management to law enforcement, the financial sector, robotics, the military, and international law. There are many concerns that there is not enough visibility and monitoring of AI in these sectors. In the United States financial sector, for example, there have been calls for the Consumer Financial Protection Bureau to more closely examine source code and algorithms when conducting audits of financial institutions' non-public data. In the United States, on January 7, 2019, following an Executive Order on 'Maintaining American Leadership in Artificial Intelligence', the White House's Office of Science and Technology Policy released a draft Guidance for Regulation of Artificial Intelligence Applications, which includes ten principles for United States agencies when deciding whether and how to regulate AI. In response, the National Institute of Standards and Technology has released a position paper, the National Security Commission on Artificial Intelligence has published an interim report, and the Defense Innovation Board has issued recommendations on the ethical use of AI. In April 2016, for the first time in more than two decades, the European Parliament adopted a set of comprehensive regulations for the collection, storage, and use of personal information, the General Data Protection Regulation (GDPR)1 (European Union, Parliament and Council 2016). The GDPR's policy on the right of citizens to receive an explanation for algorithmic decisions highlights the pressing importance of human interpretability in algorithm design. In 2016, China published a position paper questioning the adequacy of existing international law to address the eventuality of fully autonomous weapons, becoming the first permanent member of the U.N. Security Council to broach the issue, and leading to proposals for global regulation. In the United States, steering on regulating security-related AI is provided by the National Security Commission on Artificial Intelligence. In 2017, the U.K. Vehicle Technology and Aviation Bill imposes liability on the owner of an uninsured automated vehicle when driving itself and makes provisions for cases where the owner has made "unauthorized alterations" to the vehicle or failed to update its software. Further ethical issues arise when, e.g., a self-driving car swerves to avoid a pedestrian and causes a fatal accident. In 2021, the European Commission proposed the Artificial Intelligence Act. == Algorithm certification == There is a concept of algorithm certification emerging as a method of regulating algorithms. Algorithm certification involves auditing whether the algorithm used during the life cycle 1) conforms to the protocoled requirements (e.g., for correctness, completeness, consistency, and accuracy); 2) satisfies the standards, practices, and conventions; and 3) solves the right problem (e.g., correctly model physical laws), and satisfies the intended use and user needs in the operational environment. == Regulation of blockchain algorithms == Blockchain systems provide transparent and fixed records of transactions and hereby contradict the goal of the European GDPR, which is to give individuals full control of their private data. By implementing the Decree on Development of Digital Economy, Bel
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Physical schema

A physical data model (or database design) is a representation of a data design as implemented, or intended to be implemented, in a database management system. In the lifecycle of a project it typically derives from a logical data model, though it may be reverse-engineered from a given database implementation. A complete physical data model will include all the database artifacts required to create relationships between tables or to achieve performance goals, such as indexes, constraint definitions, linking tables, partitioned tables or clusters. Analysts can usually use a physical data model to calculate storage estimates; it may include specific storage allocation details for a given database system. As of 2012 seven main databases dominate the commercial marketplace: Informix, Oracle, Postgres, SQL Server, Sybase, IBM Db2 and MySQL. Other RDBMS systems tend either to be legacy databases or used within academia such as universities or further education colleges. Physical data models for each implementation would differ significantly, not least due to underlying operating-system requirements that may sit underneath them. For example: SQL Server runs only on Microsoft Windows operating-systems (Starting with SQL Server 2017, SQL Server runs on Linux. It's the same SQL Server database engine, with many similar features and services regardless of your operating system), while Oracle and MySQL can run on Solaris, Linux and other UNIX-based operating-systems as well as on Windows. This means that the disk requirements, security requirements and many other aspects of a physical data model will be influenced by the RDBMS that a database administrator (or an organization) chooses to use. == Physical schema == Physical schema is a term used in data management to describe how data is to be represented and stored (files, indices, etc.) in secondary storage using a particular database management system (DBMS) (e.g., Oracle RDBMS, Sybase SQL Server, etc.). In the ANSI/SPARC Architecture three schema approach, the internal schema is the view of data that involved data management technology. This is as opposed to an external schema that reflects an individual's view of the data, or the conceptual schema that is the integration of a set of external schemas. The logical schema was the way data were represented to conform to the constraints of a particular approach to database management. At that time the choices were hierarchical and network. Describing the logical schema, however, still did not describe how physically data would be stored on disk drives. That is the domain of the physical schema. Now logical schemas describe data in terms of relational tables and columns, object-oriented classes, and XML tags. A single set of tables, for example, can be implemented in numerous ways, up to and including an architecture where table rows are maintained on computers in different countries.
