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  World Database of Happiness

  The World Database of Happiness is a web-based archive of research findings on subjective appreciation of life, based in the Erasmus Happiness Economics Research Organization of the Erasmus University Rotterdam in The Netherlands. The database contains both an overview of scientific publications on happiness and a digest of research findings. Happiness is defined as the degree to which an individual judges the quality of his or her life as a whole favorably. Two 'components' of happiness are distinguished: hedonic level of affect (the degree to which pleasant affect dominates) and contentment (perceived realization of wants). == Aims == The World Database of Happiness is a tool to quickly acquire an overview on the ever-growing stream of research findings on happiness Medio 2023 the database covered some 16,000 scientific publications on happiness, from which were extracted 23,000 distributional findings (on how happy people are) and another 24,000 correlational findings (on factors associated with more and less happiness). The first findings date from 1915. == Technique == The World Database of Happiness is a ‘findings archive’, which consists of electronic ‘finding pages’ on which separate research results are described in a standard format and terminology. These finding pages can be selected on various characteristics, such as population studies, the measure of happiness used and observed co-variates. All finding-pages have a specific internet address to which links can be made in scientific review papers or policy recommendations. This allows a concise presentation of many findings in a table, while providing readers with access to detail. == Scientific use == The Database has been cited in 254 scientific papers, for example to access under what conditions economic growth enhances average happiness or to show that rising mean happiness at first raises happiness inequality, but further rise will diminish these differences, or that healthy eating is associated with more happiness, even after controlling for the effect on health Another finding is that relative simple happiness training techniques raise happiness by some 5% == Popular use == The World Database of Happiness is often used by popular media to make lists of the happiest countries around the globe. An example is the Happy Planet Index, which aims to chart sustainable happiness all over the world by combining data on longevity, happiness and the size of the ecological footprint of citizens. == Strengths and weaknesses == The database has a clear conceptual focus, it includes only research findings on subjective enjoyment of one's life as a whole. Thereby it evades the Babel that has haunted the study of happiness for ages. The other side of that coin is that much interesting research is left out. The findings are reported with technical details about measurement and statistical analysis. This detail is welcomed by scholars, but makes the information difficult to digest for lay-persons. Still another limitation is that the determinants of happiness appear to vary considerably across persons and situations, which make it hard to draw general conclusions about the causes of happiness. What is clear is that poor health, separation, unemployment and lack of social contact are all strongly negatively associated with happiness. Another problem for the World database of happiness is that the studies on happiness increase with such a high rate that it gets increasingly difficult to offer a complete overview of all research findings. A further concern is that the Database of Happiness is exclusively focused on hedonic happiness (feeling good) and not on mature happiness that might exist in the face of suffering

