Computational semantics is a subfield of computational linguistics. Its goal is to elucidate the cognitive mechanisms supporting the generation and interpretation of meaning in humans. It usually involves the creation of computational models that simulate particular semantic phenomena, and the evaluation of those models against data from human participants. While computational semantics is a scientific field, it has many applications in real-world settings and substantially overlaps with Artificial Intelligence. Broadly speaking, the discipline can be subdivided into areas that mirror the internal organization of linguistics. For example, lexical semantics and frame semantics have active research communities within computational linguistics. Some popular methodologies are also strongly inspired by traditional linguistics. Most prominently, the area of distributional semantics, which underpins investigations into embeddings and the internals of Large Language Models, has roots in the work of Zellig Harris. Some traditional topics of interest in computational semantics are: construction of meaning representations, semantic underspecification, anaphora resolution, presupposition projection, and quantifier scope resolution. Methods employed usually draw from formal semantics or statistical semantics. Computational semantics has points of contact with the areas of lexical semantics (word-sense disambiguation and semantic role labeling), discourse semantics, knowledge representation and automated reasoning (in particular, automated theorem proving). Since 1999 there has been an ACL special interest group on computational semantics, SIGSEM.
Process map
Process map is a global-system process model that is used to outline the processes that make up the business system and how they interact with each other. Process map shows the processes as objects, which means it is a static and non-algorithmic view of the processes. It should be differentiated from a detailed process model, which shows a dynamic and algorithmic view of the processes, usually known as a process flow diagram. There are different notation standards that can be used for modelling process maps, but the most notable ones are TOGAF Event Diagram, Eriksson-Penker notation, and ARIS Value Added Chain. == Global process models == Global characteristics of the business system are captured by global or system models. Global process models are presented using different methodologies and sometimes under different names. Most notably, they are named process map in Visual Paradigm and MMABP, value-added chain in ARIS, and process diagram in Eriksson-Penker notation – which can easily lead to the confusion with process flow (detailed process model). Global models are mainly object-oriented and present a static view of the business system; they do not describe dynamic aspects of processes. A process map shows the presence of processes and their mutual relationships. The requirement for the global perspective of the system as a supplementary to the internal process logic description results from the necessity of taking into consideration not only the internal process logic but also its significant surroundings. The algorithmic process model cannot take the place of this perspective since it represents the system model of the process. The detailed process model and the global process model represent different perspectives on the same business system, so these models must be mutually consistent. A macro process map represents the major processes required to deliver a product or service to the customer. These macro process maps can be further detailed in sub-diagrams. It is often the case that process maps cross different functional areas of the organization. Process maps are used by many companies to have a holistic view of all processes and the connections between them. Maps help in navigating the sub-processes and make understanding of the organization's operations easier. The process map shows relationships and dependencies between processes and its focus should be on core business processes of the organization. A process map can be seen as the most abstract level of the process architecture, and it acts as the introduction to the more detailed levels. A process map that is correctly designed is able to provide a general understanding of a company's operations. Designing the process map is an important and strategic step for the organization, and it is followed by further business process modelling implementation. == Context == Methodology for Modelling and Analysis of Business Process (MMABP) is a business process modelling methodology developed at the Department of Information Technology, Faculty of Informatics and Statistics of the Prague University of Economics and Business. The methodology is defined as a “general methodology for modelling business systems using informatics methods and approaches”. Methodology is used to analyse business processes and to develop a comprehensive model of the system. The goal of developing a model is to be used for process optimization. The model should be created following the characteristics and specifics of the organization in question and following external influences that can affect the organization. The model should be optimal from an economic perspective, but it should also be optimal from a factual perspective, meaning that it should be as simple as possible while maintaining complete functionality. Business system modelling is based on a two-dimensional approach: Real World structure (substance) – set of objects and their relationships Real