In the data analysis of time series, Time Warp Edit Distance (TWED) is a measure of similarity (or dissimilarity) between pairs of discrete time series, controlling the relative distortion of the time units of the two series using the physical notion of elasticity. In comparison to other distance measures, (e.g. DTW (dynamic time warping) or LCS (longest common subsequence problem)), TWED is a metric. Its computational time complexity is O ( n 2 ) {\displaystyle O(n^{2})} , but can be drastically reduced in some specific situations by using a corridor to reduce the search space. Its memory space complexity can be reduced to O ( n ) {\displaystyle O(n)} . It was first proposed in 2009 by P.-F. Marteau. == Definition == δ λ , ν ( A 1 p , B 1 q ) = M i n { δ λ , ν ( A 1 p − 1 , B 1 q ) + Γ ( a p ′ → Λ ) d e l e t e i n A δ λ , ν ( A 1 p − 1 , B 1 q − 1 ) + Γ ( a p ′ → b q ′ ) m a t c h o r s u b s t i t u t i o n δ λ , ν ( A 1 p , B 1 q − 1 ) + Γ ( Λ → b q ′ ) d e l e t e i n B {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{p},B_{1}^{q})=Min{\begin{cases}\delta _{\lambda ,\nu }(A_{1}^{p-1},B_{1}^{q})+\Gamma (a_{p}^{'}\to \Lambda )&{\rm {delete\ in\ A}}\\\delta _{\lambda ,\nu }(A_{1}^{p-1},B_{1}^{q-1})+\Gamma (a_{p}^{'}\to b_{q}^{'})&{\rm {match\ or\ substitution}}\\\delta _{\lambda ,\nu }(A_{1}^{p},B_{1}^{q-1})+\Gamma (\Lambda \to b_{q}^{'})&{\rm {delete\ in\ B}}\end{cases}}} whereas Γ ( α p ′ → Λ ) = d L P ( a p ′ , a p − 1 ′ ) + ν ⋅ ( t a p − t a p − 1 ) + λ {\displaystyle \Gamma (\alpha _{p}^{'}\to \Lambda )=d_{LP}(a_{p}^{'},a_{p-1}^{'})+\nu \cdot (t_{a_{p}}-t_{a_{p-1}})+\lambda } Γ ( α p ′ → b q ′ ) = d L P ( a p ′ , b q ′ ) + d L P ( a p − 1 ′ , b q − 1 ′ ) + ν ⋅ ( | t a p − t b q | + | t a p − 1 − t b q − 1 | ) {\displaystyle \Gamma (\alpha _{p}^{'}\to b_{q}^{'})=d_{LP}(a_{p}^{'},b_{q}^{'})+d_{LP}(a_{p-1}^{'},b_{q-1}^{'})+\nu \cdot (|t_{a_{p}}-t_{b_{q}}|+|t_{a_{p-1}}-t_{b_{q-1}}|)} Γ ( Λ → b q ′ ) = d L P ( b p ′ , b p − 1 ′ ) + ν ⋅ ( t b q − t b q − 1 ) + λ {\displaystyle \Gamma (\Lambda \to b_{q}^{'})=d_{LP}(b_{p}^{'},b_{p-1}^{'})+\nu \cdot (t_{b_{q}}-t_{b_{q-1}})+\lambda } Whereas the recursion δ λ , ν {\displaystyle \delta _{\lambda ,\nu }} is initialized as: δ λ , ν ( A 1 0 , B 1 0 ) = 0 , {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{0},B_{1}^{0})=0,} δ λ , ν ( A 1 0 , B 1 j ) = ∞ f o r j ≥ 1 {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{0},B_{1}^{j})=\infty \ {\rm {{for\ }j\geq 1}}} δ λ , ν ( A 1 i , B 1 0 ) = ∞ f o r i ≥ 1 {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{i},B_{1}^{0})=\infty \ {\rm {{for\ }i\geq 1}}} with a 0 ′ = b 0 ′ = 0 {\displaystyle a'_{0}=b'_{0}=0} === Implementations === An implementation of the TWED algorithm in C with a Python wrapper is available at TWED is also implemented into the Time Series Subsequence Search Python package (TSSEARCH for short) available at [1]. An R implementation of TWED has been integrated into the TraMineR, a R package for mining, describing and visualizing sequences of states or events, and more generally discrete sequence data. Additionally, cuTWED is a CUDA- accelerated implementation of TWED which uses an improved algorithm due to G. Wright (2020). This method is linear in memory and massively parallelized. cuTWED is written in CUDA C/C++, comes with Python bindings, and also includes Python bindings for Marteau's reference C implementation. ==== Python ==== Backtracking, to find the most cost-efficient path: ==== MATLAB ==== Backtracking, to find the most cost-efficient path:
Quantification (machine learning)
In machine learning, quantification (variously called learning to quantify, or supervised prevalence estimation, or class prior estimation) is the task of using supervised learning in order to train models (quantifiers) that estimate the relative frequencies (also known as prevalence values) of the classes of interest in a sample of unlabelled data items. For instance, in a sample of 100,000 unlabelled tweets known to express opinions about a certain political candidate, a quantifier may be used to estimate the percentage of these tweets which belong to class `Positive' (i.e., which manifest a positive stance towards this candidate), and to do the same for classes `Neutral' and `Negative'. Quantification may also be viewed as the task of training predictors that estimate a (discrete) probability distribution, i.e., that generate a predicted distribution that approximates the unknown true distribution of the items across the classes of interest. Quantification is different from classification, since the goal of classification is to predict the class labels of individual data items, while the goal of quantification it to predict the class prevalence values of sets of data items. Quantification is also different from regression, since in regression the training data items have real-valued labels, while in quantification the training data items have class labels. It has been shown in multiple research works that performing quantification by classifying all unlabelled instances and then counting the instances that have been