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Deadbot

A deadbot, deathbot, or griefbot is a digital avatar, created with artificial intelligence, which resembles a person who is dead. Griefbots employ natural language processing and machine-learning techniques to approximate the style and personality of a deceased person. They may appear as chatbots, voice assistants, or animated avatars, and are often trained on an individual's digital remains. == History == Among the earliest researchers, Muhammad Aurangzeb Ahmad of the University of Washington, developed the Grandpa Bot project, a conversational simulation of his late father designed for his children to interact with. Other efforts include journalist James Vlahos's Dadbot, which evolved into the commercial platform HereAfter AI. Hossein Rahnama's Augmented Eternity research at MIT Media Lab and Toronto Metropolitan University, and game designer Jason Rohrer's "Project December", have enabled users to converse with language-model representations of loved ones. Early commercial projects such as Eternime, founded by Marius Ursache, also popularized the notion of interactive digital immortality. == Cultural and societal impact == Scholars have proposed frameworks and critiques addressing the ethics of these technologies. Tomasz Hollanek and Katarzyna Nowaczyk-Basińska developed a design-ethics taxonomy distinguishing the data donor, data recipient, and interactant. Edina Harbinja and Lilian Edwards formalized the concept of post-mortem privacy, and Carl J. Öhman at the Oxford Internet Institute studied the management of large-scale digital remains. Cultural acceptance varies: while some view them as expressions of remembrance, others regard them as unsettling or ethically problematic. Concerns have been raised about deadbots' potential for creating psychological harm. Griefbots are considered part of the phenomenon of artificial intimacy.
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Hindley–Milner type system

A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity. HM is preferably used for functional programming languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably with type class constraints like those in Haskell. == Introduction == As a type inference method, Hindley–Milner is able to deduce the types of variables, expressions and functions from programs written in an entirely untyped style. Being scope sensitive, it is not limited to deriving the types only from a small portion of source code, but rather from complete programs or modules. Being able to cope with parametric types, too, it is core to the type systems of many functional programming languages. It was first applied in this manner in the ML programming language. The origin is the type inference algorithm for the simply typed lambda calculus that was devised by Haskell Curry and Robert Feys in 1958. In 1969, J. Roger Hindley extended this work and proved that their algorithm always inferred the most general type. In 1978, Robin Milner, independently of Hindley's work, provided an equivalent algorithm, Algorithm W. In 1982, Luis Damas finally proved that Milner's algorithm is complete and extended it to support systems with polymorphic references. === Monomorphism vs. polymorphism === In the simply typed lambda calculus, types T are either atomic type constants or function types of form T → T {\displaystyle T\rightarrow T} . Such types are monomorphic. Typical examples are the types used in arithmetic values: 3 : N u m b e r a d d 3 4 : N u m b e r a d d : N u m b e r → N u m b e r → N u m b e r {\displaystyle {\begin{array}{ll}3&:{\mathtt {Number}}\\{\mathtt {add}}\ 3\ 4&:{\mathtt {Number}}\\{\mathtt {add}}&:{\mathtt {Number}}\rightarrow {\mathtt {Number}}\rightarrow {\mathtt {Number}}\end{array}}} Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function i d ≡ λ x . x {\displaystyle {\mathtt {id}}\equiv \lambda x.x} which simply returns whatever value it is applied to. Less trivial examples include parametric types like lists. While polymorphism in general means that operations accept values of more than one type, the polymorphism used here is parametric. One finds the notation of type schemes in the literature, too, emphasizing the parametric nature of the polymorphism. Additionally, constants may be typed with (quantified) type variables. For example, the following type schemes quantify universally over α {\displaystyle \alpha } , meaning that they are true for all possible α {\displaystyle \alpha } : c o n s : ∀ α . α → L i s t α → L i s t α n i l : ∀ α . L i s t α i d : ∀ α . α → α {\displaystyle {\begin{array}{ll}{\mathtt {cons}}&:\forall \alpha .\alpha \rightarrow {\mathtt {List}}\ \alpha \rightarrow {\mathtt {List}}\ \alpha \\{\mathtt {nil}}&:\forall \alpha .{\mathtt {List}}\ \alpha \\{\mathtt {id}}&:\forall \alpha .