Basic Formal Ontology (BFO) is a top-level ontology developed by Barry Smith and colleagues to promote interoperability among domain ontologies. The BFO methodology accomplishes this through a process of downward population. BFO is a formal ontology. The structure of BFO is based on a division of entities into two disjoint categories of continuant and occurrent, the former consists of objects and spatial regions, the latter contains processes conceived as extended through (or spanning) time. BFO thereby seeks to consolidate both time and space within a single framework A guide to building BFO-conformant domain ontologies was published by MIT Press in 2015. In 2021, the standard ISO/IEC 21838-2:2021 Information Technology — Top-level Ontologies (TLO) — Part 2: Basic Formal Ontology (BFO) was published by the Joint Technical Committee of the International Standards Organization and the International Electrotechnical Commission. ISO/IEC 21838 is a multi-part standard. Part 1 of the standard specifies the requirements that must be met if an ontology is to be classified as a top-level ontology by the standard. == History == BFO arose against the background of research in ontologies in the domain of geospatial information science by David Mark, Pierre Grenon, Achille Varzi and others, with a special role for the study of vagueness and of the ways sharp boundaries in the geospatial and other domains are created by fiat. BFO has passed through four major releases. 2001: release of BFO 1 2007: release of BFO 1.1 2015: release of BFO 2.0 2020: release of BFO 2020 2021: release of BFO 2020 as an ISO/IEC Standard The current revision was released in 2020, and this forms the basis of the standard ISO/IEC 21838-2, which was released by the Joint Committee of the International Standards Organization and International Electrotechnical Commission in 2021. == Applications == BFO has been adopted as a foundational ontology by over 650 ontology projects, principally in the areas of biomedical ontology, security and defense (intelligence) ontology, and industry ontologies. Example applications of BFO can be seen in the Ontology for Biomedical Investigations (OBI). In January 2024, BFO and the Common Core Ontologies (CCO), a suite of BFO-extension ontologies, were adopted as the "baseline standards for formal DOD and IC ontology" development work in the DOD and Intelligence Community. A memorandum to this effect was signed by the chief data officers of the DOD, the Office of the Director of National Intelligence and the Chief Digital and Artificial Intelligence Office.
Shearlet
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r
Michael I. Jordan
Michael Irwin Jordan (born February 25, 1956) is an American scientist, professor at the University of California, Berkeley, research scientist at the Inria Paris, and researcher in machine learning, statistics, and artificial intelligence. Jordan was elected a member of the National Academy of Engineering in 2010 for contributions to the foundations and applications of machine learning. He is one of the leading figures in machine learning, and in 2016 Science reported him as the world's most influential computer scientist. In 2022, Jordan won the inaugural World Laureates Association Prize in Computer Science or Mathematics, "for fundamental contributions to the foundations of machine learning and its application." == Education == Jordan received a Bachelor of Science magna cum laude in psychology from the Louisiana State University in 1978, a Master of Science in mathematics from Arizona State University in 1980, and a Doctor of Philosophy in cognitive science from the University of California, San Diego in 1985. At UC San Diego, Jordan was a student of David Rumelhart and a member of the Parallel Distributed Processing (PDP) Group in the 1980s. == Career and research == Jordan is the Pehong Chen Distinguished Professor at the University of California, Berkeley, where his appointment is split across EECS and Statistics. He was a professor at the Department of Brain and Cognitive Sciences at MIT from 1988 to 1998. In the 1980s Jordan started developing recurrent neural networks as a cognitive model. In recent years, his work is less driven from a cognitive perspective and more from the background of traditional statistics. Jordan popularised Bayesian networks in the machine learning community and is known for pointing out links between machine learning and statistics. He was also prominent in the formalisation of variational methods for approximate inference and the popularisation of the expectation–maximization algorithm in machine learning. === Resignation from Machine Learning === In 2001, Jordan and others resigned from the editorial board of the journal Machine Learning. In a public letter, they argued for less restrictive access and pledged support for a new open access journal, the Journal of Machine Learning Research, which was created by Leslie Kaelbling to support the evolution of the field of machine learning. === Honors and awards === Jordan has received numerous awards, including a best student paper award (with X. Nguyen and M. Wainwright) at the International Conference on Machine Learning (ICML 2004), a best paper award (with R. Jacobs) at the American Control Conference (ACC 1991), the ACM-AAAI Allen Newell Award, the IEEE Neural Networks Pioneer Award, and an NSF Presidential Young Investigator Award. In 2002 he was named an AAAI Fellow "for significant contributions to reasoning under uncertainty, machine learning, and human motor control." In 2004 he was named an IMS Fellow "for contributions to graphical models and machine learning." In 2005 he was named an IEEE Fellow "for contributions to probabilistic graphical models and neural information processing systems." In 2007 he was named an ASA Fellow. In 2010 he was named a Cognitive Science Society Fellow and named an ACM Fellow "for contributions to the theory and application of machine learning." In 2012 he was named a SIAM Fellow "for contributions to machine learning, in particular variational approaches to statistical inference." In 2014 he was named an International Society for Bayesian Analysis Fellow "for his outstanding research contributions at the interface of statistics, computer sciences and probability, for his leading role in promoting Bayesian methods in machine learning, engineering and other fields, and for his extensive service to ISBA in many roles." Jordan is a member of the National Academy of Sciences, a member of the National Academy of Engineering and a member of the American Academy of Arts and Sciences. He has been named a Neyman Lecturer and a Medallion Lecturer by the Institute of Mathematical Statistics. He received the David E. Rumelhart Prize in 2015 and the ACM/AAAI Allen Newell Award in 2009. He also won the 2020 IEEE John von Neumann Medal. In 2016, Jordan was identified as the "most influential computer scientist", based on an analysis of the published literature by the Semantic Scholar project. In 2019, Jordan argued that the artificial intelligence revolution hasn't happened yet and that the AI revolution required a blending of computer science with statistics. In 2022, Jordan was awarded the inaugural World Laureates Association Prize by non-governmental and non-profit international organization World Laureates Association, for fundamental contributions to the foundations of machine learning and its application. For 2024 he received the BBVA Foundation Frontiers of Knowledge Award in the category of "Information and Communication Technologies".
