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Multivariate Nonlinear Regression with Semiparametric Latent Factor Models

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Binary regression

In statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output binary variable. Generally the probability of the two alternatives is modeled, instead of simply outputting a single value, as in linear regression. Binary regression is usually analyzed as a special case of binomial regression, with a single outcome (), and one of the two alternatives considered as "success" and coded as 1: the value is the count of successes in 1 trial, either 0 or 1.

Nonparametric statistics

Nonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).

Linux kernel

The Linux kernel is a free and open-source, monolithic, modular, multitasking, Unix-like operating system kernel. It was originally written in 1991 by Linus Torvalds for his i386-based PC, and it was soon adopted as the kernel for the GNU operating system, which was written to be a free (libre) replacement for Unix. Linux is provided under the GNU General Public License version 2 only, but it contains files under other compatible licenses.

Loadable kernel module

In computing, a loadable kernel module (LKM) is an that contains code to extend the running kernel, or so-called base kernel, of an operating system. LKMs are typically used to add support for new hardware (as device drivers) and/or s, or for adding system calls. When the functionality provided by an LKM is no longer required, it can be unloaded in order to free memory and other resources.

Latent Dirichlet allocation

In natural language processing, Latent Dirichlet Allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) that explains a set of observations through unobserved groups, and each group explains why some parts of the data are similar. The LDA is an example of a Bayesian topic model. In this, observations (e.g., words) are collected into documents, and each word's presence is attributable to one of the document's topics. Each document will contain a small number of topics.

Mixture distribution

In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.

Bootstrapping (statistics)

Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution.

Multilevel model

Multilevel models (also known as hierarchical linear models, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped.

Gibbs sampling

In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables).

Predictive analytics

Predictive analytics is a form of business analytics applying machine learning to generate a predictive model for certain business applications. As such, it encompasses a variety of statistical techniques from predictive modeling and machine learning that analyze current and historical facts to make predictions about future or otherwise unknown events. It represents a major subset of machine learning applications; in some contexts, it is synonymous with machine learning.