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  Best arm identification

  Best arm identification (BAI) is a sequential one-player game where the player has to find the best action (arm) among a list of actions (arms) by collecting information in the most efficient way. It is a multi-armed bandit game as a player only gets information about an arm by playing it. The most common objective in multi-armed bandit games is to minimize the regret (i.e., play the best action as much as possible), but in BAI, the goal is to find the best arm as efficiently as possible. This problem naturally arises in scenarios such as adaptive clinical trials where the number of patients is limited and the quantification of the confidence in a treatment is important. It also arises in hyperparameter optimization where the goal is to find the optimal choice of hyperparameters for an algorithm with the smallest possible number of experiments, as it can be costly in terms of time, energy, or money. == Stochastic multi-armed bandit == The stochastic multi-armed bandit (MAB) is a sequential game with one player and K {\displaystyle K} actions (arms). Each arm has an unknown probability distribution associated with it. At each turn, the player has to choose one action and receive an observation from the probability distribution associated with the arm. The more you play an arm, the more you get information on its probability distribution. === Best arm identification === In BAI the goal is to find the arm that has the probability distribution with the highest mean. BAI may be either fixed confidence or fixed horizon. In a fixed-confidence game, a confidence level δ {\displaystyle \delta } is fixed at the beginning of the game and the goal is to find the best arm with this confidence level in as few turns as possible. In a fixed horizon game, the number of turns T {\displaystyle T} is fixed, and the goal is to find the best arm with the highest possible confidence in T {\displaystyle T} turns. === Math formalisation === We have one player and K {\displaystyle K} actions (arms). Behind each arm k ∈ { 1 , … , K } {\displaystyle k\in \{1,\ldots ,K\}} lies an unknown distribution ν k {\displaystyle \nu _{k}} with mean μ k {\displaystyle \mu _{k}} . Each distribution ν k {\displaystyle \nu _{k}} belongs to a known family D {\displaystyle {\mathcal {D}}} (such as the set of Gaussian distributions or Bernoulli distributions). At each time step t {\displaystyle t} , the player selects an arm a t {\displaystyle a_{t}} and observes an independent sample X t ∼ ν a t {\displaystyle X_{t}\sim \nu _{a_{t}}} from the corresponding distribution. We will note μ ∗ := max μ a {\displaystyle \mu ^{}:=\max \mu _{a}} the highest mean. An arm a {\displaystyle a} that satisfies μ a = μ ∗ {\displaystyle \mu _{a}=\mu ^{}} is called an optimal arm; otherwise it is called suboptimal arm. In best arm identification (BAI) the objective is to identify an optimal arm. Two main settings for BAI appear in the literature: Fixed confidence: In this setting, one typically assumes that there exists a unique optimal arm. A confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} is specified at the beginning. The algorithm must stop at some finite stopping time τ δ < + ∞ {\displaystyle \tau _{\delta }<+\infty } and return an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that the probability of error is bounded: P ( a ^ τ δ ≠ a ∗ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{})\leq \delta } . The objective is to minimize the expected sample complexity E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} . Such a setting appears, for example, when a constraint on the confidence is required (for example, if we require a confidence level of 95%, so δ = 1 − 0.95 = 0.05 {\displaystyle \delta =1-0.95=0.05} ). Fixed horizon: In this setting, the number of samples T {\displaystyle T} is fixed in advance. The goal is to design an algorithm that minimizes the probability of misidentifying the optimal arm: P ( a ^ T ≠ a ∗ ) {\displaystyle \mathbb {P} ({\hat {a}}_{T}\neq a^{})} . This setting appears when the number of experiments is limited (for drug tests, the number of patients can be fixed in advance). === Example of simple modelling === In the case where we have K {\displaystyle K} treatments and we want to be sure with a confidence level of 95% which treatment is the best to heal a specific disease. Each treatment heals or does not heal the disease with a probability μ k {\displaystyle \mu _{k}} , which means that each distribution is a Bernoulli distribution, so D {\displaystyle {\mathcal {D}}} is the set of Bernoulli distributions. We can use a BAI algorithm to minimize E [ τ 0.05 ] {\displaystyle \mathbb {E} [\tau _{0.05}]} , the number of patients required to find the best treatment with probability 95%. == Applications == Best arm identification naturally arises in several practical domains: Adaptive clinical trials: The objective is to identify the most effective treatment based on sequentially collected patient data. Each treatment can be modeled as having an underlying distribution of outcomes. The goal is to identify the treatment with the highest expected outcome with high confidence (fixed confidence setting δ {\displaystyle \delta } ) while minimizing the number of drug test patients (minimise E [ τ δ ] {\displaystyle \mathbb {E} [\tau _{\delta }]} ), as it costs to pay patients for this and we would like to use as little as possible less effective drugs. Hyperparameter tuning: Selecting the best configuration for machine learning models efficiently by treating each hyperparameter setting as an arm. The goal is to find the best hyperparameter with as few experiments possible as experiments are costly in time and in energy == Fixed confidence level == In the fixed-confidence setting, the goal is to design an algorithm that identifies the best arm with a prescribed confidence level δ {\displaystyle \delta } while minimizing the expected number of samples. Any such algorithm requires two key components: Stopping rule: A decision criterion that determines when to stop sampling. Formally, this defines a stopping time τ δ {\displaystyle \tau _{\delta }} and returns an arm a ^ τ δ {\displaystyle {\hat {a}}_{\tau _{\delta }}} such that P ( a ^ τ δ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau _{\delta }}\neq a^{\star })\leq \delta } and P ( τ δ < + ∞ ) = 1 {\displaystyle \mathbb {P} (\tau _{\delta }<+\infty )=1} . Sampling rule: A policy π {\displaystyle \pi } that, at each round t {\displaystyle t} , selects the next arm to sample a t {\displaystyle a_{t}} based on all previous observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s Read more →

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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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  Paper data storage