\alpha \rightarrow \alpha \end{array}}} Polymorphic types can become monomorphic by consistent substitution of their variables. Examples of monomorphic instances are: i d ′ : S t r i n g → S t r i n g n i l ′ : L i s t N u m b e r {\displaystyle {\begin{array}{ll}{\mathtt {id}}'&:{\mathtt {String}}\rightarrow {\mathtt {String}}\\{\mathtt {nil}}'&:{\mathtt {List}}\ {\mathtt {Number}}\end{array}}} More generally, types are polymorphic when they contain type variables, while types without them are monomorphic. Contrary to the type systems used for example in Pascal (1970) or C (1972), which only support monomorphic types, HM is designed with emphasis on parametric polymorphism. The successors of the languages mentioned, like C++ (1985), focused on different types of polymorphism, namely subtyping in connection with object-oriented programming and overloading. While subtyping is incompatible with HM, a variant of systematic overloading is available in the HM-based type system of Haskell. === Let-polymorphism === When extending the type inference for the simply-typed lambda calculus towards polymorphism, one has to decide whether assigning a polymorphic type not only as type of an expression, but also as the type of a λ-bound variable is admissible. This would allow the generic identity type to be assigned to the variable 'id' in: (λ id . ... (id 3) ... (id "text") ... ) (λ x . x) Allowing this gives rise to the polymorphic lambda calculus; however, type inference in this system is not decidable. Instead, HM distinguishes variables that are immediately bound to an expression from more general λ-bound variables, calling the former let-bound variables, and allows polymorphic types to be assigned only to these. This leads to let-polymorphism where the above example takes the form let id = λ x . x in ... (id 3) ... (id "text") ... which can be typed with a polymorphic type for 'id'. As indicated, the expression syntax is extended to make the let-bound variables explicit, and by restricting the type system to allow only let-bound variable to have polymorphic types, while the parameters in lambda-abstractions must get a monomorphic type, type inference becomes decidable. == Overview == The remainder of this article proceeds as follows: The HM type system is defined. This is done by describing a deduction system that makes precise what expressions have what type, if any. From there, it works towards an implementation of the type inference method. After introducing a syntax-driven variant of the above deductive system, it sketches an efficient implementation (algorithm J), appealing mostly to the reader's metalogical intuition. Because it remains open whether algorithm J indeed realises the initial deduction system, a less efficient implementation (algorithm W), is introduced and its use in a proof is hinted. Finally, further topics related to the algorithm are discussed. The same description of the deduction system is used throughout, even for the two algorithms, to make the various forms in which the HM method is presented directly comparable. == The Hindley–Milner type system == The type system can be formally described by syntax rules that fix a language for the expressions, types, etc. The presentation here of such a syntax is not too formal, in that it is written down not to study the surface grammar, but rather the depth grammar, and leaves some syntactical details open. This form of presentation is usual. Building on this, typing rules are used to define how expressions and types are related. As before, the form used is a bit liberal. === Syntax === The expressions to be typed are exactly those of the lambda calculus extended with a let-expression as shown in the adjacent table. Parentheses can be used to disambiguate an expression. The application is left-binding and binds stronger than abstraction or the let-in construct. Types are syntactically split into two groups, monotypes and polytypes. ==== Monotypes ==== Monotypes always designate a particular type. Monotypes τ {\displaystyle \tau } are syntactically represented as terms. Examples of monotypes include type constants like i n t {\displaystyle {\mathtt {int}}} or s t r i n g {\displaystyle {\mathtt {string}}} , and parametric types like M a p ( S e t s t r i n g ) i n t {\displaystyle {\mathtt {Map\ (Set\ string)\ int}}} . The latter types are examples of applications of type functions, for example, from the set { M a p 2 , S e t 1 , s t r i n g 0 , i n t 0 , → 2 } {\displaystyle \{{\mathtt {Map^{2},\ Set^{1},\ string^{0},\ int^{0}}},\ \rightarrow ^{2}\}} , where the superscript indicates the number of type parameters. The complete set of type functions C {\displaystyle C} is arbitrary in HM, except that it must contain at least → 2 {\displaystyle \rightarrow ^{2}} , the type of functions. It is often written in infix notation for convenience. For example, a function mapping integers to strings has type i n t → s t r i n g {\displaystyle {\mathtt {int}}\rightarrow {\mathtt {string}}} . Again, parentheses can be used to disambiguate a type expression. The application binds stronger than the infix arrow, which is right-binding. Type variables are admitted as monotypes. Monotypes are not to be confused with monomorphic types, which exc
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DONE

The Data-based Online Nonlinear Extremumseeker (DONE) algorithm is a black-box optimization algorithm. DONE models the unknown cost function and attempts to find an optimum of the underlying function. The DONE algorithm is suitable for optimizing costly and noisy functions and does not require derivatives. An advantage of DONE over similar algorithms, such as Bayesian optimization, is that the computational cost per iteration is independent of the number of function evaluations. == Methods == The DONE algorithm was first proposed by Hans Verstraete and Sander Wahls in 2015. The algorithm fits a surrogate model based on random Fourier features and then uses a well-known L-BFGS algorithm to find an optimum of the surrogate model. == Applications == DONE was first demonstrated for maximizing the signal in optical coherence tomography measurements, but has since then been applied to various other applications. For example, it was used to help extending the field of view in light sheet fluorescence microscopy.
