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Gradient Boosting
Gradient boosting is a machine learning technique based on boosting in a functional space, where the target is ''pseudo-residuals'' instead of residuals as in traditional boosting. It gives a prediction model in the form of an ensemble of weak prediction models, i.e., models that make very few assumptions about the data, which are typically simple decision trees. When a decision tree is the weak learner, the resulting algorithm is called gradient-boosted trees; it usually outperforms random forest. As with other boosting methods, a gradient-boosted trees model is built in stages, but it generalizes the other methods by allowing optimization of an arbitrary differentiable loss function. History The idea of gradient boosting originated in the observation by Leo Breiman that boosting can be interpreted as an optimization algorithm on a suitable cost function. Explicit regression gradient boosting algorithms were subsequently developed, by Jerome H. Friedman, (in 1999 and later ... [...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] |
Gradient Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperparameter (machine Learning)
In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer). These are named ''hyper''parameters in contrast to parameters, which are characteristics that the model learns from the data. Hyperparameters are not required by every model or algorithm. Some simple algorithms such as ordinary least squares regression require none. However, the LASSO algorithm, for example, adds a regularization hyperparameter to ordinary least squares which must be set before training. Even models and algorithms without a strict requirement to define hyperparameters may not produce meaningful results if these are not carefully chosen. However, optimal values for hyperparameters are not always easy to predict. Some ... [...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] |
Regularization (mathematics)
In mathematics, statistics, Mathematical finance, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the Problem solving, answer to a problem to a simpler one. It is often used in solving ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: * Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be Prior probability, priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems. The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. * Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers. Implicit regularizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Stump
A decision stump is a machine learning model consisting of a one-level decision tree. That is, it is a decision tree with one internal node (the root) which is immediately connected to the terminal nodes (its leaves). A decision stump makes a prediction based on the value of just a single input feature. Sometimes they are also called 1-rules. Depending on the type of the input feature, several variations are possible. For nominal features, one may build a stump which contains a leaf for each possible feature value or a stump with the two leaves, one of which corresponds to some chosen category, and the other leaf to all the other categories.This is what has been implemented in Weka's DecisionStump classifier. For binary features these two schemes are identical. A missing value may be treated as a yet another category. For continuous features, usually, some threshold feature value is selected, and the stump contains two leaves — for values below and above the threshold. However, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more Variable (statistics), variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive map, additive). Although commonly thought of in terms of Causality, causal relationships, the concept of an interaction can also describe non-causal associations (then also called Moderation (statistics), ''moderation'' or ''effect modification''). Interactions are often considered in the context of regression analysis, regression analyses or factorial experiments. The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indicator Notation
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , then the indicator function of is the function \mathbf_A defined by \mathbf_\!(x) = 1 if x \in A, and \mathbf_\!(x) = 0 otherwise. Other common notations are and \chi_A. The indicator function of is the Iverson bracket of the property of belonging to ; that is, \mathbf_(x) = \left x\in A\ \right For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers. Definition Given an arbitrary set , the indicator function of a subset of is the function \mathbf_A \colon X \mapsto \ defined by \operatorname\mathbf_A\!( x ) = \begin 1 & \text x \in A \\ 0 & \text x \notin A \,. \end The Iverson bracket provides the equivalent notation \left x\in A\ \right/math> or that can be used instead of \mathbf_\!(x). T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classification And Regression Tree
Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. More generally, the concept of regression tree can be extended to any kind of object equipped with pairwise dissimilarities such as categorical sequences. Decision trees are among the most popular machine learning algorithms given their intelligibility and simplicity because they produce algorithms that are easy to interpret and visualize, even for users without a stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, line search is a basic iterative approach to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. It first finds a descent direction along which the objective function f will be reduced, and then computes a step size that determines how far \mathbf should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly. One-dimensional line search Suppose ''f'' is a one-dimensional function, f:\mathbb R\to\mathbb R, and assume that it is unimodal, that is, contains exactly one local minimum ''x''* in a given interval 'a'',''z'' This means that ''f'' is strictly decreasing in ,x*and strictly increasing in *,''z'' There are several ways to find an (approximate) minimum point in this case. Zero-order methods Zero-order methods use only function evaluations (i.e., a value oracle) - not derivatives: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steepest Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a :First order methods, first-order Iterative algorithm, iterative algorithm for minimizing a differentiable function, differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with Local search (optimization), local search algorithms, although both are Iterative method, iterative methods for Global optimization, optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard indepe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greedy Algorithm
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time. For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids and give constant-factor approximations to optimization problems with the submodular structure. Specifics Greedy algori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