  Paper data storage refers to the use of paper as a data storage device. This includes writing, illustrating, and the use of data that can be interpreted by a machine or is the result of the functioning of a machine. A defining feature of paper data storage is the ability of humans to produce it with only simple tools and interpret it visually. Though now mostly obsolete, paper was once an important form of computer data storage as both paper tape and punch cards were a common staple of working with computers before the 1980s. == History == Before paper was used for storing data, it had been used in several applications for storing instructions to specify a machine's operation. The earliest use of paper to store instructions for a machine was the work of Basile Bouchon who, in 1725, used punched paper rolls to control textile looms. This technology was later developed into the wildly successful Jacquard loom. The 19th century saw several other uses of paper for controlling machines. In 1846, telegrams could be prerecorded on punched tape and rapidly transmitted using Alexander Bain's automatic telegraph. Several inventors took the concept of a mechanical organ and used paper to represent the music. In the late 1880s Herman Hollerith invented the recording of data on a medium that could then be read by a machine. Prior uses of machine readable media, above, had been for control (automatons, piano rolls, looms, ...), not data. "After some initial trials with paper tape, he settled on punched cards..." Hollerith's method was used in the 1890 census. Hollerith's company eventually became the core of IBM. Other technologies were also developed that allowed machines to work with marks on paper instead of punched holes. This technology was widely used for tabulating votes and grading standardized tests. Banks used magnetic ink on checks, supporting MICR scanning. In an early electronic computing device, the Atanasoff–Berry Computer, electric sparks were used to singe small holes in paper cards to represent binary data. The altered dielectric constant of the paper at the location of the holes could then be used to read the binary data back into the machine by means of electric sparks of lower voltage than the sparks used to create the holes. This form of paper data storage was never made reliable and was not used in any subsequent machine. == Modern techniques == === 1D barcodes === Barcodes make it possible for any object that was to be sold or transported to have some computer readable information securely attached to it. Universal Product Code barcodes, first used in 1974, are ubiquitous today. Some people recommend a width of at least 3 pixels for each minimum-width gap and each minimum-width bar for 1D barcodes. The density is about 50 bits per linear inch (about 2 bit/mm). === 2D barcodes === 2D barcodes allow to store much more data on paper, up to 2.9 kbyte per barcode. It is recommended to have a width of at least 4 pixels—e.g., a 4 × 4 pixel = 16 pixel module. == Limits == The limits of data storage depend on the technology to write and read such data. The theoretical limits assume a scanner that can perfectly reproduce the printed image at its printing resolution, and a program which can accurately interpret such an image. For example, an 8 in × 10 in (200 mm × 250 mm) 600 dpi black-and-white image contains 3.43 MiB of data, as does a 300 dpi CMYK printed image. A 2,400 ppi True color (24-bit) image contains about 1.29 GiB of information; printing an image maintaining this data would require a printing resolution of about 120,000 dpi in black and white, or 60,000 dpi with CMYK dots.

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  Automated machine learning

  Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.