World behaviour – set of mutually connected business processes Additionally, there are also two views of the systems: Global view of the system Detailed view of the system's parts This results in the need to model the system from four different perspectives in order to achieve the complete and comprehensive view of the business system. MMABP also proposes which notation languages can be used for modelling each perspective, and it also suggests some improvements to the notation languages in order to fit the purpose. Global view of the objects – Conceptual model (Class diagram) Detailed view of the objects – Object life cycle (State Chart) Global view of the processes – Process map (Eriksson-Penker Diagram/TOGAF Event Diagram/ARIS VAC) Detailed view of the processes – Model of the process flow (BPMN Diagram) Data Flow Diagram (DFD) is additional diagram used for describing the required functionalities of the information system. == Notation standards == === Eriksson-Penker Diagram === Eriksson-Penker diagram is a tool used in business model analysis and design. It is named after Hans-Erik Eriksson and Magnus Penker, who developed the concept in their book "Business modelling with UML: Business Patterns at Work”. Eriksson-Penker diagrams are used to map out the key components of a business model and how they interact with one another. The diagrams typically consist of a series of boxes and lines that represent the different elements of the business model, such as the value proposition, customer segments, channels, revenue streams, and key resources. The lines between the boxes represent the relationships and dependencies between the different elements of the business model. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. These diagrams are useful for visualizing and understanding the various components of a business model, and can help organizations identify potential areas for improvement or areas of risk. They can also be used as a communication tool to help stakeholders understand the business model and its underlying assumptions. It is possible to use Eriksson-Penker diagrams to create a global process view of a business. In this case, a diagram would be used to map out the key processes and activities that are involved in the business, as well as the relationships and dependencies between these processes. For example, an Eriksson-Penker diagram could be used to depict the various steps involved in the product development process, from concept development to market launch. It could also be used to show how different functions within the organization, such as marketing, sales, and production, interact and depend on one another to support the overall business. Eriksson-Penker diagram is one of the most popular de facto standards that can be used for an object-oriented global view of business processes. It is developed as an extension of the UML, and it is often used together with the BPMN to compensate for the lack of possibility to model the global view with this widely accepted standard. === TOGAF Event Diagram === TOGAF (The Open Group Architecture Framework) is a framework for enterprise architecture that provides a common language and set of standards for designing, planning, implementing, and governing an enterprise's IT architecture. TOGAF event diagrams are diagrams used in the TOGAF framework to represent the flow of events within a system or process. The TOGAF Event Diagram is a visual representation of the events within an organization or system. It can be used to show the sequence of events that occur in a particular process, as well as the relationships between the events and the stakeholders involved. TOGAF Event Diagrams can be useful in creating a global process view because they provide a visual representation of the events, which can be helpful in understanding how the process fits into the larger context of the organization. TOGAF Event Diagram is the most perspective standard for the system view of processes today. It is used to represent the system of processes as well as their connections to the functional organizational structure. === ARIS Value Added Chain === ARIS (Architecture of Integrated Information Systems) is a methodology and a set of tools for designing and managing business processes. It is based on the idea that business processes are the core of an organization and that they can be modelled and optimized to improve efficiency and effectiveness. The ARIS methodology provides a framework for understanding and analysing business processes, as well as for designing and implementing improvements to those processes. It includes a set of graphical modelling languages and tools for creating process models, as well as a database for storing and managing pr
Semantic query
Semantic queries allow for queries and analytics of associative and contextual nature. Semantic queries enable the retrieval of both explicitly and implicitly derived information based on syntactic, semantic and structural information contained in data. They are designed to deliver precise results (possibly the distinctive selection of one single piece of information) or to answer more fuzzy and wide open questions through pattern matching and digital reasoning. Semantic queries work on named graphs, linked data or triples. This enables the query to process the actual relationships between information and infer the answers from the network of data. This is in contrast to semantic search, which uses semantics (meaning of language constructs) in unstructured text to produce a better search result. (See natural language processing.) From