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Structured Support Vector Machine
The structured support-vector machine is a machine learning algorithm that generalizes the Support-Vector Machine (SVM) classifier. Whereas the SVM classifier supports binary classification, multiclass classification and regression, the structured SVM allows training of a classifier for general structured output labels. As an example, a sample instance might be a natural language sentence, and the output label is an annotated parse tree. Training a classifier consists of showing pairs of correct sample and output label pairs. After training, the structured SVM model allows one to predict for new sample instances the corresponding output label; that is, given a natural language sentence, the classifier can produce the most likely parse tree. Training For a set of n training instances (\boldsymbol_i,y_i) \in \mathcal\times\mathcal, i=1,\dots,n from a sample space \mathcal and label space \mathcal, the structured SVM minimizes the following regularized risk function. :\underset ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Support-vector Machine
In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning, supervised Maximum-margin hyperplane, max-margin models with associated learning algorithms that analyze data for Statistical classification, classification and regression analysis. Developed at AT&T Bell Laboratories, SVMs are one of the most studied models, being based on statistical learning frameworks of VC theory proposed by Vladimir Vapnik, Vapnik (1982, 1995) and Alexey Chervonenkis, Chervonenkis (1974). In addition to performing linear classifier, linear classification, SVMs can efficiently perform non-linear classification using the Kernel method#Mathematics: the kernel trick, ''kernel trick'', representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel function, which transforms them into coordinates in a higher-dimensional feature space. Thus, SVMs use the kernel trick to implicitly map their inputs int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Classification
Binary classification is the task of classifying the elements of a set into one of two groups (each called ''class''). Typical binary classification problems include: * Medical testing to determine if a patient has a certain disease or not; * Quality control in industry, deciding whether a specification has been met; * In information retrieval, deciding whether a page should be in the result set of a search or not * In administration, deciding whether someone should be issued with a driving licence or not * In cognition, deciding whether an object is food or not food. When measuring the accuracy of a binary classifier, the simplest way is to count the errors. But in the real world often one of the two classes is more important, so that the number of both of the different types of errors is of interest. For example, in medical testing, detecting a disease when it is not present (a '' false positive'') is considered differently from not detecting a disease when it is present (a '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiclass Classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (notably multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structured Learning
Structured prediction or structured output learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than discrete or real values. Similar to commonly used supervised learning techniques, structured prediction models are typically trained by means of observed data in which the predicted value is compared to the ground truth, and this is used to adjust the model parameters. Due to the complexity of the model and the interrelations of predicted variables, the processes of model training and inference are often computationally infeasible, so approximate inference and learning methods are used. Applications An example application is the problem of translating a natural language sentence into a syntactic representation such as a parse tree. This can be seen as a structured prediction problem in which the structured output domain is the set of all possible parse trees. Structured prediction is used in a wide variety o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parse Tree
A parse tree or parsing tree (also known as a derivation tree or concrete syntax tree) is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar. The term ''parse tree'' itself is used primarily in computational linguistics; in theoretical syntax, the term ''syntax tree'' is more common. Concrete syntax trees reflect the syntax of the input language, making them distinct from the abstract syntax trees used in computer programming. Unlike Reed-Kellogg sentence diagrams used for teaching grammar, parse trees do not use distinct symbol shapes for different types of constituents. Parse trees are usually constructed based on either the constituency relation of constituency grammars ( phrase structure grammars) or the dependency relation of dependency grammars. Parse trees may be generated for sentences in natural languages (see natural language processing), as well as during processing of computer languages, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric (mathematics)
In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another. Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Program
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers to a formal procedure for solving mathematical problems. This usage dates to the 1940s and is not specifically tied to the more recent notion of "computer programming." To avoid confusion, some practitioners prefer the term "optimization" — e.g., "quadratic optimization." Problem formulation The quadratic programming problem with variables and constraints can be formulated as follows. Given: * a real-valued, -dimensional vector , * an -dimensional real symmetric matrix , * an -dimensional real matrix , and * an -dimensional real vector , the objective of quadratic programming is to find an -dimensional vector , that wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delayed Constraint Generation
Delay or DeLay may refer to: People * B. H. DeLay (1891–1923), American aviator and movie stunt pilot * Dorothy DeLay (1917–2002), American violin instructor * Florence Delay (born 1941), French academician and actor * Jan Delay, stage name of German musician Jan Phillip Eißfeldt (born 1976) * Jason Delay (born 1995), American baseball player * Jean Delay (1907–1987), French psychiatrist, neurologist, and writer * Paul deLay (1952–2007), American blues musician * Tom DeLay (born 1947), American politician * Tom Delay (businessman) (born 1959), British businessman * Vladislav Delay (born 1976), Finnish musician Other uses * Delay (audio effect), a technology for producing delayed playback of an audio signal * Delay (programming), a programming language construct for delaying evaluation of an expression * ''Delay 1968 ''Delay 1968'' is a compilation album by the German experimental rock band Can released in 1981. It comprises previously unreleased work recorded for Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feasible Set
In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. For example, consider the problem of minimizing the function x^2+y^4 with respect to the variables x and y, subject to 1 \le x \le 10 and 5 \le y \le 12. \, Here the feasible set is the set of pairs (''x'', ''y'') in which the value of ''x'' is at least 1 and at most 10 and the value of ''y'' is at least 5 and at most 12. The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x^2+y^4. In many problems, the feasible set reflects a constraint that one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thorsten Joachims
Thorsten (Thorstein, Torstein, Torsten) is a Scandinavian given name. The Old Norse name was ''Þórsteinn''. It is a compound of the theonym ''Þór'' (''Thor'') and ''steinn'' "stone", which became ''Thor'' and ''sten'' in Old Danish and Old Swedish. The name is one of a group of Old Norse names containing the theonym ''Thor'', besides other such as ''Þórarin, Þórhall, Þórkell, Þórfinnr, Þórvald, Þórvarðr, Þórolf'', most of which, however, do not survive as modern names given with any frequency. The name is attested in medieval Iceland, e.g. Þorsteinn rauður Ólafsson (c. 850 – 880), Þórsteinn Eiríksson (late 10th century), and in literature such as ''Draumr Þorsteins Síðu-Hallssonar''. The Old English equivalent of the Scandinavian and Norman name is ''Thurstan'', attested after the Norman conquest of England in the 11th century as the name of a medieval archbishop of York (died 1140), of an abbot of Pershore (1080s) and of an abbot of Glastonbur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
