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Gradient Boosting
Gradient boosting is a machine learning technique used in regression and classification tasks, among others. It gives a prediction model in the form of an ensemble of weak prediction models, which are typically decision trees. When a decision tree is the weak learner, the resulting algorithm is called gradient-boosted trees; it usually outperforms random forest. A gradient-boosted trees model is built in a stage-wise fashion as in other boosting methods, 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, simultaneously with the more general functional gradient boosting perspective of Llew Mason, Jonathan Baxter, Peter Bartlett and Marcus Frean. Th ... [...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] |
Learning To Rank
Learning to rank. Slides from Tie-Yan Liu's talk at WWW 2009 conference aravailable online or machine-learned ranking (MLR) is the application of machine learning, typically supervised, semi-supervised or reinforcement learning, in the construction of ranking models for information retrieval systems. Training data consists of lists of items with some partial order specified between items in each list. This order is typically induced by giving a numerical or ordinal score or a binary judgment (e.g. "relevant" or "not relevant") for each item. The goal of constructing the ranking model is to rank new, unseen lists in a similar way to rankings in the training data. Applications In information retrieval Ranking is a central part of many information retrieval problems, such as document retrieval, collaborative filtering, sentiment analysis, and online advertising. A possible architecture of a machine-learned search engine is shown in the accompanying figure. Training data con ... [...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 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). Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations (then also called moderation or effect modification). Interactions are often considered in the context of 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, this makes it more difficult to predict the consequences of changing the value of a variable, particu ... [...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 , one has \mathbf_(x)=1 if x\in A, and \mathbf_(x)=0 otherwise, where \mathbf_A is a common notation for the indicator function. Other common notations are I_A, and \chi_A. The indicator function of is the Iverson bracket of the property of belonging to ; that is, :\mathbf_(x)= \in A For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers. Definition The indicator function of a subset of a set is a function \mathbf_A \colon X \to \ defined as \mathbf_A(x) := \begin 1 ~&\text~ x \in A~, \\ 0 ~&\text~ x \notin A~. \end The Iverson bracket provides the equivalent notation, \in A/math> or to be used instead of \mathbf_(x)\,. The function \mathbf_A is sometimes denoted , , , or even just . Notatio ... [...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. Decision trees are among the most popular machine learning algorithms given their intelligibility and simplicity. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data (but the resulting classification tree can be an input for decision making). General Dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. The other approach is trust region. The line search approach 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. Example use Here is an example gradient method that uses a line search in step 4. # Set iteration counter \displaystyle k=0, and make an initial guess \mathbf_0 for the minimum # Repeat: # Compute a descent direction \mathbf_k # Choose \displaystyle \alpha_k to 'loosely' minimize h(\alpha_k)=f(\mathbf_k+\alpha_k\mathbf_k) over \alpha_k\in\mathbb R_+ # &nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Search
In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. The other approach is trust region. The line search approach 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. Example use Here is an example gradient method that uses a line search in step 4. # Set iteration counter \displaystyle k=0, and make an initial guess \mathbf_0 for the minimum # Repeat: # Compute a descent direction \mathbf_k # Choose \displaystyle \alpha_k to 'loosely' minimize h(\alpha_k)=f(\mathbf_k+\alpha_k\mathbf_k) over \alpha_k\in\mathbb R_+ # &nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steepest Descent
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable 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 local maximum of that function; the procedure is then known as gradient ascent. 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 Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades. Description Gradient descent is based on the observation that if the multi-variable function F(\mathbf) is def ... [...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 algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Risk Minimization
Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on their performance. The core idea is that we cannot know exactly how well an algorithm will work in practice (the true "risk") because we don't know the true distribution of data that the algorithm will work on, but we can instead measure its performance on a known set of training data (the "empirical" risk). Background Consider the following situation, which is a general setting of many supervised learning problems. We have two spaces of objects X and Y and would like to learn a function \ h: X \to Y (often called ''hypothesis'') which outputs an object y \in Y, given x \in X. To do so, we have at our disposal a ''training set'' of n examples \ (x_1, y_1), \ldots, (x_n, y_n) where x_i \in X is an input and y_i \in Y is the corresponding response that we wish to get from h(x_i). To put it more formally, we assume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Learner
In machine learning, boosting is an ensemble meta-algorithm for primarily reducing bias, and also variance in supervised learning, and a family of machine learning algorithms that convert weak learners to strong ones. Boosting is based on the question posed by Kearns and Valiant (1988, 1989):Michael Kearns(1988)''Thoughts on Hypothesis Boosting'' Unpublished manuscript (Machine Learning class project, December 1988) "Can a set of weak learners create a single strong learner?" A weak learner is defined to be a classifier that is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification. Robert Schapire's affirmative answer in a 1990 paper to the question of Kearns and Valiant has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting. When first introduced, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
