In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population.
Econometric models involving data sampled at different frequencies are of general interest. Mixed-data sampling (MIDAS) is an econometric regression developed by Eric Ghysels with several co-authors. There is now a substantial literature on MIDAS regressions and their applications, including Ghysels, Santa-Clara and Valkanov (2006), Ghysels, Sinko and Valkanov, Andreou, Ghysels and Kourtellos (2010) and Andreou, Ghysels and Kourtellos (2013).
Sir David Roxbee Cox was a British statistician and educator. His wide-ranging contributions to the field of statistics included introducing logistic regression, the proportional hazards model and the Cox process, a point process named after him.
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context of machine learning and more generally statistical analysis, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice.
Bootstrapping is any test or metric that uses random sampling with replacement, and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods.
Bradley Efron is an American statistician. Efron has been president of the American Statistical Association (2004) and of the Institute of Mathematical Statistics (1987–1988). He is a past editor of the Journal of the American Statistical Association, and he is the founding editor of the Annals of Applied Statistics. Efron is also the recipient of many awards.
Eric Ghysels is a Belgian economist with interest in finance and time series econometrics, and in particular the fields of financial econometrics and financial technology. He is the Edward M. Bernstein Distinguished Professor of Economics at the University of North Carolina and a Professor of Finance at the Kenan-Flagler Business School. He is also the Faculty Research Director of the Rethinc.Labs at the Frank Hawkins Kenan Institute of Private Enterprise.
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.
In machine learning and computational learning theory, LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani.
In statistical theory, the field of high-dimensional statistics studies data whose dimension is larger than typically considered in classical multivariate analysis. The area arose owing to the emergence of many modern data sets in which the dimension of the data vectors may be comparable to, or even larger than, the sample size, so that justification for the use of traditional techniques, often based on asymptotic arguments with the dimension held fixed as the sample size increased, was lacking.
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The AM uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM, like many other machine learning methods, include model selection, overfitting, and multicollinearity.
In statistics and machine learning, lasso is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model. It was originally introduced in geophysics, and later by Robert Tibshirani, who coined the term.
In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods.
Trevor John Hastie is an American statistician and computer scientist. He is currently serving as the John A. Overdeck Professor of Mathematical Sciences and Professor of Statistics at Stanford University. Hastie is known for his contributions to applied statistics, especially in the field of machine learning, data mining, and bioinformatics. He has authored several popular books in statistical learning, including The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Hastie has been listed as an ISI Highly Cited Author in Mathematics by the ISI Web of Knowledge.
In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution over a set of classes, rather than only outputting the most likely class that the observation should belong to. Probabilistic classifiers provide classification that can be useful in its own right or when combining classifiers into ensembles.
In statistics, the graphical lasso is a sparsepenalized maximum likelihood estimator for the concentration or precision matrix of a multivariate elliptical distribution. The original variant was formulated to solve Dempster's covariance selection problem for the multivariate Gaussian distribution when observations were limited. Subsequently, the optimization algorithms to solve this problem were improved and extended to other types of estimators and distributions.
Out-of-bag (OOB) error, also called out-of-bag estimate, is a method of measuring the prediction error of random forests, boosted decision trees, and other machine learning models utilizing bootstrap aggregating (bagging). Bagging uses subsampling with replacement to create training samples for the model to learn from. OOB error is the mean prediction error on each training sample xi, using only the trees that did not have xi in their bootstrap sample.
The following outline is provided as an overview of and topical guide to machine learning:
Hui Zou is currently a professor of statistics at the University of Minnesota.
Daniela M. Witten is an American biostatistician. She is a professor and the Dorothy Gilford Endowed Chair of Mathematical Statistics at the University of Washington. Her research investigates the use of machine learning to understand high-dimensional data.
