An Analysis of Transformations

By G. Box, D. R. Cox. 1964

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In Mathematical Optimization

Citations in the corpus

DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks (2017, methodology): “The network output h i,t = h ( h i,t − 1 , z i,t − 1 , x i,t , Θ) is then used to compute the parameters θ i,t = θ ( h i,t , Θ) of the likelihood (cid:96) ( z | θ ) , which is used for training the model parameters.”
Forecasting Across Time Series Databases using Long Short-Term Memory Networks on Groups of Similar Series (2017, background): “onservative way (see Section 3.7), and stabilizing the variance enables us to model greater dynamics in the trend. Popular transformations for variance stabilization are, e.g., the Box-Cox transform (Box and Cox, 1964) or the log transform. The log transform is a strongly non-linear transform and is”
High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019, methodology): “We use the GARCH implementation of [4].”
Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels (2018, methodology): “To exploit the benefits of both the noise-robustness provided by MAE and the implicit weighting scheme of CCE, we propose using the the negative Box-Cox transformation [4] as a loss function:”
Model-free model-fitting and predictive distributions (2010, methodology): “g(Yn+1) − Π(g, ĝn+1, Y n,Xn+1, F̂n) (7)”
Most Likely Transformations (2015, methodology): “Since the introduction of transformation models based on non-linear transformations of some response variable by Box and Cox (1964), this attractive class of models has received much interest. In regression problems, transformation models can be understood as models for the conditional distribution ”
Positively skewed data: revisiting the box-cox power transformation. (2010, methodology): “Box and Cox (1964) introduced a method for choosing the best transformation from a family of power transformations.”
Comparison of logistic regression and linear discriminant analysis (2004, methodology): “The Box-Cox type of transformation (Box and Cox, 1964) is used to make normal distribuion skewed.”
Non-linear regression models for Approximate Bayesian Computation (2008, background): “These transformations have the further potential advantage of stabilizing the variance of the response when performing regression (Box and Cox 1964).”
An extensive experimental survey of regression methods (2019, methodology): “As usual, the 100 output was pre-processed using the Box-Cox transformation [4] in order to 101 make it more similar to a symmetric uni-modal distribution, with the boxcox 102 function (MASS package) of the R statistical computing language [5].”
Absolute Income, Relative Income, Income Inequality, and Mortality (2004, methodology): “To nd the optimal functional relationship between income and the mortality rate, a Box-Cox analysis is carried out (Box and Cox 1964); that is, we estimate the optimal Box-Cox transformation parameter q as de ned by the operator: X(q)5 (Xq21) /q for q ¹ 0 or ln X for q 5 0, where X is income.”
Do not log‐transform count data (2010, background): “This can be done in an exploratory manner (e.g. Box & Cox 1964), but transformations often have sensible interpretations, e.g. the log-transfor- mation implies that the mechanisms are multiplicative on the *Correspondence author.”
Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, background): “We posit that data transformations [e.g., Box and Cox, 1964], or a more flexible likelihood function that is especially designed to handle nontraditional residual distributions [e.g., Schoups and Vrugt, 2010; Erdal et al., 2012] will further improve the modeling results.”
Robust rank correlation based screening (2010, methodology): “lies of models (Lin and Peng, 2010). For example, when H(·) is taken as the form of a power function and F is a normal distribution, model (1.2) reduces to the familiar Box-Cox transformation models (Box and Cox, 1964; Bickel and Doksum, 1981). 3 If H(Y) = Y, the model (1.2) reduces to the model (1.”