Rule-based machine translation (RBMT) is a classical approach of machine translation systems based on linguistic information about source and target languages. Such information is retrieved from (unilingual, bilingual or multilingual) dictionaries and grammars covering the main semantic, morphological, and syntactic regularities of each language. Having input sentences, an RBMT system generates output sentences on the basis of analysis of both the source and the target languages involved. RBMT has been progressively superseded by more efficient methods, particularly neural machine translation. == History == The first RBMT systems were developed in the early 1970s. The most important steps of this evolution were the emergence of the following RBMT systems: Systran Japanese MT systems Today, other common RBMT systems include: Apertium GramTrans == Types of RBMT == There are three different types of rule-based machine translation systems: Direct Systems (Dictionary Based Machine Translation) map input to output with basic rules. Transfer RBMT Systems (Transfer Based Machine Translation) employ morphological and syntactical analysis. Interlingual RBMT Systems (Interlingua) use an abstract meaning. RBMT systems can also be characterized as the systems opposite to Example-based Systems of Machine Translation (Example Based Machine Translation), whereas Hybrid Machine Translations Systems make use of many principles derived from RBMT. == Basic principles == The main approach of RBMT systems is based on linking the structure of the given input sentence with the structure of the demanded output sentence, necessarily preserving their unique meaning. The following example can illustrate the general frame of RBMT: A girl eats an apple. Source Language = English; Demanded Target Language = German Minimally, to get a German translation of this English sentence one needs: A dictionary that will map each English word to an appropriate German word. Rules representing regular English sentence structure. Rules representing regular German sentence structure. And finally, we need rules according to which one can relate these two structures together. Accordingly, we can state the following stages of translation: 1st: getting basic part-of-speech information of each source word: a = indef.article; girl = noun; eats = verb; an = indef.article; apple = noun 2nd: getting syntactic information about the verb "to eat": NP-eat-NP; here: eat – Present Simple, 3rd Person Singular, Active Voice 3rd: parsing the source sentence: (NP an apple) = the object of eat Often only partial parsing is sufficient to get to the syntactic structure of the source sentence and to map it onto the structure of the target sentence. 4th: translate English words into German a (category = indef.article) => ein (category = indef.article) girl (category = noun) => Mädchen (category = noun) eat (category = verb) => essen (category = verb) an (category = indef. article) => ein (category = indef.article) apple (category = noun) => Apfel (category = noun) 5th: Mapping dictionary entries into appropriate inflected forms (final generation): A girl eats an apple. => Ein Mädchen isst einen Apfel. == Ontologies == An ontology is a formal representation of knowledge that includes the concepts (such as objects, processes etc.) in a domain and some relations between them. If the stored information is of linguistic nature, one can speak of a lexicon. In NLP, ontologies can be used as a source of knowledge for machine translation systems. With access to a large knowledge base, rule-based systems can be enabled to resolve many (especially lexical) ambiguities on their own. In the following classic examples, as humans, we are able to interpret the prepositional phrase according to the context because we use our world knowledge, stored in our lexicons:I saw a man/star/molecule with a microscope/telescope/binoculars.Since the syntax does not change, a traditional rule-based machine translation system may not be able to differentiate between the meanings. With a large enough ontology as a source of knowledge however, the possible interpretations of ambiguous words in a specific context can be reduced. === Building ontologies === The ontology generated for the PANGLOSS knowledge-based machine translation system in 1993 may serve as an example of how an ontology for NLP purposes can be compiled: A large-scale ontology is necessary to help parsing in the active modules of the machine translation system. In the PANGLOSS example, about 50,000 nodes were intended to be subsumed under the smaller, manually-built upper (abstract) region of the ontology. Because of its size, it