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  Information audit

  The information audit (IA) extends the concept of auditing from a traditional scope of accounting and finance to the organisational information management system. Information is representative of a resource which requires effective management and this led to the development of interest in the use of an IA. Prior the 1990s and the methodologies of Orna, Henczel, Wood, Buchanan and Gibb, IA approaches and methodologies focused mainly upon an identification of formal information resources (IR). Later approaches included an organisational analysis and the mapping of the information flow. This gave context to analysis within an organisation's information systems and a holistic view of their IR and as such could contribute to the development of the information systems architecture (ISA). In recent years the IA has been overlooked in favour of the systems development process which can be less expensive than the IA, yet more heavily technically focused, project specific (not holistic) and does not favour the top-down analysis of the IA. == Definition == A definition for the Information Audit cannot be universally agreed-upon amongst scholars, however the definition offered by ASLIB received positive support from a few notable scholars including Henczel, Orna and Wood; “(the IA is a) systematic examination of information use, resources and flows, with a verification by reference to both people and existing documents, in order to establish the extent to which they are contributing to an organisation’s objectives” In summary, the term audit itself implies a counting, the IA being much the same yet it counts IR and analyses how they are used and how critical they are to the success of a given task. == Role and scope of an IA == In much the same way as the IA is difficult to define, it can be utilised in a range of contexts by the information professional, from complying with freedom of information legislation to identifying any existing gaps, duplications, bottlenecks or other inefficiencies in information flows and to understand how existing channels can be used for knowledge transfer In 2007 Buchanan and Gibb developed upon their 1998 examination of the IA process by outlining a summary of its main objectives: To identify an organisation’s information resource To identify an organisation’s information needs Furthermore, Buchanan and Gibb went on to state that the IA also had to meet the following additional objectives: To identify the cost/benefits of information resources To identify the opportunities to use the information resources for strategic competitive advantage To integrate IT investment with strategic business initiatives To identify information flow and processes To develop an integrated information strategy and/or policy To create an awareness of the importance of Information Resource Management (IRM) To monitor/evaluate conformance to information related standards, legislations, policy and guidelines. == Methodology evolution == === Overview === In 1976 Riley first published a definition of IA as a way of analysing IR based on a cost-benefit model. Since Riley, scholars have outlined further developed methodologies. Henderson took a cost-benefit approach hoping to draw focus from manpower-costing to information storage and acquisition which he felt was being overlooked. In 1985 Gillman focused upon identifying the relationships which existed between various components in order to map them to one another. Neither Henderson nor Gillman’s methods offered alternative approaches beyond the existing organisational frameworks. Quinn took a hybrid-approach combining Gillman and Henderson’s methods to identify the purpose of existing IR and to position them within the organisation, as did Worlock. The differentiator between Quinn and Worlock lay in Worlock’s consideration of solutions outside of the current organisational structure. These approaches had thus far had paid little attention to the needs of the user or in making structured recommendations for the development of a corporate information strategy. Therefore, here follows a brief outline and overall comparison of four published strategic approaches in order that one might understand the development of the IA methodology. === Burk and Horton === In 1988 Burk and Horton developed InfoMap, the first IA methodology developed for widespread use. It aimed to discover, map and evaluate the IR within an organisation using a 4-stage process: Survey staff using questionnaires/interviews Measure the IR against cost/value Analyse resources Synthesise the findings and map the strengths and weaknesses of the IR against the objectives of the organisation. Although the method inventoried all IR (and therefore met standard ISO 1779) this bottom-up approach revealed limited analysis of the organisation holistically and the steps were not explicit enough. === Orna === Orna produced a top-down methodology in contrast to Burk and Horton, placing emphasis upon the importance of organisational analysis and aimed to assist in the production of a corporate information policy. Initially the method had just 4-stages, this later revised to a 10-stage process which included pre and post-audit stages as below: Conduct a preliminary review to confirm operational/strategic direction Gain support/resource from management Gain commitment from the other stakeholders (staff) Planning including the project, team, tools and techniques Identify the IR, information flow and produce a cost/value assessment Interpret findings based upon current versus desired state Produce a report to present findings Implement recommendations Monitor effects of change Repeat the IA Orna’s method introduced the need for a cyclical IA to be put in place in order for the IR to be continually tracked and improvements made regularly. Again this method was criticised for lacking some practical application and in 2004 Orna revised the methodology once more to try to rectify this problem === Buchanan and Gibb === In 1998, similarly to Orna's earlier publication, Buchanan and Gibb took a top-down approach, drawing techniques from established management disciplines to provide a framework and a level of familiarity for information professionals. This set of techniques was a notable contribution to IA methodologies and understood the need to be flexible for each organisation. Theirs was a 5-stage process: Promote benefits of the IA through seminars/surveys/CEO letter for cooperation Identify the mission objectives of the organisation, define environment (PEST), map information flow and examine organisation culture. Analyse and formulate action plan for problem areas, flow diagrams and a report of findings and recommendations Account for cost of IR and related services using Activity Based Costing (ABC) and Output Based Specification (OBS). Synthesise the whole process in final audit report and provide an information strategy (strategic direction) in relation to the organisation’s mission statement. This was the introduction of a new approach to costing the IR and had an integrated strategic direction, yet the scholars admitted that this method may be impractical for smaller organisations. === Henczel === Henczel’s methodology drew upon the strengths of Orna and Buchanan and Gibb to produce a 7-stage process: Planning and submission of business case for approval to proceed Data collection and development of an IR database and population through survey techniques Structured data analysis Data evaluation, interpretation and formulation of recommendations Communication of recommendations through a report Implementing recommendations through a devised programme The IA as a continuum-establishment of a cyclical process Focus was made once more on the strategic direction of the organisation conducting the IA. Furthermore, Henczel made examination into the use of the IA as a first-step in the development of a knowledge audit or knowledge management strategy as discussed in the later section. == Case studies == Scholars and information professionals have since tested the above methodologies with varied results. An early case study produced by Soy and Bustelo in a Spanish financial institution in 1999 aimed to identify the use of information resources for qualitative and quantitative data analysis due to the rapid expansion of the organisation within a six-year period. Although the methodology was not explicitly credited to any of the above-mentioned scholars, it did follow a strategic (post 1990's) IA process including gaining support from management, the use of questionnaires for data collection, analysis and evaluation of the data, identification and mapping of the IR, cost-analysis and outlining recommendations to assist with the establishment of an Information policy. In addition the IA report suggested that the process would need to be continual (cyclical as Orna, Henczel and Buchanan and Gibb suggest). Conclusions of this case-study stated that th

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  Data janitor

  A data janitor is a person who works to take big data and condense it into useful amounts of information. Also known as a "data wrangler", a data janitor sifts through data for companies in the information technology industry. A multitude of start-ups rely on large amounts of data, so a data janitor works to help these businesses with this basic, but difficult process of interpreting data. While it is a commonly held belief that data janitor work is fully automated, many data scientists are employed primarily as data janitors. The information technology industry has been increasingly turning towards new sources of data gathered on consumers, so data janitors have become more commonplace in recent years.

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  Behavior selection algorithm

  In artificial intelligence, a behavior selection algorithm, or action selection algorithm, is an algorithm that selects appropriate behaviors or actions for one or more intelligent agents. In game artificial intelligence, it selects behaviors or actions for one or more non-player characters. Common behavior selection algorithms include: Finite-state machines Hierarchical finite-state machines Decision trees Behavior trees Hierarchical task networks Hierarchical control systems Utility systems Dialogue tree (for selecting what to say) == Related concepts == In application programming, run-time selection of the behavior of a specific method is referred to as the strategy design pattern.

