Bootstrap aggregating. Bootstrap aggregating (bagging) is a machine learning ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification and regression. It also reduces variance and helps to avoid overfitting. Although it is usually applied to decision tree methods, it can be used with any type of method. Bagging is a special case of the model averaging approach. Description of the technique[edit] Given a standard training set D of size n, bagging generates m new training sets Bagging leads to "improvements for unstable procedures" (Breiman, 1996), which include, for example, neural nets, classification and regression trees, and subset selection in linear regression (Breiman, 1994). An interesting application of bagging showing improvement in preimage learning is provided here.[2] On the other hand, it can mildly degrade the performance of stable methods such as K-nearest neighbors (Breiman, 1996).
Example: Ozone data[edit] diverges but. Knowledge market. A knowledge market is a mechanism for distributing knowledge resources.[1] There are two views on knowledge and how knowledge markets can function.[2] One view uses a legal construct of intellectual property to make knowledge a typical scarce resource, so the traditional commodity market mechanism can be applied directly to distribute it.[2] An alternative model is based on treating knowledge as a public good and hence encouraging free sharing of knowledge.[2] This is often referred to as attention economy.[2] Currently there is no consensus among researchers on relative merits of these two approaches.[2] History[edit] A knowledge economy include the concept of exchanging knowledge-based products and services.[1] However, as discussed by Stewart (1996)[3] knowledge is very different from physical products. Knowledge services[edit] St. Internet-based knowledge markets[edit] Free knowledge markets use an alternative model treating knowledge as a public good.[1] See also[edit] Wells Digest.
Particle filter. Particle filters or Sequential Monte Carlo (SMC) methods are a set of on-line posterior density estimation algorithms that estimate the posterior density of the state-space by directly implementing the Bayesian recursion equations. SMC methods use a grid-based approach, and use a set of particles to represent the posterior density. These filtering methods make no restrictive assumption about the dynamics of the state-space or the density function. SMC methods provide a well-established methodology for generating samples from the required distribution without requiring assumptions about the state-space model or the state distributions. The state-space model can be non-linear and the initial state and noise distributions can take any form required.
However, these methods do not perform well when applied to high-dimensional systems. History[edit] Objective[edit] The objective of a particle filter is to estimate the posterior density of the state variables given the observation variables. . Importance sampling. In statistics, importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution rather than the distribution of interest. It is related to umbrella sampling in computational physics. Depending on the application, the term may refer to the process of sampling from this alternative distribution, the process of inference, or both.
Basic theory[edit] Let be a random variable in some probability space. . , generated according to P, then an empirical estimate of E[X;P] is The basic idea of importance sampling is to change the probability measure P so that the estimation of E[X;P] is easier. Such that E[L;P]=1 and that P-almost everywhere . That satisfies The variable X/L will thus be sampled under P(L) to estimate as above. . When X is of constant sign over Ω, the best variable L would clearly be , so that X/L* is the searched constant E[X;P] and a single sample under P(L*) suffices to give its value. Resampling (statistics) In statistics, resampling is any of a variety of methods for doing one of the following: Common resampling techniques include bootstrapping, jackknifing and permutation tests.
Jackknifing, which is similar to bootstrapping, is used in statistical inference to estimate the bias and standard error (variance) of a statistic, when a random sample of observations is used to calculate it. Historically this method preceded the invention of the bootstrap with Quenouille inventing this method in 1949 and Tukey extending it in 1958.[1][2] This method was foreshadowed by Mahalanobis who in 1946 suggested repeated estimates of the statistic of interest with half the sample chosen at random.[3] He coined the name 'interpenetrating samples' for this method. Quenouille invented this method with the intention of reducing the bias of the sample estimate.
Instead of using the jackknife to estimate the variance, it may instead be applied to the log of the variance. This avoids "self-influence". And After ).