Ridge Regression applied to the determination of Abalone age from physical measurements

Résumé du document

Abalone are marine gastropods, inhabiting warm shores around the world and used as food in various parts of Asia, Oceania, North & South America and Europe.

Extraits

[...] Similarly the F1 test score is 0.5356 Furthermore the residuals distribution plotted below are fairly symmetrical around zero. CONCLUSION The ridge regression present a quite straightforward way to significantly improve over the modelling accuracy obtained from linear regression while still being easy to implement and very fast to compute as long as the polynomial order remains low, and always much faster than making a bottom- up estimator from the underlying phenomenon analysis (when available) Here the regression is further harder to realise as the number of rings is discreet by nature whereas the other measurement are continuous, yet the ridge regression give satisfactory predictor in many case One last note is that the size of the training set seems to have little influence on the quality of the model as long as it is large enough few hundred data points) REFERENCE and BIBLIOGRAPHY George Mu, IMS Health; Yong Cai, IMS Health; Yi Han « Quantile Regression in Pharmaceutical Marketing Research » Paper 163-2013 in SAS Global Forum 2013 Kano, M., & Nakagawa, Y. [...]

[...] However it is also clear that the raw correlation coefficient between any of these variables and rings or age is lower. Yet the measurements exhibiting the highest raw correlation with age are Shell weight and height Establishing the Ridge Regression model: The target data is set to be “Age” (linearly correlated to the number of rings) and thus defined as Y The variable Age and Rings are removed from the potential independent variable set along with Sex (defined as a character and converted to set of 3 Boolean flags Male, Female or Immature) and also with the DeltaWeight variable (percentage used only for coherence control) Once the data set is prepared we run a 10 fold cross validation for our Ridge Model and we evaluate the Error for various values of the parameter alpha and also for the polynomial features. [...]

[...] F., Fisher, L., Jensen, M. C., & Roll, R. (1969). « The adjustment of stock prices to new information. » International economic review, 1-21. Smith, S. D. [...]

[...] We then compare how the ridge regression model built fit the remainder of the experimental data and compare it to the classic linear regression model built from the same training set of data point. Last, we compare the results provided by the ridge model to the results obtained from the same training set but built using Theil-Sen regression Exploratory Analysis of the Abalone dataset: All type of statistical analysis of data are highly dependent on the quality of the data input. [...]

[...] The simplicity comes from the potentially very large reduction of data array from N independent variables to 1 independent variable. The speed and efficiency comes from that the computational costs of calculating least squares is much lower than using exponential smoothing or stepwise modelling. Last the linear regression can often be applied to non-linear relation by using simple transform of the dependent or the independent variables However, the models obtained from simple linear regression are not robust: the regression coefficient obtained can vary quickly with changes of even only a few values in a large dataset. [...]