**Sliced Inverse Regression (SIR)**

Sliced inverse regression (SIR) is a tool for dimension reduction in the field of multivariate statistics. In statistics, regression analysis is a popular way of studying the relationship between a response variable y and its explanatory variable x _ {\displaystyle {\underline {x}}} {\underline {x}}, which is a p-dimensional vector. There are several approaches which come under the term of regression. For example parametric methods include multiple linear regression; non-parametric techniques include local smoothing. With high-dimensional data (as p grows), the number of observations needed to use local smoothing methods escalates exponentially. Reducing the number of dimensions makes the operation computable. Dimension reduction aims to show only the most important directions of the data. SIR uses the inverse regression curve, E ( x _ | y ) {\displaystyle E({\underline {x}}\,|\,y)} E({\underline {x}}\,|\,y) to perform a weighted principal component analysis, with which one identifies the effective dimension reducing directions.

Sliced Inverse Regression for Dimension Reduction … **Statistical Recurrent Unit (SRU)**

Sophisticated gated recurrent neural network architectures like LSTMs and GRUs have been shown to be highly effective in a myriad of applications. We develop an un-gated unit, the statistical recurrent unit (SRU), that is able to learn long term dependencies in data by only keeping moving averages of statistics. The SRU’s architecture is simple, un-gated, and contains a comparable number of parameters to LSTMs; yet, SRUs perform favorably to more sophisticated LSTM and GRU alternatives, often outperforming one or both in various tasks. We show the efficacy of SRUs as compared to LSTMs and GRUs in an unbiased manner by optimizing respective architectures’ hyperparameters in a Bayesian optimization scheme for both synthetic and real-world tasks. … **Zero/One Inflated Beta Regression (ZOIB)**

A general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters.

➚ “Beta Regression” …

# If you did not already know

**13**
*Monday*
Nov 2017

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