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  Language-Theoretic Security

  Language-theoretic security, or LangSec, is an approach to software security that focuses on input handling, complexity, and program design as strategies to improve the verifiability of computer programs. It was introduced in 2005 by Robert J. Hansen and Meredith L. Patterson at BlackHat and in 2011 by Len Sassaman and Patterson. It aims to create a formal description of which software is likely to have security vulnerabilities of particular classes, and why. It considers programs to have an inherent parser component, whether or not explicit, composed of that part of the program which operates on external input before that input is fully parsed. A central hypothesis of language-theoretic security is that vulnerabilities in software increase according to the computational power of the notional input-accepting automaton equivalent to this parser, using the definitions of automata theory. The lower bound on this computational power is the input language complexity of the program. The extent to which reducing this complexity is possible is a function of the specification of the communication protocol or file format the program takes as input. == Parsing as a security mechanism == The behaviour of a program is defined with reference to its expected input. Unexpected input being used by a program is a factor in numerous security bugs, including the so-called Android master key vulnerability (CVE-2013-4787), because accepting unexpected input renders the program's specification ambiguous. In that instance, the unexpected ambiguity came in the form of a ZIP file with duplicate filenames. If a program fully parses its input and only acts on input that unambiguously meets the specification, it follows that the program will avoid these types of vulnerabilities. This is an intentional inversion of the Postel principle. Accepting only unambiguous and valid input is a more formal requirement than input validation or sanitization, and narrows the number of possible but unanticipated program states that can be induced in an application via user input. Conversely, failure to do this is associated with security vulnerabilities. Input sanitization in particular is held to be an inadequate approach to avoiding malicious input because it inherently ignores context-sensitive properties of the input; it can therefore result in paradoxical effects, such as sanitization code activating otherwise inert cross-site scripting payloads in browsers. === Parser differentials === If the language of accepted program input is sufficiently simple, it is possible to verify that two implementations parse the same input language consistently. This is advantageous because it shows no parser differential exists between the two implementations. The requisite level of simplicity is theoretically that for which there is a solution to the equivalence problem. If the two parsers involved in CVE-2013-4787 were equivalent - that is, if they rendered the same output state given the same input state - the vulnerability could not have existed. One strategy for doing this is to publish machine-readable specifications of a format or protocol, and then use a parser generator to generate the parser code. An example of a parser generator built for this purpose is DaeDaLus. The combination of Lex with any of GNU Bison, ANTLR, or Yacc also accomplishes this. However, many parser generators allow the mixing of general purpose code with the parsing definitions, which weakens the guarantees provided by parsing. === Analysis of injection attacks === Injection attacks are generally the result of differences between the serializer (or "unparser") and the corresponding parser at a layer boundary in a system; therefore, they are a special case of parser differentials. In a SQL injection attack, for example, an attacker is able to cause the application with which they are interacting to serialize a SQL query that has different semantics than intended. In the simplest case where the payload ends a string and adds new code, the payload has crossed the code-data boundary in SQL. In language-theoretic security, this is treated as a bug in the serializer of the SQL query, which should instead be written in a way that constrains its possible outputs to those within the scope of the intended query. === Parser combinators === If a parser generator is not used, it is still possible to avoid implementation bugs by using parser combinator such as Nom to implement the parser code. This has the drawback of relying on a programmer correctly translating the specification into the language of the parser generator library, though this task is still less error-prone than hand-coding a parser. == Input format complexity == Complexity in computer programs is associated with security vulnerabilities. Within the domain of language-theoretic security, complexity is described with reference to the computational power of the abstract machine necessary to implement the program, or more particularly, to implement the parser for its input language. This complexity describes whether it is possible to show that there is no unintended or undesired functionality in the program which might be exploitable by an attacker. To be bounded in complexity, the program's input must be well-defined both in terms of form and of semantics. === Weird machines === A weird machine is a model of computation in a program that exists in parallel with, but is distinct from, the intended abstract model of computation in that program. Some classes of weird machine arise from the multi-layered nature of computer programs, or the context in which the programs run; others result from the unanticipated functionality a program has due to its complexity or to software bugs. The more complex the computation model of a program, the more likely it is to implement a weird machine. Depending on context, the weird machine may or may not be concretely useful for an attacker. Since the space of weird machines in the context of some program is the universe of all possible states that are not within the program's intended states, many exploited states including remote code execution and injection attacks belong to the domain of weird machines. A reduction in weird machines is therefore a likely correlate with reduced program vulnerability. === SafeDocs project === SafeDocs is a DARPA project undertaken in 2018 to take existing file formats, create safer subsets of them, and develop programming tools to work for the safer formats. The initial test case for this was PDF. The purpose of creating safer subsets in this case is to lower the minimum bound on parser complexity so that it becomes possible to create tools that will generate correct, normative parsers for them. == Relation to programming languages == The analytic framework of language-theoretic security assumes programs to be virtual machines that execute their input. A document that is read by an application is in this sense a form of machine code, in a generalization of the data as code idea, following the automata theory description of parsers. === Type-safe programming languages === Parsing input and serializing output are operations that consume one data type and emit another. A programming language can therefore check that data is correctly parsed and contains the expected structure by checking data types, and correct serializing (or unparsing) can be implemented as operations on the data types that are relevant to the program's output. This approach can be used to show that the recognizer and unparser patterns have been implemented. It is also possible to implement type checking across a distributed system to enforce parsing and unparsing of the expected structures and to verify that the assumptions made in designing the compositional properties of a distributed system have been followed. === Memory-safe programming languages === In the general case, spatial memory correctness is undecidable. If any proof of spatial memory correctness is to be made, it is therefore necessary to bound the complexity of the code. Interpreted languages such as Java and Python effectively accomplish this via runtime bounds checking, and frameworks for runtime bounds checking also exist for C. The effect of these strategies for spatial memory correctness are to create a halt state in place of a spatial memory correctness violation; therefore, it can be shown that the program will not violate spatial memory correctness, but in exchange, it cannot be shown in the general case that programs will not have runtime bounds checking exceptions. Some programming languages, such as Rust, accomplish this using borrow checking. The borrow checker acts to assure spatial memory correctness by compile-time reference counting. Code for which spatial memory correctness cannot be shown to not be violated therefore does not compile, inherently limiting the complexity of the spatial memory correctness of the program to what is decidable. Thi