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Pol.is

Polis (or Pol.is) is wiki survey software designed for large group collaborations. As a civic technology, Polis allows people to share their opinions and ideas, and its algorithm is intended to elevate ideas that can facilitate better decision-making, especially when there are lots of participants. Polis has been credited for assisting the passage of legislation in Taiwan. Pol.is has been used by governments in the United States, Canada, Singapore, Philippines, Finland, Spain and elsewhere. == History == Pol.is was founded by Colin Megill, Christopher Small, and Michael Bjorkegren after the Occupy Wall Street and Arab Spring movements. In Taiwan, pol.is has been "one of the key parts" of vTaiwan's suite of open-source tools for its citizen engagement efforts arising out of the Sunflower Student Movement. vTaiwan claims that of the 26 national issues related to technology discussed on the platform, 80% led to government action. Pol.is is also utilized by "Join," a national platform for online deliberation run by the Taiwanese government. In 2022, Wired reported that Polis was an influence on the Community Notes project at Twitter. In 2023, Megill advised OpenAI on how to facilitate deliberation at scale in a way that was more efficient than Polis, which still required significant human labor and analysis at the time. He helped to award $1 million in grants to teams working on solving the problem of deliberation at scale. In 2023, Anthropic was also exploring steering model behavior using Polis. In 2025, it helped the county that includes Bowling Green, Kentucky make a 25 year plan by facilitating the collection and review of ideas from thousands of residents, representing 10% of the county. 2,370 of 3,940 unique ideas were agreed-upon by over 80% of survey respondents. Ideas were screened by volunteers if they were redundant to an existing idea, off-topic or obscene. == How it works == Pol.is participants are anonymous and cannot reply directly to others posts, in an effort to avoid personal attacks for users. Its algorithms are designed not for engagement and scrolling, but to find areas of agreement to better understand the nuances of a wide range of opinions. Participants are prompted for ideas and vote on other participants' ideas. == Reception == Andrew Leonard, The Financial Times, and VentureBeat describe Pol.is as a possible antidote to the divisiveness of traditional internet discourse by gamifying consensus. Audrey Tang agreed saying, "Polis is quite well known in that it's a kind of social media that instead of polarizing people to drive so called engagement or addiction or attention, it automatically drives bridge making narratives and statements. So only the ideas that speak to both sides or to multiple sides will gain prominence in Polis." Niall Ferguson argues that the approach to utilize tools like Pol.is and Join in Taiwan empowers ordinary people instead of the elite and protects individual freedoms, providing a contrast to the AI-enhanced panopticon model seen in China. Carl Miller praised the technology as having "gamified finding consensus." Darshana Narayanan, in an op-ed in the Economist, argues that open-source machine-learning-based tools like Polis can help to bypass the influence of special interests or experts. Jamie Susskind cited polis and vTaiwan as a model for democracies, particularly around digital policy issues.
