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Hinge Loss
In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). For an intended output and a classifier score , the hinge loss of the prediction is defined as :\ell(y) = \max(0, 1-t \cdot y) Note that y should be the "raw" output of the classifier's decision function, not the predicted class label. For instance, in linear SVMs, y = \mathbf \cdot \mathbf + b, where (\mathbf,b) are the parameters of the hyperplane and \mathbf is the input variable(s). When and have the same sign (meaning predicts the right class) and , y, \ge 1, the hinge loss \ell(y) = 0. When they have opposite signs, \ell(y) increases linearly with , and similarly if , y, < 1, even if it has the same sign (correct prediction, but not by enough margin). Extensions While binary SVMs are commonly extended to |
Hinge Loss Vs Zero One Loss
A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation: all other Translation (geometry), translations or rotations being prevented, and thus a hinge has one degree of freedom. Hinges may be made of Flexure bearing, flexible material or of moving components. In biology, many joints function as hinges, like the elbow joint. History Ancient remains of stone, marble, wood, and bronze hinges have been found. Some date back to at least Ancient Egypt. In Ancient Rome, hinges were called wikt:cardo#Latin, cardō and gave name to the goddess Cardea and the main street Cardo. This name cardō lives on figuratively today as "the chief thing (on which something turns or depends)" in words such as ''wikt:cardinal#English, cardinal''. According to the OED, the English word hinge is related to ''wikt:hang#English, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Loss
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of ''substitutions'' required to change one string into the other, or the minimum number of ''errors'' that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming. A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field. Definition The Hamming distance between two equal-length strings of symbols is the number of positions at which the corresponding symbols are different. Examples The symbols may be letters, bits, or decimal digits, among other possibilities. For example, the Hamming distance between: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huber Loss
Huber is a German-language surname. It derives from the German word ''Hube'' meaning hide, a unit of land a farmer might possess, granting them the status of a free tenant. It is in the top ten most common surnames in the German-speaking world, especially in Austria and Switzerland where it is the surname of approximately 0.3% of the population. Variants arising from varying dialectal pronunciation of the surname include Hueber, Hüber, Huemer, Humer, Haumer, Huebner and (anglicized) Hoover. People with the surname Huber A *Adam Huber (born 1987), American actor and model. *Alexander Huber (born 1968), German climber and mountaineer *Alexander Huber (football) (born 1985), German football player * Alyson Huber (born 1972), Californian legislator elected to the State Assembly in 2008 *Anja Huber (born 1983), German skeleton racer *Anke Huber (born 1974), German tennis player *Anthony Huber (born 1994), killed in the Kenosha unrest shooting B *Bruno Huber (1930–1999), Swis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IJCAI
The International Joint Conference on Artificial Intelligence (IJCAI) is the leading conference in the field of Artificial Intelligence. The conference series has been organized by the nonprofit IJCAI Organization since 1969, making it the oldest premier AI conference series in the world.Jointly sponsored by the IJCAI Organization and the hosting national AI societies. It was held biennially in odd-numbered years from 1969 to 2015 and annually starting from 2016. More recently, IJCAI was held jointly every four years with ECAI since 2018 and PRICAI since 2020 to promote collaboration of AI researchers and practitioners. IJCAI covers a broad range of research areas in the field of AI. It is a large and highly selective conference, with only about 20% or less of the submitted papers to be accepted after peer review in 5 years leading to 2022. Lower acceptance rate usually means better quality papers and higher reputation conference. Awards Three research awards are given at each I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hinge Loss Variants
A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation: all other translations or rotations being prevented, and thus a hinge has one degree of freedom. Hinges may be made of flexible material or of moving components. In biology, many joints function as hinges, like the elbow joint. History Ancient remains of stone, marble, wood, and bronze hinges have been found. Some date back to at least Ancient Egypt. In Ancient Rome, hinges were called cardō and gave name to the goddess Cardea and the main street Cardo. This name cardō lives on figuratively today as "the chief thing (on which something turns or depends)" in words such as ''cardinal''. According to the OED, the English word hinge is related to ''hang''. Door hinges ; Barrel hinge: A barrel hinge consists of a sectional barrel (the knuckle) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subderivative
In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to convex functions which are not necessarily differentiable. Subderivatives arise in convex analysis, the study of convex functions, often in connection to convex optimization. Let f:I \to \mathbb be a real-valued convex function defined on an open interval In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers satisfying is an interval which contains , , and all numbers in between. Other ... of the real line. Such a function need not be differentiable at all points: For example, the absolute value function ''f''(''x'')=, ''x'', is nondifferentiable when ''x''=0. However, as seen in the graph on the right (where ''f(x)'' in blue has non-differentiable kinks similar to the absolute value function), for any ''x''0 in the domain of the function one can draw a line which goes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differentiable Function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If is an interior point in the domain of a function , then is said to be ''differentiable at'' if the derivative f'(x_0) exists. In other words, the graph of has a non-vertical tangent line at the point . is said to be differentiable on if it is differentiable at every point of . is said to be ''continuously differentiable'' if its derivative is also a continuous function over the domain of the function f. Generally speaking, is said to be of class if its first k derivatives f^(x), f^(x), \ldots, f^(x) exist and are continuous over the domain of the func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Function
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of a function, graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (mathematics), epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain. Well-known examples of convex functions of a single variable include the quadratic function x^2 and the exponential function e^x. In simple terms, a convex function refers to a function whose graph is shaped like a cup \cup, while a concave function's graph is shaped like a cap \cap. Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structured Prediction
Structured prediction or structured (output) learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than scalar 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 true prediction value is used to adjust model parameters. Due to the complexity of the model and the interrelations of predicted variables the process of prediction using a trained model and of training itself is often computationally infeasible and approximate inference and learning methods are used. Applications For example, the problem of translating a natural language sentence into a syntactic representation such as a parse tree 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 also used in a wide variety of application domains i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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