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  Explore-then-commit algorithm

  Explore Then Commit (ETC) is an algorithm for the multi-armed bandit problem foc,used on finding the best trade-off between exploration and exploitation. == 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} 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}} , they then get 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 Read more →

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  Artificial intelligence in Brazilian industry

  In 2022, 16.9% (1,620) of the 9,586 Brazilian industrial companies with 100 or more employees used artificial intelligence in their operations Among the companies that used AI, the areas of administration (73.8%), product project development (65.9%), processes, services and marketing (65.1%) were those that used it the most, followed by the areas of production (56.4%) and logistics (48.4%). == Current scenario == === Adoption in Brazilian industrial sectors === In senior management, the majority (56%) of executives have a long-term vision for its use. The study also shows that IT, Innovation, and Marketing are the areas where AI use is most widespread, and that 43% of companies are developing or adapting the algorithms they use. The majority of large institutions that reported some type of AI use purchased these solutions from other companies (76%). Some factors for the adoption of artificial intelligence in companies include the establishment of an autonomous strategy by the company (87.0%), and the influence of suppliers and/or customers (63.0%) and the main difficulties in using technologies were high costs (80.8%), lack of qualified personnel in the company (54.6%) and excessive economic risks (49.5%). Three variables are considered the most relevant to explain the option to use AI: the implementation of a digital security policy, the size of companies with 250 or more employees and the characteristics of the company related to information and communication. When analyzing AI use by company size in Brazil, large companies have the highest proportion of AI use, mainly due to their investment capacity and technology experimentation. However, when comparing Brazil and Europe, indicators show an acceleration in AI use among large European companies, while in Brazil the situation remains stable. In 2023, 30% of large companies in the European bloc used some type of AI, a figure that rose to 41% in 2024, while in Brazil these proportions were 41% in 2023 and 38% in 2024. === Workforce === The challenge of upskilling begins with employees who are capable of understanding recent technological changes. Similarly, companies must create the environment and conditions for workforce development conducive to innovation, and universities must be prepared to provide knowledge aligned with the transition process, which in turn must be supported by public policies. The concern with training a specialized workforce in AI can be seen in the low number of graduates and PhDs in computer science and computer engineering in Brazil, compared to the number shown in other countries. As recorded in the document Recommendations for the Advancement of Artificial Intelligence in Brazil, 2019 data from the Coordination for the Improvement of Higher Education Personnel (CAPES) indicate that "the number of PhDs graduated annually in computing remained below 400 in 2016, and is not expected to have increased during the Covid-19 pandemic" (ABC, 2023). In the United States, by contrast, the number of PhDs graduated in these two areas has remained around 1,800 for the past 11 years, and during this period, the number of PhDs specializing in AI jumped from 10% to 19%. Based on data from the CNPq Lattes Platform (October 2019), it is possible to observe that the number of professionals in the AI field in Brazil is 4,429 specialists. This is still a small number compared to the 415,166 IT jobs in the country's business sector alone. === R&D, scientific production and integration with industry === China and the United States lead in the number of publications. These two countries are followed by the G7 members: India, Austria, South Korea, and Spain. Brazil appears in the next group, alongside the Netherlands, Russia, Indonesia, and Ireland. Regarding the promotion of research and technologies related to AI, public entities such as the Coordination for the Improvement of Higher Education Personnel (Capes) and the National Council for Scientific and Technological Development (CNPq) stood out as the main funders. Currently, different countries and territories have been promoting the development of Artificial Intelligence (AI). In the Brazilian case, one of the main initiatives is the creation of Engineering Research Centers/Applied Research Centers (CPE/CPA) in AI by the São Paulo Research Foundation (FAPESP), in collaboration with the Ministry of Science, Technology and Innovation (MCTI), the Ministry of Communications (MC) and the Brazilian Internet Steering Committee (CGI.br). In terms of the number of patents filed and the volume of investments, the leading nations in AI are the United States, China, France, Germany, the United Kingdom, Russia, India, Switzerland, Japan, South Korea, the Netherlands, Sweden, Finland, Ireland, Singapore, Canada, Israel, and Italy. Brazil appears among the top twenty countries in some rankings, mainly due to its good number of publications (approximately 10% of the number of articles published by the United States). The US is home to approximately 60% of the world's top AI researchers, followed by China (11%), Europe (10%), and Canada (6%). To change this scenario, in August 2024, the Brazilian government announced an investment of R$23 billion until 2028 in artificial intelligence, seeking to “transform the country into a global reference in innovation”. == Future challenges == The Organization for Economic Cooperation and Development (2020) report highlighted three factors that hinder the digital transformation journey and application of AI in Brazil: insufficient infrastructure, high costs due to the tax system, and financial limitations, such as limited access to financing. The costs of adopting technology, its incompatibility with the business, and the lack of training also represent obstacles that Brazilian industry must overcome. There are also inherent obstacles for companies. A McKinsey review emphasizes that once a company chooses one or more sectors to focus on, it must select specific applications. Buyers aren't interested in artificial intelligence simply because it's a breakthrough technology; they want AI to generate a good return on investment, whether by solving specific problems, saving money, or increasing sales. If an AI vendor tried to offer a horizontal solution, the value proposition might not be as compelling. Part of the solution to Brazil's technological backwardness involves building an ecosystem fueled by private institutions, universities, and governments.