had to be created automatically. The goal was to merge the two resources LDOCE online and WordNet to combine the benefits of both: concise definitions from Longman, and semantic relations allowing for semi-automatic taxonomization to the ontology from WordNet. A definition match algorithm was created to automatically merge the correct meanings of ambiguous words between the two online resources, based on the words that the definitions of those meanings have in common in LDOCE and WordNet. Using a similarity matrix, the algorithm delivered matches between meanings including a confidence factor. This algorithm alone, however, did not match all meanings correctly on its own. A second hierarchy match algorithm was therefore created which uses the taxonomic hierarchies found in WordNet (deep hierarchies) and partially in LDOCE (flat hierarchies). This works by first matching unambiguous meanings, then limiting the search space to only the respective ancestors and descendants of those matched meanings. Thus, the algorithm matched locally unambiguous meanings (for instance, while the word seal as such is ambiguous, there is only one meaning of seal in the animal subhierarchy). Both algorithms complemented each other and helped constructing a large-scale ontology for the machine translation system. The WordNet hierarchies, coupled with the matching definitions of LDOCE, were subordinated to the ontology's upper region. As a result, the PANGLOSS MT system was able to make use of this knowledge base, mainly in its generation element. == Components == The RBMT system contains: a SL morphological analyser - analyses a source language word and provides the morphological information; a SL parser - is a syntax analyser which analyses source language sentences; a translator - used to translate a source language word into the target language; a TL morphological generator - works as a generator of appropriate target language words for the given grammatica information; a TL parser - works as a composer of suitable target language sentences; Several dictionaries - more specifically a minimum of three dictionaries: a SL dictionary - needed by the source language morphological analyser for morphological analysis, a bilingual dictionary - used by the translator to translate source language words into target language words, a TL dictionary - needed by the target language morphological generator to generate target language words. The RBMT system makes use of the following: a Source Grammar for the input language which builds syntactic constructions from input sentences; a Source Lexicon which captures all of the allowable vocabulary in the domain; Source Mapping Rules which indicate how syntactic heads and grammatical functions in the source language are mapped onto domain concepts and semantic roles in the interlingua; a Domain Model/Ontology which defines the classes of domain concepts and restricts the fillers of semantic roles for each class; Target Mapping Rules which indicate how domain concepts and semantic roles in the interlingua are mapped onto syntactic heads and grammatical functions in the target language; a Target Lexicon which contains appropriate target lexemes for each domain concept; a Target Grammar for the target language which realizes target syntactic constructions as linearized output sentences. == Advantages == No bilingual texts are required. This makes it possible to create translation systems for languages that have no texts in common, or even no digitized data whatsoever. Domain independent. Rules are usually written in a domain independent manner, so the vast majority of rules will "just work" in every domain, and only a few specific cases per domain may need rules written for them. No quality ceiling. Every error can be corrected with a targeted rule, even if the trigger case is extremely rare. This is in contrast to statistical systems where infrequent forms will be washed away by default. Total control. Because all rules are hand-written, you can easily debug a rule-based system to see exactly where a given error enters the system, and why. Reusability. Because RBMT systems are generally built from a strong source language analysis that is fed to a transfer step and target language generator, the source language analysis and targe
Resilience week