attributed to each class (the 'classify and count' method) usually leads to suboptimal quantification accuracy. This suboptimality may be seen as a direct consequence of 'Vapnik's principle', which states: If you possess a restricted amount of information for solving some problem, try to solve the problem directly and never solve a more general problem as an intermediate step. It is possible that the available information is sufficient for a direct solution but is insufficient for solving a more general intermediate problem. In our case, the problem to be solved directly is quantification, while the more general intermediate problem is classification. As a result of the suboptimality of the 'classify and count' method, quantification has evolved as a task in its own right, different (in goals, methods, techniques, and evaluation measures) from classification. == Quantification tasks == === Quantification tasks according to the set of classes === The main variants of quantification, according to the characteristics of the set of classes used, are: Binary quantification, corresponding to the case in which there are only n = 2 {\displaystyle n=2} classes and each data item belongs to exactly one of them; Single-label multiclass quantification, corresponding to the case in which there are n > 2 {\displaystyle n>2} classes and each data item belongs to exactly one of them; Multi-label multiclass quantification, corresponding to the case in which there are n ≥ 2 {\displaystyle n\geq 2} classes and each data item can belong to zero, one, or several classes at the same time; Ordinal quantification, corresponding to the single-label multiclass case in which a total order is defined on the set of classes. Regression quantification, a task which stands to 'standard' quantification as regression stands to classification. Strictly speaking, this task is not a quantification task as defined above (since the individual items do not have class labels but are labelled by real values), but has enough commonalities with other quantification tasks to be considered one of them. Most known quantification methods address the binary case or the single-label multiclass case, and only few of them address the multi-label, ordinal, and regression cases. Binary-only methods include the Mixture Model (MM) method, the HDy method, SVM(KLD), and SVM(Q). Methods that can deal with both the binary case and the single-label multiclass case include probabilistic classify and count (PCC), adjusted classify and count (ACC), probabilistic adjusted classify and count (PACC), the Saerens-Latinne-Decaestecker EM-based method (SLD), and KDEy. Methods for multi-label quantification include regression-based quantification (RQ) and label powerset-based quantification (LPQ). Methods for the ordinal case include ordinal versions of the above-mentioned ACC, PACC, and SLD methods, and ordinal versions of the above-mentioned HDy method. Methods for the regression case include Regress and splice and Adjusted regress and sum. === Quantification tasks according to the type of data === Several subtasks of quantification may be identified according to the type of data involved. Example such tasks are: Quantification of networked data. This task consists of performing quantification when the datapoints are members of a relation, i.e., are interlinked. As such, this task is a strict relative of collective classification. Quantification over time. This task consists of performing quantification on sets that become available in a temporal sequence, i.e., as a data stream, and finds application in contexts in which class prevalence values must be monitored over time. == Evaluation measures for quantification == Several evaluation measures can be used for evaluating the error of a quantification method. Since quantification consists of generating a predicted probability distribution that estimates a true probability distribution, these evaluation measures are ones that compare two probability distributions. Most evaluation measures for quantification belong to the class of divergences. Evaluation measures for binary quantification, single-label multiclass quantification, and multi-label quantification, are Absolute Error Squared Error Relative Absolute Error Kullback–Leibler divergence Pearson Divergence Evaluation measures for ordinal quantification are Normalized Match Distance (a particular case of the Earth Mover's Distance) Root Normalized Order-Aware Distance == Applications == Quantification is of special interest in fields such as the social sciences, epidemiology, market research, allocating resources, and ecological modelling, since these fields are inherently concerned with aggregate data. However, quantification is also useful as a building block for solving other downstream tasks, such as improving the accuracy of classifiers on out-of-distribution data, measuring classifier bias and ranker bias, and estimating the accuracy of classifiers on out-of-distribution data. == Resources == LQ 2021: the 1st International Workshop on Learning to Quantify LQ 2022: the 2nd International Workshop on Learning to Quantify LQ 2023: the 3rd International Workshop on Learning to Quantify LQ 2024: the 4th International Workshop on Learning to Quantify LQ 2025: the 5th International Workshop on Learning to Quantify LeQua 2022: the 1st Data Challenge on Learning to Quantify LeQua 2024: the 2nd Data Challenge on Learning to Quantify QuaPy: An open-source Python-based software library for quantification QuantificationLib: A Python library for quantification and prevalence estimation