a technical point of view, semantic queries are precise relational-type operations much like a database query. They work on structured data and therefore have the possibility to utilize comprehensive features like operators (e.g. >, < and =), namespaces, pattern matching, subclassing, transitive relations, semantic rules and contextual full text search. The semantic web technology stack of the W3C is offering SPARQL to formulate semantic queries in a syntax similar to SQL. Semantic queries are used in triplestores, graph databases, semantic wikis, natural language and artificial intelligence systems. == Background == Relational databases represent all relationships between data in an implicit manner only. For example, the relationships between customers and products (stored in two content-tables and connected with an additional link-table) only come into existence in a query statement (SQL in the case of relational databases) written by a developer. Writing the query demands exact knowledge of the database schema. Linked-Data represent all relationships between data in an explicit manner. In the above example, no query code needs to be written. The correct product for each customer can be fetched automatically. Whereas this simple example is trivial, the real power of linked-data comes into play when a network of information is created (customers with their geo-spatial information like city, state and country; products with their categories within sub- and super-categories). Now the system can automatically answer more complex queries and analytics that look for the connection of a particular location with a product category. The development effort for this query is omitted. Executing a semantic query is conducted by walking the network of information and finding matches (also called Data Graph Traversal). Another important aspect of semantic queries is that the type of the relationship can be used to incorporate intelligence into the system. The relationship between a customer and a product has a fundamentally different nature than the relationship between a neighbourhood and its city. The latter enables the semantic query engine to infer that a customer living in Manhattan is also living in New York City whereas other relationships might have more complicated patterns and "contextual analytics". This process is called inference or reasoning and is the ability of the software to derive new information based on given facts. == Articles == Velez, Golda (2008). "Semantics Help Wall Street Cope With Data Overload". Wall Street & Technology. wallstreetandtech.com. Zhifeng, Xiao (2009). "Spatial information semantic query based on SPARQL". In Liu, Yaolin; Tang, Xinming (eds.). International Symposium on Spatial Analysis, Spatial-Temporal Data Modeling, and Data Mining. Vol. 7492. SPIE. pp. 74921P. Bibcode:2009SPIE.7492E..60X. doi:10.1117/12.838556. S2CID 62191842. Aquin, Mathieu (2010). "Watson, more than a Semantic Web search engine" (PDF). Semantic Web Journal. Dworetzky, Tom (2011). "How Siri Works: iPhone's 'Brain' Comes from Natural Language Processing". International Business Times. Horwitt, Elisabeth (2011). "The semantic Web gets down to business". computerworld.com. Rodriguez, Marko (2011). "Graph Pattern Matching with Gremlin". Marko A. Rodriguez. markorodriguez.com on Graph Computing. Sequeda, Juan (2011). "SPARQL Nuts & Bolts". Cambridge Semantics. Freitas, Andre (2012). "Querying Heterogeneous Datasets on the Linked Data Web" (PDF). IEEE Internet Computing. Kauppinen, Tomi (2012). "Using the SPARQL Package in R to handle Spatial Linked Data". linkedscience.org. Lorentz, Alissa (2013). "With Big Data, Context is a Big Issue". Wired.
Record linkage
Record linkage (also known as data matching, data linkage, entity resolution, and many other terms) is the task of finding records in a data set that refer to the same entity across different data sources (e.g., data files, books, websites, and databases). Record linkage is necessary when joining different data sets based on entities that may or may not share a common identifier (e.g., database key, URI, National identification number), which may be due to differences in record shape, storage location, or curator style or preference. A data set that has undergone RL-oriented reconciliation may be referred to as being cross-linked. == Naming conventions == "Record linkage" is the term used by statisticians, epidemiologists, and historians, among others, to describe the process of joining records from one data source with another that describe the same entity. However, many other terms are used for this process. Unfortunately, this profusion of terminology has led to few cross-references between these research communities. Computer scientists often refer to it as "data matching" or as the "object identity problem". Commercial mail and database applications refer to it as "merge/purge processing" or "list washing". Other names used to describe the same concept include: "coreference/entity/identity/name/record resolution", "entity disambiguation/linking", "fuzzy matching", "duplicate detection", "deduplication", "record matching", "(reference) reconciliation", "object identification", "data/information integration" and "conflation". While they share similar names, record linkage and linked data are two separate approaches to processing and structuring data. Although both involve identifying matching entities across different data sets, record linkage standardly equates "entities" with human individuals; by contrast, Linked Data is based on the possibility of interlinking any web resource