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Support Vector Machines
In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms that analyze data for 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 Vapnik (1982, 1995) and Chervonenkis (1974). In addition to performing linear classification, SVMs can efficiently perform non-linear classification using the ''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 into high-dimensional feature spaces, where linear classification can be performed. Being max-margin models, SVMs are resilient to noisy data (e.g., misclassified examples). ... [...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] |
Linear Separability
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are ''linearly separable'' if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if the line is replaced by a hyperplane. The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises in several areas. In statistics and machine learning, classifying certain types of data is a problem for which good algorithms exist that are based on this concept. Mathematical definition Let X_ and X_ be two sets of points in an ''n''-dimensional Euclidean space. Then X_ and X_ are ''linearly separable'' if ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel Machine
Kernel may refer to: Computing * Kernel (operating system), the central component of most operating systems * Kernel (image processing), a matrix used for image convolution * Compute kernel, in GPGPU programming * Kernel method, in machine learning * Kernelization, a technique for designing efficient algorithms ** Kernel, a routine that is executed in a vectorized loop, for example in general-purpose computing on graphics processing units * KERNAL, the Commodore operating system Mathematics Objects * Kernel (algebra), a general concept that includes: ** Kernel (linear algebra) or null space, a set of vectors mapped to the zero vector ** Kernel (category theory), a generalization of the kernel of a homomorphism ** Kernel (set theory), an equivalence relation: partition by image under a function ** Difference kernel, a binary equalizer: the kernel of the difference of two functions Functions * Kernel (geometry), the set of points within a polygon from which the whole polygo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overfitting
In mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be justified by the data. In the special case where the model consists of a polynomial function, these parameters represent the degree of a polynomial. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the Statistical noise, noise) as if that variation represented underlying model structure. Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. Underfitting would occur, for example, when fitting a linear model to nonlinear data. Such a model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalization Error
For supervised learning applications in machine learning and statistical learning theory, generalization errorMohri, M., Rostamizadeh A., Talwakar A., (2018) ''Foundations of Machine learning'', 2nd ed., Boston: MIT Press (also known as the out-of-sample errorY S. Abu-Mostafa, M.Magdon-Ismail, and H.-T. Lin (2012) Learning from Data, AMLBook Press. or the risk) is a measure of how accurately an algorithm is able to predict outcomes for previously unseen data. As learning algorithms are evaluated on finite samples, the evaluation of a learning algorithm may be sensitive to sampling error. As a result, measurements of prediction error on the current data may not provide much information about the algorithm's predictive ability on new, unseen data. The generalization error can be minimized by avoiding overfitting in the learning algorithm. The performance of machine learning algorithms is commonly visualized by Learning curve (machine learning), learning curve plots that show estimates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