Resilience week is an annual symposium established to enable cross-disciplinary and role based discussions to advance strategies and research that engenders resilience in critical infrastructure systems and communities. Damaging storms, cyber attack and the interconnection of critical infrastructure systems can lead to cascading events that not only affect local but also across regions. However, many of these interdependencies are not easily recognized and obscure and complicate the mitigation of risk. The purpose of the symposia series is hence to facilitate best practice in managing critical infrastructure risks, by bringing together businesses, government and researchers. == Background == Originally organized in 2008 as a focus on the new research area of resilient control systems, including the disciplinary areas of control system, cyber-security, cognitive psychology and any number of critical infrastructure domains. Resilience has long been recognized as an area that requires not only the contributions of multiple disciplines or multidisciplinary participation, but interdisciplinary interaction where there is a common language and familiarity of the contributors to what other disciplines (and roles) contribute. The resulting interactions developed by Resilience Week and associated activities are intended to culture this sharing environment as a safe zone for inclusion; more importantly, an environment that lends to developing the new science and practice. As the attributes of resilience are complex, the contributions and topics for the event have included both the disciplinary and the project considerations, in keynotes, panels and research presentations. Keynotes have included senior leadership in the Department of Energy, Department of Defense, Department of Homeland Security, the National Science Foundation, and other agencies in addition to National Academy and professional organization fellows and senior industry leaders. Project panels and research presentations include emergent topics in resilience to climate change, cyber attack, damaging storms and the energy assurance. Topics Areas of focus have included: Control Systems Cyber Systems Cognitive Systems Communications Systems Communities and Infrastructure Project Focus Areas have included: Dependencies and Interdependencies Cyber Resilience for Operating Technology Commercializing Research and Development Building Critical Infrastructure Resilience through Distributed Energy Resources Energy Equity and Community Resilience Proceedings are developed for each year of the event, documenting the diversity of the research and engagements within these topical areas. == Impacts for the future == Since its inception, the Resilience Week community has evolved from one that primarily included only university researchers to one that includes many government laboratories, universities and private industries in the US and internationally. This type of collaboration forms a feedback loop that informs the research with the current needs and hones best practices. The future of the event is to further advance discussions that advance investment, recognize priorities and expedite technologies and tools to proactively address our energy future, in light of the natural and manmade challenges, and rationalizing the complex relationships that exist in critical infrastructure.
ChromaDB
Chroma or ChromaDB is open-source data infrastructure tailored to applications with large language models. Its headquarters are in San Francisco. In April 2023, it raised 18 million US dollars as seed funding. ChromaDB has been used in academic studies on artificial intelligence, particularly as part of the tech stack for retrieval-augmented generation.
CLAWS (linguistics)
The Constituent Likelihood Automatic Word-tagging System (CLAWS) is a program that performs part-of-speech tagging. It was developed in the 1980s at Lancaster University by the University Centre for Computer Corpus Research on Language. It has an overall accuracy rate of 96–97% with the latest version (CLAWS4) tagging around 100 million words of the British National Corpus. == History == A Part-Of-Speech Tagger (POS Tagger) is a piece of software that reads text in some language and assigns parts of speech to each word (and other token), such as noun, verb, adjective, etc., although generally computational applications use more fine-grained POS tags like 'noun-plural'. Developed in the early 1980s, CLAWS was built to fill the ever-growing gap created by always-changing POS necessities. Originally created to add part-of-speech tags to the LOB corpus of British English, the CLAWS tagset has since been adapted to other languages as well, including Urdu and Arabic. Since its inception, CLAWS has been hailed for its functionality and adaptability. Still, it is not without flaws, and though it boasts an error-rate of only 1.5% when judged in major categories, CLAWS still remains with c.3.3% ambiguities unresolved. Ambiguity arises in cases such