across data sets, using a correspondingly broader concept of identifier, namely a URI. == History == The initial idea of record linkage goes back to Halbert L. Dunn in his 1946 article titled "Record Linkage" published in the American Journal of Public Health. Howard Borden Newcombe then laid the probabilistic foundations of modern record linkage theory in a 1959 article in Science. These were formalized in 1969 by Ivan Fellegi and Alan Sunter, in their pioneering work "A Theory For Record Linkage", where they proved that the probabilistic decision rule they described was optimal when the comparison attributes were conditionally independent. In their work they recognized the growing interest in applying advances in computing and automation to large collections of administrative data, and the Fellegi-Sunter theory remains the mathematical foundation for many record linkage applications. Since the late 1990s, various machine learning techniques have been developed that can, under favorable conditions, be used to estimate the conditional probabilities required by the Fellegi-Sunter theory. Several researchers have reported that the conditional independence assumption of the Fellegi-Sunter algorithm is often violated in practice; however, published efforts to explicitly model the conditional dependencies among the comparison attributes have not resulted in an improvement in record linkage quality. On the other hand, machine learning or neural network algorithms that do not rely on these assumptions often provide far higher accuracy, when sufficient labeled training data is available. Record linkage can be done entirely without the aid of a computer, but the primary reasons computers are often used to complete record linkages are to reduce or eliminate manual review and to make results more easily reproducible. Computer matching has the advantages of allowing central supervision of processing, better quality control, speed, consistency, and better reproducibility of results. == Methods == === Data preprocessing === Record linkage is highly sensitive to the quality of the data being linked, so all data sets under consideration (particularly their key identifier fields) should ideally undergo a data quality assessment before record linkage. Many key identifiers for the same entity can be presented quite differently between (and even within) data sets, which can greatly complicate record linkage unless understood ahead of time. For example, key identifiers for a man named William J. Smith might appear in three different data sets as follows: In this example, the different formatting styles lead to records that look different but in fact all refer to the same entity with the same logical identifier values. Most, if not all, record linkage strategies would result in more accurate linkage if these values were first normalized or standardized into a consistent format (e.g., all names are "Surname, Given name", and all dates are "YYYY/MM/DD"). Standardization can be accomplished through simple rule-based data transformations or more complex procedures such as lexicon-based tokenization and probabilistic hidden Markov models. Several of the packages listed in the Software Implementations section provide some of these features to simplify the process of data standardization. === Entity resolution === Entity resolution is an operational intelligence process, typically powered by an entity resolution engine or middleware, whereby organizations can connect disparate data sources with a view to understand possible entity matches and non-obvious relationships across multiple data silos. It analyzes all of the information relating to individuals and/or entities from multiple sources of data, and then applies likelihood and probability scoring to determine which identities are a match and what, if any, non-obvious relationships exist between those identities. Entity resolution engines are typically used to uncover risk, fraud, and conflicts of interest, but are also useful tools for use within customer data integration (CDI) and master data management (MDM) requirements. Typical uses for entity resolution engines include terrorist screening, insurance fraud detection, USA Patriot Act compliance, organized retail crime ring detection and applicant screening. For example, across different data silos – employee records, vendor data, watch lists, etc. – an organization may have several variations of an entity named ABC, which may or may not be the same individual. These entries may, in fact, appear as ABC1, ABC2, or ABC3 within those data sources. By comparing similarities between underlying attributes such as address, date of birth, or social security number, the user can eliminate some possible matches and confirm others as very likely matches. Entity resolution engines then apply rules, based on common sense logic, to identify hidden relationships across the data. In the example above, perhaps ABC1 and ABC2 are not the same individual, but rather two distinct people who share common attributes such as address or phone number. ==== Data matching ==== While entity resolution solutions include data matching technology, many data matching offerings do not fit the definition of entity resolution. Here are four factors that distinguish entity resolution from data matching, according to John Talburt, director of the UALR Center for Advanced Research in Entity Resolution and Information Quality: Works with both structured and unstructured records, and it entails the process of extracting references when the sources are unstructured or semi-structured Uses