Steve Omohundro
Stephen Malvern Omohundro (born 1959) is an American computer scientist whose areas of research include Hamiltonian physics, dynamical systems, programming languages, machine learning, machine vision, and the social implications of artificial intelligence. His current work uses rational economics to develop safe and beneficial intelligent technologies for better collaborative modeling, understanding, innovation, and decision making. == Education == Omohundro has degrees in physics and mathematics from Stanford University (Phi Beta Kappa) and a Ph.D. in physics from the University of California, Berkeley. == Learning algorithms == Omohundro started the "Vision and Learning Group" at the University of Illinois, which produced 4 Masters and 2 Ph.D. theses. His work in learning algorithms included a number of efficient geometric algorithms, the manifold learning task and various algorithms for accomplishing this task, other related visual learning and modelling tasks, the best-first model merging approach to machine learning (including the learning of Hidden Markov Models and Stochastic Context-free Grammars), and the Family Discovery Learning Algorithm, which discovers the dimension and structure of a parameterized family of stochastic models. == Self-improving artificial intelligence and AI safety == Omohundro started Self-Aware Systems in Palo Alto, California to research the technology and social implications of self-improving artificial intelligence. He is an advisor to the Machine Intelligence Research Institute on artificial intelligence. He argues that rational systems exhibit problematic natural "drives" that will need to be countered in order to build intelligent systems safely. His papers, talks, and videos on AI safety have generated extensive interest. He has given many talks on self-improving artificial intelligence, cooperative technology, AI safety, and connections with biological intelligence. == Programming languages == At Thinking Machines Corporation, Cliff Lasser and Steve Omohundro developed Star Lisp, the first programming language for the Connection Machine. Omohundro joined the International Computer Science Institute (ICSI) in Berkeley, California, where he led the development of the open source programming language Sather. Sather is featured in O'Reilly's History of Programming Languages poster. == Physics and dynamical systems theory == Omohundro's book Geometric Perturbation Theory in Physics describes natural Hamiltonian symplectic structures for a wide range of physical models that arise from perturbation theory analyses. He showed that there exist smooth partial differential equations which stably perform universal computation by simulating arbitrary cellular automata. The asymptotic behavior of these PDEs is therefore logically undecidable. With John David Crawford he showed that the orbits of three-dimensional period doubling systems can form an infinite number of topologically distinct torus knots and described the structure of their stable and unstable manifolds. == Mathematica and Apple tablet contest == From 1986 to 1988, he was an Assistant Professor of Computer science at the University of Illinois at Urbana-Champaign and cofounded the Center for Complex Systems Research with Stephen Wolfram and Norman Packard. While at the University of Illinois, he worked with Stephen Wolfram and five others to create the symbolic mathematics program Mathematica. He and Wolfram led a team of students that won an Apple Computer contest to design "The Computer of the Year 2000." Their design entry "Tablet" was a touchscreen tablet with GPS and other features that finally appeared when the Apple iPad was introduced 22 years later. == Other contributions == Subutai Ahmad and Steve Omohundro developed biologically realistic neural models of selective attention. As a research scientist at the NEC Research Institute, Omohundro worked on machine learning and computer vision, and was a co-inventor of U.S. Patent 5,696,964, "Multimedia Database Retrieval System Which Maintains a Posterior Probability Distribution that Each Item in the Database is a Target of a Search." === Pirate puzzle === Omohundro developed an extension to the game theoretic pirate puzzle featured in Scientific American. == Outreach == Omohundro has sat on the Machine Intelligence Research Institute board of advisors. He has written extensively on artificial intelligence, and has warned that "an autonomous weapons arms race is already taking place" because "military and economic pressures are driving the rapid development of autonomous systems".