as with the word flies, and whether it should be classified as a noun or a verb. It's these ambiguities that will require the various upgrades and tagsets that CLAWS will endure. == Rules and processing == CLAWS uses a Hidden Markov model to determine the likelihood of sequences of words in anticipating each part-of-speech label. === Sample output === This excerpt from Bram Stoker's Dracula (1897) has been tagged using both the CLAWS C5 and C7 tagsets. This is what a CLAWS output will generally look like, with the most likely part-of-speech tag following each word. == Tagsets == === CLAWS1 tagset === The first tagset developed in CLAWS, CLAWS1 tagset, has 132 word tags. In terms of form and application, C1 tagset is similar to Brown Corpus tags. See Table of tags in C1 tagset here. === CLAWS2 tagset === From 1983 to 1986, updated versions leading to CLAWS2 were part of a larger attempt to deal with aspects such as recognizing sentence breaks, in order to avoid the need for manual pre-processing of a text before the tags were applied, moving instead to optional manual post-editing to adjust the output of the automatic annotation, if needed. The CLAWS2 tagset has 166 word tags. See Table of tags in C2 tagset here. === CLAWS4 tagset === The CLAWS4 was used for the 100-million-word British National Corpus (BNC). A general-purpose grammatical tagger, it is a successor of the CLAWS1 tagger. In tagging the BNC, the many rounds of work that went into CLAWS4 focused on making the CLAWS program independent from the tagsets. For example, the BNC project used two tagset versions: "a main tagset (C5) with 62 tags with which the whole of the corpus has been tagged, and a larger (C7) tagset with 152 tags, which has been used to make a selected 'core' sample corpus of two million words." The latest version of CLAWS4 is offered by UCREL, a research center of Lancaster University. === CLAWS5 tagset === The CLAWS5 tagset, which was used for BNC, has over 60 tags. See Table of tags in C5 tagset here. === CLAWS6 tagset === The CLAWS6 tagset was used for the BNC sampler corpus and the COLT corpus. It has over 160 tags, including 13 determiner subtypes. See Table of tags in C6 tagset here. === CLAWS7 tagset === The standard CLAWS7 tagset is used currently. It is only different in the punctuation tags when compared to the CLAWS6 tagset. See Table of tags in C7 tagset here. === CLAWS8 tagset === CLAWS8 tagset was extended from C7 tagset with further distinctions in the determiner and pronoun categories, as well as 37 new auxiliary tags for forms of be, do, and have. See Table of tags in C8 tagset here
Text Retrieval Conference
The Text REtrieval Conference (TREC) is an ongoing series of workshops focusing on a list of different information retrieval (IR) research areas, or tracks. It is co-sponsored by the National Institute of Standards and Technology (NIST) and the Intelligence Advanced Research Projects Activity (part of the office of the Director of National Intelligence), and began in 1992 as part of the TIPSTER Text program. Its purpose is to support and encourage research within the information retrieval community by providing the infrastructure necessary for large-scale evaluation of text retrieval methodologies and to increase the speed of lab-to-product transfer of technology. TREC's evaluation protocols have improved many search technologies. A 2010 study estimated that "without TREC, U.S. Internet users would have spent up to 3.15 billion additional hours using web search engines between 1999 and 2009." Hal Varian the Chief Economist at Google wrote that "The TREC data revitalized research on information retrieval. Having a standard, widely available, and carefully constructed set of data laid the groundwork for further innovation in this field." Each track has a challenge wherein NIST provides participating groups with data sets and test problems. Depending on track, test problems might be questions, topics, or target extractable features. Uniform scoring is performed so the systems can be fairly evaluated. After evaluation of the results, a workshop provides a place for participants to collect together thoughts and ideas and present current and future research work.Text Retrieval Conference started in 1992, funded by DARPA (US Defense Advanced Research Project) and run by NIST. Its purpose was to support research within the information retrieval community by providing the infrastructure necessary for large-scale evaluation of text retrieval methodologies. == Goals == Encourage retrieval search based on large text collections Increase communication among industry, academia, and government by creating an