elaborate business rules and concept models to deal with missing, conflicting, and corrupted information Utilizes non-matching, asserted linking (associate) information in addition to direct matching Uncovers non-obvious relationships and association networks (i.e. who's associated with whom) In contrast to data quality products, more powerful identity resolution engines also include a rules engine and workflow process, which apply business intelligence to the resolved identities and their relationships. These advanced technologies make automated decisions and impact business processes in real time, limiting the need for human intervention. === Deterministic record linkage === The simplest kind of record linkage, called deterministic or rules-based record linkage, generates links based on the number of individual identifiers that match among the available data sets. Two records are said to match via a deterministic record linkage procedure if all or some identifiers (above a certain threshold) are identical. Deterministic record linkage is a good option when the entities in the data sets are identified by a common identifier, or when there are several representative identifiers (e.g., name, date of birth, and sex when identifying a person) whose quality of data is relatively high. As an example, consider two standardized data sets, Set A and Set B, that contain different bits of information about patients in a hospital system. T
EdgeRank
EdgeRank is the name commonly given to the algorithm that Facebook uses to determine what articles should be displayed in a user's News Feed. As of 2011, Facebook has stopped using the EdgeRank system and uses a machine learning algorithm that, as of 2013, takes more than 100,000 factors into account. EdgeRank was developed and implemented by Serkan Piantino. == Formula and factors == In 2010, a simplified version of the EdgeRank algorithm was presented as: ∑ e d g e s e u e w e d e {\displaystyle \sum _{\mathrm {edges\,} e}u_{e}w_{e}d_{e}} where: u e {\displaystyle u_{e}} is user affinity. w e {\displaystyle w_{e}} is how the content is weighted. d e {\displaystyle d_{e}} is a time-based decay parameter. User Affinity: The User Affinity part of the algorithm in Facebook's EdgeRank looks at the relationship and proximity of the user and the content (post/status update). Content Weight: What action was taken by the user on the content. Time-Based Decay Parameter: New or old. Newer posts tend to hold a higher place than older posts. Some of the methods that Facebook uses to adjust the parameters are proprietary and not available to the public. A study has shown that it is possible to hypothesize a disadvantage of the "like" reaction and advantages of other interactions (e.g., the "haha" reaction or "comments") in content algorithmic ranking on Facebook. The "like" button can decrease the organic reach as a "brake effect of viral reach". The "haha" reaction, "comments" and the "love" reaction could achieve the highest increase in total organic reach. == Impact == EdgeRank and its successors have a broad impact on what users actually see out of what they ostensibly follow: for instance, the selection can produce a filter bubble (if users are exposed to updates which confirm their opinions etc.) or alter people's mood (if users are shown a disproportionate amount of positive or negative updates). As a result, for Facebook pages, the typical engagement rate is less than 1% (or less than 0.1% for the bigger ones), and organic reach 10% or less for most non-profits. As a consequence, for pages, it may be nearly impossible to reach any significant audience without paying to promote their content.
Manifold regularization
In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm
Algorithmic transparency
Algorithmic transparency is the principle that the factors that influence the decisions made by algorithms should be visible, or transparent, to the people who use, regulate, and are affected by systems that employ those algorithms. Although the phrase was coined in 2016 by Nicholas Diakopoulos and Michael Koliska about the role of algorithms in deciding the content of digital journalism services, the underlying principle dates back to the 1970s and the rise of automated systems for scoring consumer credit. The phrases "algorithmic transparency" and "algorithmic accountability" are sometimes used interchangeably – especially since they were coined by the same people – but they have subtly different meanings. Specifically, "algorithmic transparency" states that the inputs to the algorithm and the algorithm's use itself must be known, but they need not be fair. "Algorithmic accountability" implies that the organizations that use algorithms must be accountable for the decisions made by those algorithms, even though the decisions are being made by a machine, and not by a human being. Current research around algorithmic transparency interested in both societal effects of accessing remote services running algorithms, as well as mathematical and computer science approaches that can be used to achieve algorithmic transparency. In the United States, the Federal Trade Commission's Bureau of Consumer Protection studies how algorithms are used by consumers by conducting its own research on algorithmic transparency and by funding external research. In the European Union, the data protection laws that came into effect in May 2018 include a "right to explanation" of decisions made by algorithms, though it is unclear what this means. Furthermore, the European Union founded The European Center for Algorithmic Transparency (ECAT).