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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[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, with all other translations or rotations prevented; thus a hinge has one degree of freedom. Hinges may be made of flexible material or moving components. In biology, many joints function as hinges, such as the elbow joint. History Ancient remains of stone, marble, wood, and bronze hinges have been found. Some date back to at least Ancient Egypt, although it is nearly impossible to pinpoint exactly where and when the first hinges were used. 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 Oxford English Dictionary, the English word ''hinge' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Loss
In information theory, the Hamming distance between two strings or vectors 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 equivalently, 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huber Loss
In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. Definition The Huber loss function describes the penalty incurred by an estimation procedure . Huber (1964) defines the loss function piecewise by L_\delta (a) = \begin \frac & \text , a, \le \delta, \\ pt \delta \cdot \left(, a, - \frac\delta\right), & \text \end This function is quadratic for small values of , and linear for large values, with equal values and slopes of the different sections at the two points where , a, = \delta. The variable often refers to the residuals, that is to the difference between the observed and predicted values a = y - f(x), so the former can be expanded to L_\delta(y, f(x)) = \begin \frac ^2 & \text \left, y - f(x)\ \le \delta, \\ pt \delta\ \cdot \left(\left, y - f(x)\ - \frac\delta\right), & \text \en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IJCAI
The International Joint Conference on Artificial Intelligence (IJCAI) is a conference in the field of artificial intelligence. The conference series has been organized by the nonprofit IJCAI Organization since 1969.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 accepted after peer review in the 5 years leading up to 2022. Awards Three research awards are given at each IJCAI conference. * The IJCAI Computers and Thought Award is given to outstanding young scientists under the age of 35 in AI. * The Donald E. Walker Distinguished Se ... [...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 (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. 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 ... [...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, with all other translations or rotations prevented; thus a hinge has one degree of freedom. Hinges may be made of flexible material or moving components. In biology, many joints function as hinges, such as the elbow joint. History Ancient remains of stone, marble, wood, and bronze hinges have been found. Some date back to at least Ancient Egypt, although it is nearly impossible to pinpoint exactly where and when the first hinges were used. 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 Oxford English Dictionary, the English word ''hinge' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subderivative
In mathematics, the subderivative (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of subderivatives at a point is called the subdifferential at that point. 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 of the real line. Such a function need not be differentiable at all points: For example, the absolute value function f(x)=, x, is non-differentiable 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 through the point (x_0,f(x_0)) and which is everywhere either touching or below the graph of ''f''. The slope of such a line is called a ''subderivative''. Definition Rigorously, a ''subderivative'' of a c ... [...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 t ... [...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 distinct points on the graph of a function, graph of the function lies above or on 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. In simple terms, a convex function graph is shaped like a cup \cup (or a straight line like a linear function), while a concave function's graph is shaped like a cap \cap. A twice-differentiable function, differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain of a function, domain. Well-known examples of convex functions of a single variable include a linear function f(x) = cx (where c is a real number), a quadratic function cx^2 (c as a nonnegative real number) and an exponential function ce^x (c as a nonnegative real number). Convex functions pl ... [...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 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] |
Structured Prediction
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