open forum for the exchange of research ideas Speed the transfer of technology from research labs into commercial products by demonstrating substantial improvements retrieval methodologies on real world problems To increase the availability of appropriate evaluation techniques for use by industry and academia including development of new evaluation techniques more applicable to current systems TREC is overseen by a program committee consisting of representatives from government, industry, and academia. For each TREC, NIST provide a set of documents and questions. Participants run their own retrieval system on the data and return to NIST a list of retrieved top-ranked documents. NIST pools the individual result judges the retrieved documents for correctness and evaluates the results. The TREC cycle ends with a workshop that is a forum for participants to share their experiences. == Relevance judgments in TREC == TREC defines relevance as: "If you were writing a report on the subject of the topic and would use the information contained in the document in the report, then the document is relevant." Most TREC retrieval tasks use binary relevance: a document is either relevant or not relevant. Some TREC tasks use graded relevance, capturing multiple degrees of relevance. Most TREC collections are too large to perform complete relevance assessment; for these collections it is impossible to calculate the absolute recall for each query. To decide which documents to assess, TREC usually uses a method call pooling. In this method, the top-ranked n documents from each contributing run are aggregated, and the resulting document set is judged completely. == Various TRECs == In 1992 TREC-1 was held at NIST. The first conference attracted 28 groups of researchers from academia and industry. It demonstrated a wide range of different approaches to the retrieval of text from large document collections .Finally TREC1 revealed the facts that automatic construction of queries from natural language query statements seems to work. Techniques based on natural language processing were no better no worse than those based on vector or probabilistic approach. TREC2 Took place in August 1993. 31 group of researchers participated in this. Two types of retrieval were examined. Retrieval using an ‘ad hoc’ query and retrieval using a ‘routing' query In TREC-3 a small group experiments worked with Spanish language collection and others dealt with interactive query formulation in multiple databases TREC-4 they made even shorter to investigate the problems with very short user statements TREC-5 includes both short and long versions of the topics with the goal of carrying out deeper investigation into which types of techniques work well on various lengths of topics In TREC-6 Three new tracks speech, cross language, high precision information retrieval were introduced. The goal of cross language information retrieval is to facilitate research on system that are able to retrieve relevant document regardless of language of the source document TREC-7 contained seven tracks out of which two were new Query track and very large corpus track. The goal of the query track was to create a large query collection TREC-8 contain seven tracks out of which two –question answering and web tracks were new. The objective of QA query is to explore the possibilities of providing answers to specific natural language queries TREC-9 Includes seven tracks In TREC-10 Video tracks introduced Video tracks design to promote research in content based retrieval from digital video In TREC-11 Novelty tracks introduced. The goal of novelty track is to investigate systems abilities to locate relevant and new information within the ranked set of documents returned by a traditional document retrieval system TREC-12 held in 2003 added three new tracks; Genome track, robust retrieval track, HARD (Highly Accurate Retrieval from Documents) == Tracks == === Current tracks === New tracks are added as new research needs are identified, this list is current for TREC 2018. CENTRE Track – Goal: run in parallel CLEF 2018, NTCIR-14, TREC 2018 to develop and tune an IR reproducibility evaluation protocol (new track for 2018). Common Core Track – Goal: an ad hoc search task over news documents. Complex Answer Retrieval (CAR) – Goal: to develop systems capable of answering complex information needs by collating information from an entire corpus. Incident Streams Track – Goal: to research technologies to automatically process social media streams during emergency situations (new track for TREC 2018). The News Track – Goal: partnership with The Washington Post to develop test collections