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Vulnerability assessment (computing)

Vulnerability assessment is a process of defining, identifying and classifying the security holes in information technology systems. An attacker can exploit a vulnerability to violate the security of a system. Some known vulnerabilities are Authentication Vulnerability, Authorization Vulnerability and Input Validation Vulnerability. == Purpose == Before deploying a system, it first must go through from a series of vulnerability assessments that will ensure that the build system is secure from all the known security risks. When a new vulnerability is discovered, the system administrator can again perform an assessment, discover which modules are vulnerable, and start the patch process. After the fixes are in place, another assessment can be run to verify that the vulnerabilities were actually resolved. This cycle of assess, patch, and re-assess has become the standard method for many organizations to manage their security issues. The primary purpose of the assessment is to find the vulnerabilities in the system, but the assessment report conveys to stakeholders that the system is secured from these vulnerabilities. If an intruder gained access to a network consisting of vulnerable Web servers, it is safe to assume that he gained access to those systems as well. Because of assessment report, the security administrator will be able to determine how intrusion occurred, identify compromised assets and take appropriate security measures to prevent critical damage to the system. == Assessment types == Depending on the system a vulnerability assessment can have many types and level. === Host assessment === A host assessment looks for system-level vulnerabilities such as insecure file permissions, application level bugs, backdoor and Trojan horse installations. It requires specialized tools for the operating system and software packages being used, in addition to administrative access to each system that should be tested. Host assessment is often very costly in term of time, and thus is only used in the assessment of critical systems. Tools like COPS and Tiger are popular in host assessment. === Network assessment === In a network assessment one assess the network for known vulnerabilities. It locates all systems on a network, determines what network services are in use, and then analyzes those services for potential vulnerabilities. This process does not require any configuration changes on the systems being assessed. Unlike host assessment, network assessment requires little computational cost and effort. == Vulnerability assessment vs penetration testing == Vulnerability assessment and penetration testing are two different testing methods. They are differentiated on the basis of certain specific parameters. == Regulatory requirements == Vulnerability assessments are mandated or strongly recommended by several regulatory frameworks. In the United States healthcare sector, the Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to conduct periodic evaluations of their security posture, and a December 2024 Notice of Proposed Rulemaking would explicitly require vulnerability scanning at least every six months for systems containing electronic protected health information. The Payment Card Industry Data Security Standard (PCI DSS) requires quarterly vulnerability scans for organizations that process credit card transactions, and the NIST Cybersecurity Framework includes vulnerability assessment as a core component of its Identify function.
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Kullback–Leibler Upper Confidence Bound

In multi-armed bandit problems, KL-UCB (for Kullback–Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent Lai-Robbins lower bound. == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {D}},\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} δ t {\displaystyle \delta _{t}} is a well-chosen sequence of positive numbers, often equal to ln ⁡ t + c ln ⁡ ln ⁡ t {\displaystyle \ln t+c\ln \ln t} with c > 0 {\displaystyle c>0} . Then we choose the arm a t {\displaystyle a_{t}} with the highest index: a t := arg ⁡ max a U a ( t ) {\displaystyle a_{t}:=\arg \max _{a}U_{a}(t)} We note that the algorithm does not require knowledge of T {\displaystyle T} . === Example === In the special case of Gaussian distribution with fixed variance σ 2 {\displaystyle \sigma ^{2}} , we have: U a ( t ) = μ ^ a ( t ) + 2 σ 2 δ t N a ( t ) {\displaystyle U_{a}(t)={\hat {\mu }}_{a}(t)+{\sqrt {\frac {2\sigma ^{2}\delta _{t}}{N_{a}(t)}}}} with μ ^ a ( t ) {\displaystyle {\hat {\mu }}_{a}(t)} being the empirical mean of arm a {\displaystyle a} at turn t {\displaystyle t} . === Pseudocode === The player gets the set D for each arm i do: n[i] ← 1; nu[i] ← None; d ← ln(K) for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution for t from K+1 to T do: for each arm i do: index[i] ← compute_index(n[i], nu[i], D, d) select arm a with highest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution d ← ln(t+1) == Theoretical results == In the multi-armed bandit problem we have the Lai–Robbins asymptotic lower bound on regret. The algorithm KL-UCB matches this lower bound for one-dimensional exponential families with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} with δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} . === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. It states that for every consistent