Rayid Ghani
Rayid Ghani (born 1977) is a Distinguished Career Professor in the Machine Learning Department (in the School of Computer Science) and the Heinz College of Information Systems and Public Policy at Carnegie Mellon University. Previously, he was the director of the Center for Data Science and Public Policy, research associate professor in the department of computer science, and a senior fellow at the Harris School of Public Policy at the University of Chicago. He was also the co-founder of Edgeflip, an analytics startup that grew out of the Obama 2012 Campaign, focused on social media products for non-profits, advocacy groups, and charities. In September 2019, it was announced that he will be leaving the University of Chicago and joining Carnegie Mellon University's School of Computer Science and Heinz College of Information Systems and Public Policy. Prior to that, Rayid was the Chief Scientist of the Obama 2012 Election Campaign and focused on using data science, machine learning, and technology to improve fundraising, volunteer mobilization, voter registration, persuasion, and turnout. Ghani started and runs the Eric & Wendy Schmidt Data Science for Social Good Summer Fellowship. He's also the co-founder of Coleridge Initiative, a nonprofit organization working with governments to ensure that data and evidence is used more effectively for policymaking. == Education and career == Ghani completed his schooling at the Karachi Grammar School, in Karachi, Pakistan. Ghani completed his graduate studies in the machine learning department at Carnegie Mellon University with Tom M. Mitchell on machine learning and text classification and received his undergraduate degrees in computer science and mathematics from University of the South. Before his role at the University of Chicago, he was the chief scientist of the Obama 2012 Campaign. Before that, he was a senior research scientist and director of analytics research at Accenture Labs, where he led a technology research team focused on applied R&D in analytics, machine learning, and data mining for large-scale and emerging business problems. == Policy efforts == Ghani has been actively working with government agencies and non-profits on designing AI and Machine Learning Systems to help tackle societal problems in public health, criminal justice, social services, education, economic development, and workforce development He has also testified in front of the US Senate in 2023 and the US House of Representatives in 2020, on AI Governance and Regulation. == Research contributions == Ghani's research focuses on developing and applying machine learning, data science, and artificial intelligence methods to large-scale social problems in areas such as education, healthcare, economic development, criminal justice, energy, transportation, and public safety. His work has previously focused on text analytics, fundraising, volunteer, and voter mobilization using analytics, social media, and machine learning., and data mining. Rayid's research contributions have been in the areas of text mining, co-training, active learning, consumer behavior modeling, and fraud detection. His research focus has been on 1) dealing with bias and fairness issues in machine learning and AI, 2) designing Human-AI collaborative systems that support people in making decisions, and 3) evaluating AI systems to focus on the entire workflow and outcomes He has given keynote speeches on Analytics and the Presidential Elections (for example at Predictive Analytics World, Digital Leaders Forum, Carnegie Mellon University, and CeBIT Australia), on Business Applications of Data Mining, and Data Science for Social Good. == Selected publications == Big Data and Social Science: A Practical Guide to Methods and Tools. Editors: Ian Foster, Rayid Ghani, Ron Jarmin, Frauke Kreuter, Julia Lane. CRC Press 2016. Empirical observation of negligible fairness–accuracy trade-offs in machine learning for public policy. Kit Rodolfa, Hemank Lamba, Rayid Ghani. Nature Machine Intelligence 2021. Explainable machine learning for public policy: Use cases, gaps, and research directions. Kasun Amarasinghe, Kit T. Rodolfa, Hemank Lamba, Rayid Ghani. Data and Policy 2023. Data Mining for Business Applications. Editors: Carlos Soares, Rayid Ghani. Book. IOS Press 2010. Mining the Web to Add Semantics to Retail Data Mining. R. Ghani. Invited Paper. Web Mining: From Web to Semantic Web. Springer Lecture Notes in Artificial Intelligence, Vol. 3209. Berendt, B.; Hotho, A.; Mladenic, D.; van Someren, M.; Spiliopoulou, M.; Stumme, G. (Eds.) 2004
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JAX (software)
JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. It is developed by Google with contributions from Nvidia and other community contributors. It is described as bringing together a modified version of the automatic differentiation system autograd and OpenXLA's XLA (Accelerated Linear Algebra). It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary features of JAX are: Providing a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings. Built-in Just-In-Time (JIT) compilation via OpenXLA, an open-source machine learning compiler ecosystem. Efficient evaluation of gradients via its automatic differentiation transformations. Automatic vectorization to efficiently map functions over arrays representing batches of inputs. == Libraries using Jax == Flax Equinox Optax
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