in news environment (new for 2018). Precision Medicine Track – Goal: a specialization of the Clinical Decision Support track to focus on linking oncology patient data to clinical trials. Real-Time Summarization Track (RTS) – Goal: to explore techniques for real-time update summaries from social media streams. === Past tracks === Chemical Track – Goal: to develop and evaluate technology for large scale search in chemistry-related documents, including academic papers and patents, to better meet the needs of professional searchers, and specifically patent searchers and chemists. Clinical Decision Support Track – Goal: to investigate techniques for linking medical cases to information relevant for patient care Contextual Suggestion Track – Goal: to investigate search techniques for complex information needs that are highly dependent on context and user interests. Crowdsourcing Track – Goal: to provide a collaborative venue for exploring crowdsourcing methods both for evaluating search and for performing search tasks. Genomics Track – Goal: to study the retrieval of genomic data, not just gene sequences but also supporting documentation such as research papers, lab reports, etc. Last ran on TREC 2007. Dynamic Domain Track – Goal: to investigate domain-specific search algorithms that adapt to the dynamic information needs of professional users as they explore in complex domains. Enterprise Track – Goal: to study search over the data of an organization to complete some task. Last ran on TREC 2008. Entity Track – Goal: to perform entity-related search on Web data. These search tasks (such as finding entities and properties of entities) address common information needs that are not that well modeled as ad hoc document search. Cross-Language Track – Goal: to investigate the ability of retrieval systems to find documents topically regardless of source language. After 1999, this track spun off into CLEF. FedWeb Track – Goal: to select best resources to forward a query to, and merge the results so that most relevant are on the top. Federated Web Search Track – Goal: to investigate techniques for the selection and combination of search results from a large number of real on-line web search services. Filtering Track – Goal: to binarily decide retrieval of new
Matrix regularization
In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x ‖ A x − y ‖ 2 + λ ‖ x ‖ 2 {\displaystyle \min _{x}\left\|Ax-y\right\|^{2}+\lambda \left\|x\right\|^{2}} to find a vector x {\displaystyle x} that is a stable solution to the regression problem. When the system is described by a matrix rather than a vector, this problem can be written as min X ‖ A X − Y ‖ 2 + λ ‖ X ‖ 2 , {\displaystyle \min _{X}\left\|AX-Y\right\|^{2}+\lambda \left\|X\right\|^{2},} where the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning. == Basic definition == Consider a matrix W {\displaystyle W} to be learned from a set of examples, S = ( X i t , y i t ) {\displaystyle S=(X_{i}^{t},y_{i}^{t})} , where i {\displaystyle i} goes from 1 {\displaystyle 1} to n {\displaystyle n} , and t {\displaystyle t} goes from 1 {\displaystyle 1} to T {\displaystyle T} . Let each input matrix X i {\displaystyle X_{i}} be ∈ R D T {\displaystyle \in \mathbb {R} ^{DT}} , and let W {\displaystyle W} be of size D × T {\displaystyle D\times T} . A general model for the output y {\displaystyle y} can be posed as y i t = ⟨ W , X i t ⟩ F , {\displaystyle y_{i}^{t}=\left\langle W,X_{i}^{t}\right\rangle _{F},} where the inner product is the Frobenius inner product. For different applications the matrices X i {\displaystyle X_{i}} will have different forms, but for each of these the optimization problem to infer W {\displaystyle W} can be written as min W ∈ H E ( W ) + R ( W ) , {\displaystyle \min _{W\in {\mathcal {H}}}E(W)+R(W),} where E {\displaystyle E} defines the empirical error for a given W {\displaystyle W} , and R ( W ) {\displaystyle R(W)} is a matrix regularization penalty. The function R ( W ) {\displaystyle R(W)} is typically chosen to be convex and is often selected to enforce sparsity (using ℓ 1 {\displaystyle \ell ^{1}} -norms) and/or smoothness (using ℓ 2 {\displaystyle \ell ^{2}} -norms). Finally, W {\displaystyle W} is in the space of matrices H {\displaystyle {\mathcal {H}}} with Frobenius inner product ⟨ … ⟩ F {\displaystyle \langle \dots \rangle _{F}} . == General applications == === Matrix completion === In the problem of matrix completion, the matrix X i t {\displaystyle X_{i}^{t}} takes the form X i t = e t ⊗ e i ′ , {\displaystyle X_{i}^{t}=e_{t}\otimes e_{i}',} where ( e t ) t {\displaystyle (e_{t})_{t}} and ( e i ′ ) i {\displaystyle (e_{i}')_{i}} are