algorithm on the set D {\displaystyle {\mathcal {D}}} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ D K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {D}}^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + o T → + ∞ ( ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+o_{T\to +\infty }(\ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it. === Regret bound for KL-UCB === The algorithm matches the Lai–Robbins lower bound for one-dimensional exponential-family distributions and for distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} . ==== One-dimensional exponential family ==== For D {\displaystyle {\mathcal {D}}} being the set of one-dimensional exponential families, with δ t := ln ⁡ t + 3 ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+3\ln \ln t} we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}({\sqrt {\ln T}}).} ==== Bounded distributions in [0,1] ==== For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} (the set of distributions supported on [ 0 , 1 ] {\displaystyle [0,1]} ), and for δ t := ln ⁡ t + ln ⁡ ln ⁡ t {\displaystyle \delta _{t}:=\ln t+\ln \ln t} , we have the following upper bound on the regret of KL-UCB: R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ , D ) ) ln ⁡ T + O T ( ( ln ⁡ T ) 4 / 5 ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{},{\mathcal {D}})}}\right)\ln T+O_{T}{\big (}(\ln T)^{4/5}\ln \ln T{\big )}.} === Runtime === For D = P ( [ 0 , 1 ] ) {\displaystyle {\mathcal {D}}={\mathcal {P}}([0,1])} , the runtime needed per step and for an arm k {\displaystyle k} with n {\displaystyle n} observations is O ( n ( ln ⁡ n ) 2 ) {\displaystyle {\mathcal {O}}{\big (}n(\ln n)^{2}{\big )}} . This is higher than that of other optimal algorithms, such as NPTS with O ( n ) {\displaystyle {\mathcal {O}}(n)} . MED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . and IMED with O ( n ln ⁡ n ) {\displaystyle {\mathcal {O}}(n\ln n)} . The high runtime of KL-UCB is due to a two-level optimisation: for each arm and candidate mean μ {\displaystyle \mu } , the algorithm evaluates K inf ( ν ^ a ( t ) , μ , D ) {\displaystyle {\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})} and then maximises μ {\displaystyle \mu } subject to N a ( t ) K inf ( ν ^ a ( t ) , μ , D ) ≤ δ t {\displaystyle N_{a}(t)\,{\mathcal {K}}_{\inf }({\hat {\nu }}_{a}(t),\mu ,{\mathcal {D}})\leq \delta _{t}} . For distributions bounded in [ 0 , 1 ] {\displaystyle [0,1]} the inner problem has no closed form and must be solved numerically, which increases the per-step cost.
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Small data

Small data is data that is 'small' enough for human comprehension. It is data in a volume and format that makes it accessible, informative and actionable. The term "big data" is about machines and "small data" is about people. This is to say that eyewitness observations or five pieces of related data could be small data. Small data is what we used to think of as data. The only way to comprehend Big data is to reduce the data into small, visually-appealing objects representing various aspects of large data sets (such as histogram, charts, and scatter plots). Big Data is all about finding correlations, but Small Data is all about finding the causation, the reason why. A formal definition of small data has been proposed by Allen Bonde, former vice-president of Innovation at Actuate - now part of OpenText: "Small data connects people with timely, meaningful insights (derived from big data and/or “local” sources), organized and packaged – often visually – to be accessible, understandable, and actionable for everyday tasks." Another definition of small data is: The small set of specific attributes produced by the Internet of Things. These are typically a small set of sensor data such as temperature, wind speed, vibration and status. It was estimated (2016) that “If one takes the top 100 biggest innovations of our time, perhaps around 60% to 65% percent are really based on Small Data.” as Martin Lindstrom puts it. Small data includes everything from Snapchat to simple objects such as the post-it note. Lindstrom believes we become so focused on Big-Data that we tend to forget about more basic concepts and creativity. Lindstrom defines Small Data "as seemingly insignificant observations you identify in consumers’ homes, is everything from how you place your shoes on how you hang your paintings". He thus considers that one should perfectly master the basic (Small Data) in order to mine and find correlations. == Academic Recognition and Methodology == The growing significance of "small data" as a distinct field of inquiry was highlighted by the 2024 Thematic Einstein Semester (TES) on Small Data Analysis, hosted by the Berlin Mathematics Research Center MATH+. A central focus of this semester was the transition from theoretical analysis to practical decision-making. Because small data sets are primarily used to drive specific actions, the presentation of results becomes an essential methodological step. The semester’s findings emphasized that while small data may lack volume, it often contains a high density of "many possible interpretations." Consequently, the final conference of the TES was structured around the pillars of interpretation, explanation, and knowledge gain. Participants sought to develop new mathematical and methodical representations that could accurately depict this wealth of interpretative possibilities. This work underscores