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Linguistics Research Center at UT Austin
The Linguistics Research Center (LRC) at the University of Texas is a center for computational linguistics research & development. It was directed by Prof. Winfred Lehmann until his death in 2007, and subsequently by Dr. Jonathan Slocum. Since its founding, virtually all projects at the LRC have involved processing natural language texts with the aid of computers. The principal activities of the Center at present focus on Indo-European languages and comprise historical study, lexicography, and web-based teaching; staff members engage in several independent but often complementary projects in these fields using a variety of software, almost all of it developed in-house. == History == The LRC was founded by Winfred Lehmann in 1961. In the early days, research efforts at the LRC concentrated on machine translation (MT) -- the translation of texts from one human language to another with the aid of computers, very developed nowadays in the field of language industry—funded by the USAF and other sponsors. The LRC concentrated on German English translation, though a copy of the Russian Master Dictionary was deposited at the LRC after the ALPAC report. After a general hiatus ca. 1975-78, new funding led to the development by Jonathan Slocum and others of a new system with the same name (the METAL MT system), but with new sets of tools for linguists and vastly greater success, resulting in the delivery a production prototype then later a full-fledged commercial MT system. MT R&D continued at the LRC, with funding by various sponsors, until well into the 1990s. From its early years to the present, the LRC has mounted a number of smaller projects resulting in the publication of significant works relating to Indo-European languages and/or their common ancestor, Proto-Indo-European. The hallmark of this work has been the use of computers to transcribe texts and prepare them for publication. A prominent example of the LRC using computers to prepare texts for print publication is the book by Winfred P. Lehmann, A Gothic Etymological Dictionary (Leiden: Brill, 1986). The final print-ready version was produced with the aid of a laser printer (exotic new technology, in those days) using, for the various languages included in the entries, approximately 500 special characters—many of them designed at the Center. This was the first major etymological dictionary for Indo-European languages to be produced with the aid of computers. Current LRC projects have concentrated on transcribing early Indo-European texts, developing language lessons based on them, and publishing on the web these and other materials related to the study of Indo-European languages, of their common ancestor Proto-Indo-European, and of historical linguistics more generally. == Alumni == Winfred Lehmann Rolf A. Stachowitz Jonathan Slocum Winfield S. Bennett John White
World Database of Happiness
The World Database of Happiness is a web-based archive of research findings on subjective appreciation of life, based in the Erasmus Happiness Economics Research Organization of the Erasmus University Rotterdam in The Netherlands. The database contains both an overview of scientific publications on happiness and a digest of research findings. Happiness is defined as the degree to which an individual judges the quality of his or her life as a whole favorably. Two 'components' of happiness are distinguished: hedonic level of affect (the degree to which pleasant affect dominates) and contentment (perceived realization of wants). == Aims == The World Database of Happiness is a tool to quickly acquire an overview on the ever-growing stream of research findings on happiness Medio 2023 the database covered some 16,000 scientific publications on happiness, from which were extracted 23,000 distributional findings (on how happy people are) and another 24,000 correlational findings (on factors associated with more and less happiness). The first findings date from 1915. == Technique == The World Database of Happiness is a ‘findings archive’, which consists of electronic ‘finding pages’ on which separate research results are described in a standard format and terminology. These finding pages can be selected on various characteristics, such as population studies, the measure of happiness used and observed co-variates. All finding-pages have a specific internet address to which links can be made in scientific review papers or policy recommendations. This allows a concise presentation of many findings in a table, while providing readers with access to detail. == Scientific use == The Database has been cited in 254 scientific papers, for example to access under what conditions economic growth enhances average happiness or to show that rising mean happiness at first raises happiness inequality, but further rise will diminish these differences, or that healthy eating is associated with more happiness, even after controlling for the effect on health Another finding is that relative simple happiness training techniques raise happiness by some 5% == Popular use == The World Database of Happiness is often used by popular media to make lists of the happiest countries around the globe. An example is the Happy Planet Index, which aims to chart sustainable happiness all over the world by combining data on longevity, happiness and the size of the ecological footprint of citizens. == Strengths and weaknesses == The database has a clear conceptual focus, it includes only research findings on subjective enjoyment of one's life as a whole. Thereby it evades the Babel that has haunted the study of happiness for ages. The other side of that coin is that much interesting research is left out. The findings are reported with technical details about measurement and statistical analysis. This detail is welcomed by scholars, but makes the information difficult to digest for lay-persons. Still another limitation is that the determinants of happiness appear to vary considerably across persons and situations, which make it hard to draw general conclusions about the causes of happiness. What is clear is that poor health, separation, unemployment and lack of social contact are all strongly negatively associated with happiness. Another problem for the World database of happiness is that the studies on happiness increase with such a high rate that it gets increasingly difficult to offer a complete overview of all research findings. A further concern is that the Database of Happiness is exclusively focused on hedonic happiness (feeling good) and not on mature happiness that might exist in the face of suffering
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