the canonical basis in R T {\displaystyle \mathbb {R} ^{T}} and R D {\displaystyle \mathbb {R} ^{D}} . In this case the role of the Frobenius inner product is to select individual elements w i t {\displaystyle w_{i}^{t}} from the matrix W {\displaystyle W} . Thus, the output y {\displaystyle y} is a sampling of entries from the matrix W {\displaystyle W} . The problem of reconstructing W {\displaystyle W} from a small set of sampled entries is possible only under certain restrictions on the matrix, and these restrictions can be enforced by a regularization function. For example, it might be assumed that W {\displaystyle W} is low-rank, in which case the regularization penalty can take the form of a nuclear norm. R ( W ) = λ ‖ W ‖ ∗ = λ ∑ i | σ i | , {\displaystyle R(W)=\lambda \left\|W\right\|_{}=\lambda \sum _{i}\left|\sigma _{i}\right|,} where σ i {\displaystyle \sigma _{i}} , with i {\displaystyle i} from 1 {\displaystyle 1} to min D , T {\displaystyle \min D,T} , are the singular values of W {\displaystyle W} . === Multivariate regression === Models used in multivariate regression are parameterized by a matrix of coefficients. In the Frobenius inner product above, each matrix X {\displaystyle X} is X i t = e t ⊗ x i {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}} such that the output of the inner product is the dot product of one row of the input with one column of the coefficient matrix. The familiar form of such models is Y = X W + b {\displaystyle Y=XW+b} Many of the vector norms used in single variable regression can be extended to the multivariate case. One example is the squared Frobenius norm, which can be viewed as an ℓ 2 {\displaystyle \ell ^{2}} -norm acting either entrywise, or on the singular values of the matrix: R ( W ) = λ ‖ W ‖ F 2 = λ ∑ i ∑ j | w i j | 2 = λ Tr ( W ∗ W ) = λ ∑ i σ i 2 . {\displaystyle R(W)=\lambda \left\|W\right\|_{F}^{2}=\lambda \sum _{i}\sum _{j}\left|w_{ij}\right|^{2}=\lambda \operatorname {Tr} \left(W^{}W\right)=\lambda \sum _{i}\sigma _{i}^{2}.} In the multivariate case the effect of regularizing with the Frobenius norm is the same as the vector case; very complex models will have larger norms, and, thus, will be penalized more. === Multi-task learning === The setup for multi-task learning is almost the same as the setup for multivariate regression. The primary difference is that the input variables are also indexed by task (columns of Y {\displaystyle Y} ). The representation with the Frobenius inner product is then X i t = e t ⊗ x i t . {\displaystyle X_{i}^{t}=e_{t}\otimes x_{i}^{t}.} The role of matrix regularization in this setting can be the same as in multivariate regression, but matrix norms can also be used to couple learning problems across tasks. In particular, note that for the optimization problem min W ‖ X W − Y ‖ 2 2 + λ ‖ W ‖ 2 2 {\displaystyle \min _{W}\left\|XW-Y\right\|_{2}^{2}+\lambda \left\|W\right\|_{2}^{2}} the solutions corresponding to each column of Y {\displaystyle Y} are decoupled. That is, the same solution can be found by solving the joint problem, or by solving an isolated regression problem for each column. The problems can be coupled by adding an additional regularization penalty on the covariance of solutions min W , Ω ‖ X W − Y ‖ 2 2 + λ 1 ‖ W ‖ 2 2 + λ 2 Tr ( W T Ω − 1 W ) {\displaystyle \min _{W,\Omega }\left\|XW-Y\right\|_{2}^{2}+\lambda _{1}\left\|W\right\|_{2}^{2}+\lambda _{2}\operatorname {Tr} \left(W^{T}\Omega ^{-1}W\right)} where Ω {\displaystyle \Omega } models the relationship between tasks. This scheme can be used to both enforce similarity of solutions across tasks, and to learn the specific structure of task similarity by alternating between optimizations of W {\displaystyle W} and Ω {\displaystyle \Omega } . When the relationship between tasks is known to lie on a graph, the Laplacian matrix of the graph can be used to couple the learning problems. == Spectral regularization == Regularization by spectral filtering has been used to find stable solutions to problems such as those discussed above by addressing ill-posed matrix inversions (see for example Filter function for Tikhonov regularization). In many cases the regularization function acts on the input (or kernel) to ensure a bounded inverse by eliminating small singular values, but it can also be useful to have spectral norms that act on the matrix that is to be learned. There are a number of matrix norms that act on the singular values of the matrix. Frequently used examples include the Schatten p-norms, with p = 1 or 2. For example, matrix regularization with a Schatten 1-norm, also called the nuclear norm, can be used to enforce sparsity in the spectrum of a matrix. This has been used in the context of matrix completion when the matrix in question is believed to have a restricted rank. In this case the optimization problem becomes: min ‖ W ‖ ∗ subject to W i , j = Y i j . {\displaystyle \min \left\|W\right\|_{}~~{\text{ subject to }}~~W_{i,j}=Y_{ij}.