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  Manufacture Modules Technologies

  Manufacture Modules Technologies Sarl (MMT) is a Swiss company established in Geneva in 2015 which originally specialised in the development and commercialization of "Horological Smartwatch modules", firmware, apps and cloud. Located at Geneva's Skylab high-tech hub, it expanded into the development and manufacturing of "E-Straps" operated with a mobile application. Philippe Fraboulet is the CEO. == History == In June 2015, Fullpower Technologies and Union Horlogère Suisse (Swiss Watchmakers Corporation) formed MMT as a joint venture, which then launched the MotionX Horological Smartwatch Open Platform for the Swiss watch industry. The initial licensees were Frederique Constant, Alpina and Mondaine, brands owned by Union Horlogère Suisse. Fullpower created and managed the circuit design, firmware, smartphone applications (including sleep activity), as well as the cloud Infrastructure. MMT managed the Swiss watch movement development and production as well as licensing and support. In July 2016, Union Horlogere Holding and MMT were spun-out of the Frédérique Constant Group. Fullpower Technologies' 19.99% share was acquired by Union Horlogere Holding BV, giving it 100% of MMT's shares. == Business == The company offers firmware, a cloud, manufacturing, service and over-the-air facilities for upgrades. The company also offers its own apps, which bear the label “Swiss Made software”.

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  GNU Binutils

  The GNU Binary Utilities, or binutils, is a collection of programming tools maintained by the GNU Project for working with executable code including assembly, linking and many other development operations. The tools are originally from Cygnus Solutions. The tools are typically used along with other GNU tools such as GNU Compiler Collection, and the GNU Debugger. == Tools == The tools include: == elfutils == Ulrich Drepper wrote elfutils, to partially replace GNU Binutils, purely for Linux and with support only for ELF and DWARF. It distributes three libraries with it for programmatic access.

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  Quality of Data

  Quality of Data (QoD) is a designation coined by L. Veiga, that specifies and describes the required Quality of Service of a distributed storage system from the Consistency point of view of its data. It can be used to support big data management frameworks, Workflow management, and HPC systems (mainly for data replication and consistency). It takes into account data semantics, namely the Time interval of data freshness, the Sequence of tolerable number of outstanding versions of the data read before ore refresh, and the Value divergence allowed before displaying it. Initially it was based on a model from an existing research work regarding vector-field Consistency, awarded the best-paper prize in the ACM/IFIP/Usenix Middleware Conference 2007 and later enhanced for increased scalability and fault-tolerance. This consistency model has been successfully applied and proven in big data key/value store Apache HBase, initially designed as a middleware module seating between clusters from separate data centres. The HBase-QoD coupling minimises bandwidth usage and optimises resources allocation during replication achieving the desired consistency level at a more fine-grained level. QoD is defined by the three-dimensions of vector k=(θ,σ,ν), but with a broader view of the issue, applicable also to large-scale data management techniques in regards to their timely delivery. == Other descriptions == Quality of Data should not be confused with other definitions for data quality such as completeness, validity, and accuracy.