that analyzing small data is not purely a computational task; it requires a robust interface between mathematics and diverse disciplines to ensure that insights are both contextually grounded and scientifically rigorous. == Uses in business == === Marketing === Bonde has written about the topic for Forbes, Direct Marketing News, CMO.com and other publications. According to Martin Lindstrom, in his book, Small Data: "{In customer research, small data is} Seemingly insignificant behavioural observations containing very specific attributes pointing towards an unmet customer need. Small data is the foundation for breakthrough ideas or completely new ways to turnaround brands." His approach is based on the combination of the observation of small samples with intuition. Marketers can obtain market insights from gathering Small Data by engaging with and observing people in their own environments. In comparison to Big Data, Small Data has the power to trigger emotions and to provide insights into the reasons behind the behaviours of customers. It may uncover detailed information on a person's extroversion or introversion, self-confidence, whether one is having problems in his/her relationship, etc. According to Lindstrom, relationships among people and customer segments are organized around four criteria: Climate: It reveals for example how a person's environment affects their diet. Rulership: The power or government in charge Religion: The prevalence of religion in a country, depending on its influence, indicates whether a person's decision making process is impacted by their belief system. Tradition: Cultural norms influence people's behaviors and interactions. Many companies underestimate the power of Small Data, using samples of millions of consumers instead of recognizing the value of closely observing small samples in their market research. In his book, Lindstrom defines "7Cs", which companies should consider in the attempt to derive meaningful customer insights and market trends through small data from their customers: Collecting: Understanding the manner in which observations are translated inside a home. Clues: Uncovering other distinctive emotional reflections that can be observed. Connecting: Identifying the consequences of emotional behaviour. Causation: Understanding what emotions are being evoked. Correlation: Identifying the initial date of appearance of the behaviour or emotion. Compensation: Identifying the unmet or unfulfilled desire. Concept: Defining the “big idea” compensation for the identified consumer need. Some of Lindstrom's clients such as Lowes Foods looked at data in a different way and actually chose to live with the customer. “As you enter their store, they have now created an amazing community where every staff member acts in a character mood, based on Small Data”. The supermarket made everything it can to make the customer feel at home. All the behaviours of employees are inspired by customer feedbacks gathered from interviews directly done at customer’s home. === Healthcare === Researchers at Cornell University started developing applications to monitor health problems in patients, based on small data. This is an initiative of Cornell's Small Data Lab, in close cooperation with Weill Cornell Medicine College, led by Deborah Estrin. The Small Data Lab developed a series of apps, focusing not only on gathering data from patients' pain but also tracking habits in areas such as grocery shopping. In the case of patients with rheumatoid arthritis for example, which has flares and remissions that do not follow a particular cycle, the app gathers information passively, thus allowing to forecast when a flare might be coming up based on small changes in behaviour. Other apps developed also include monitoring online grocery shopping, to use this information from every user to adapt their groceries to the recommendations of nutritionists, or monitoring email language to identify patterns that might indicate "fluctuations in cognitive performance, fatigue, side effects of medication or poor sleep, and other conditions and treatments that are typically self-reported and self-medicated". === Postal Service === The United States Postal Service (USPS) used optical character recognition (OCR) to automatically read and process 98% of all hand-addressed mail and 99.5% of machine-printed mail. By combining this technology with its small data sample of US zip codes, the USPS can now process more than 36,000 pieces of mail per hour. === Aerospace === In 2015, Boeing established the analytics lab for aerospace data in cooperation with the Carnegie Mellon University to leverage the university's leadership in machine learning, language technologies and data analytics. One of the initiatives projects aims to by standardize maintenance logs using AI to dramatically reduce costs. Currently, there is no standardized procedure to document maintenance logs leading to small but highly unstructured data sets. As a result, it becomes highly difficult for maintenance workers to translate these variations in maintenance logs within a short period of time. However, with AI and a narrow data set of common aircraft maintenance terminology, it becomes possible to dynamically translate these logs in real time. By using AI to enhance the speed and accuracy of the airline maintenance workflow, airlines stand to save billions according to the Harvard Business Review.
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