} Spectral Regularization is also used to enforce a reduced rank coefficient matrix in multivariate regression. In this setting, a reduced rank coefficient matrix can be found by keeping just the top n {\displaystyle n} singular values, but this can be extended to keep any reduced set of singular values and vectors. == Structured sparsity == Sparse optimization has become the focus of much research interest as a way to find solutions that depend on a small number of variables (see e.g. the Lasso method). In principle, entry-wise sparsity can be enforced by penalizing the entry-wise ℓ 0 {\displaystyle \ell ^{0}} -norm of the matrix, but the ℓ 0 {\displaystyle \ell ^{0}} -norm is not convex. In practice this can be implemented by convex relaxation to the ℓ 1 {\displaystyle \ell ^{1}} -norm. While entry-wise regularization with an ℓ 1 {\displaystyle \ell ^{1}} -norm will find solutions with a small number of nonzero elements, applying an ℓ 1 {
Ayoba
Ayoba is an African communication platform developed in South Africa. It is owned by Progressive Tech Holdings in Mauritius and managed by SIMFY Africa. Launched on May 4, 2019, as of April 2024, it has over 35 million active users. == History == Ayoba was first published on Google Play in February 2019. Its first marketing campaign and brand launch took place in Cameroon on May 4, 2019. In June 2019, the platform introduced its first eight channels. In November 2019, the platform reached one million active users, which increased to two million by June 2020. Subsequently, ayoba expanded its services, including the launch of games for Android in February 2020, Momo (Mobile Money) in Cameroon in May 2020, and MicroApps in May 2020. It also launched music and voice and video calling features in 12 territories in August 2020. The first version of ayoba for iOS was released in September 2020. In December of the same year, games and Messaging 2.0 were launched on the platform. In November 2020, it won Best Mobile Application at the African Digital Awards. In 2021, it won OTT Brand of the Year at the Marketing World Awards in Ghana. In December 2022, it received Top Innovative Technology and Telecom Product of the Year at the National Communications Awards in December 2022. In June 2023 ayoba partnered with BoomPlay and as of April 2024, it had 35 million monthly active users. Ayoba has partnered with Jumia Ghana to offer exclusive deals to users. Ayoba users can get a 10% discount on selected Jumia purchases through the app, with no data charges for MTN users. This partnership aims to make online shopping more affordable and accessible by integrating Jumia's offers into the ayoba app. Ayoba supports over 35 million users across Africa and provides services in 22 languages. To access the deals, users can download the ayoba app from the Google Play Store, iOS Store, or the official website. == Platform features == Chat, Call and Share: ayoba enables instant messaging, voice notes, picture sharing, and file sharing with contacts, even if they do not have the app installed. The app supports voice and video calls on both Android and iOS, as well as group chats, help channel and SMS continuity (non ayoba users receive messages as SMS, their responses appear in the ayoba app). Music: ayoba offers a free music player with daily updates on international and African music. Users can find playlists for different genres. Games: ayoba provides a selection of interactive games, including action, adventure, and children's games available on both Android and iOS. Mobile Money Transfers: In certain territories, ayoba supports mobile money transfers using MTN Mobile Money (MoMo) for transactions within the app. MicroApps: ayoba features individual MicroApps within the platform that offer content and services, including streaming channels, podcasts, and specialized apps. The availability of these apps may vary by country. == Operations == ayoba primarily focuses on the following territories: Nigeria, Cameroon, South Africa, Ghana, Côte d'Ivoire, Uganda, Republic of Congo, Benin, Zambia, Tanzania, Kenya, Senegal, Togo, Guinea Bissau, Guinea Conakry, Sudan, South Sudan, and Liberia. The company operates from its offices in Cape Town and Johannesburg, South Africa. David Gillaranz served as the CEO from 2019 to 2021, and Burak Akinci has been the CEO since 2021.