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  Flajolet–Martin algorithm

  The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet, and "HyperLogLog: The analysis of a near-optimal cardinality estimation algorithm" by Philippe Flajolet et al. In their 2010 article "An optimal algorithm for the distinct elements problem", Daniel M. Kane, Jelani Nelson and David P. Woodruff give an improved algorithm, which uses nearly optimal space and has optimal O(1) update and reporting times. == The algorithm == Assume that we are given a hash function h a s h ( x ) {\displaystyle \mathrm {hash} (x)} that maps input x {\displaystyle x} to integers in the range [ 0 ; 2 L − 1 ] {\displaystyle [0;2^{L}-1]} , and where the outputs are sufficiently uniformly distributed. Note that the set of integers from 0 to 2 L − 1 {\displaystyle 2^{L}-1} corresponds to the set of binary strings of length L {\displaystyle L} . For any non-negative integer y {\displaystyle y} , define b i t ( y , k ) {\displaystyle \mathrm {bit} (y,k)} to be the k {\displaystyle k} -th bit in the binary representation of y {\displaystyle y} , such that: y = ∑ k ≥ 0 b i t ( y , k ) 2 k . {\displaystyle y=\sum _{k\geq 0}\mathrm {bit} (y,k)2^{k}.} We then define a function ρ ( y ) {\displaystyle \rho (y)} that outputs the position of the least-significant set bit in the binary representation of y {\displaystyle y} , and L {\displaystyle L} if no such set bit can be found as all bits are zero: ρ ( y ) = { min { k ≥ 0 ∣ b i t ( y , k ) ≠ 0 } y > 0 L y = 0 {\displaystyle \rho (y)={\begin{cases}\min\{k\geq 0\mid \mathrm {bit} (y,k)\neq 0\}&y>0\\L&y=0\end{cases}}} Note that with the above definition we are using 0-indexing for the positions, starting from the least significant bit. For example, ρ ( 13 ) = ρ ( 1101 2 ) = 0 {\displaystyle \rho (13)=\rho (1101_{2})=0} , since the least significant bit is a 1 (0th position), and ρ ( 8 ) = ρ ( 1000 2 ) = 3 {\displaystyle \rho (8)=\rho (1000_{2})=3} , since the least significant set bit is at the 3rd position. At this point, note that under the assumption that the output of our hash function is uniformly distributed, then the probability of observing a hash output ending with 2 k {\displaystyle 2^{k}} (a one, followed by k {\displaystyle k} zeroes) is 2 − ( k + 1 ) {\displaystyle 2^{-(k+1)}} , since this corresponds to flipping k {\displaystyle k} heads and then a tail with a fair coin. Now the Flajolet–Martin algorithm for estimating the cardinality of a multiset M {\displaystyle M} is as follows: Initialize a bit-vector BITMAP to be of length L {\displaystyle L} and contain all 0s. For each element x {\displaystyle x} in M {\displaystyle M} : Calculate the index i = ρ ( h a s h ( x ) ) {\displaystyle i=\rho (\mathrm {hash} (x))} . Set B I T M A P [ i ] = 1 {\displaystyle \mathrm {BITMAP} [i]=1} . Let R {\displaystyle R} denote the smallest index i {\displaystyle i} such that B I T M A P [ i ] = 0 {\displaystyle \mathrm {BITMAP} [i]=0} . Estimate the cardinality of M {\displaystyle M} as 2 R / ϕ {\displaystyle 2^{R}/\phi } , where ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} . The idea is that if n {\displaystyle n} is the number of distinct elements in the multiset M {\displaystyle M} , then B I T M A P [ 0 ] {\displaystyle \mathrm {BITMAP} [0]} is accessed approximately n / 2 {\displaystyle n/2} times, B I T M A P [ 1 ] {\displaystyle \mathrm {BITMAP} [1]} is accessed approximately n / 4 {\displaystyle n/4} times and so on. Consequently, if i ≫ log 2 ⁡ n {\displaystyle i\gg \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 0, and if i ≪ log 2 ⁡ n {\displaystyle i\ll \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 1. If i ≈ log 2 ⁡ n {\displaystyle i\approx \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} can be expected to be either 1 or 0. The correction factor ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} (OEIS: A244256) is found by calculations, which can be found in the original article. == Improving accuracy == A problem with the Flajolet–Martin algorithm in the above form is that the results vary significantly. A common solution has been to run the algorithm multiple times with k {\displaystyle k} different hash functions and combine the results from the different runs. One idea is to take the mean of the k {\displaystyle k} results together from each hash function, obtaining a single estimate of the cardinality. The problem with this is that averaging is very susceptible to outliers (which are likely here). A different idea is to use the median, which is less prone to be influences by outliers. The problem with this is that the results can only take form 2 R / ϕ {\displaystyle 2^{R}/\phi } , where R {\displaystyle R} is integer. A common solution is to combine both the mean and the median: Create k ⋅ l {\displaystyle k\cdot l} hash functions and split them into k {\displaystyle k} distinct groups (each of size l {\displaystyle l} ). Within each group use the mean for aggregating together the l {\displaystyle l} results, and finally take the median of the k {\displaystyle k} group estimates as the final estimate. The 2007 HyperLogLog algorithm splits the multiset into subsets and estimates their cardinalities, then it uses the harmonic mean to combine them into an estimate for the original cardinality.

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