Research in NLP is often supported by experimental results, and improved reporting of such results can lead to better understanding and more reproducible science. In this paper we analyze three statistical estimators for expected validation performan
ce, a tool used for reporting performance (e.g., accuracy) as a function of computational budget (e.g., number of hyperparameter tuning experiments). Where previous work analyzing such estimators focused on the bias, we also examine the variance and mean squared error (MSE). In both synthetic and realistic scenarios, we evaluate three estimators and find the unbiased estimator has the highest variance, and the estimator with the smallest variance has the largest bias; the estimator with the smallest MSE strikes a balance between bias and variance, displaying a classic bias-variance tradeoff. We use expected validation performance to compare between different models, and analyze how frequently each estimator leads to drawing incorrect conclusions about which of two models performs best. We find that the two biased estimators lead to the fewest incorrect conclusions, which hints at the importance of minimizing variance and MSE.
We present in this paper the neutrosophic randomized variables,
which are a generalization of the classical random variables
obtained from the application of the neutrosophic logic (a new nonclassical
logic which was founded by the American philos
opher and
mathematical Florentin Smarandache, which he introduced as a
generalization of fuzzy logic especially the intuitionistic fuzzy logic )
on classical random variables.
We offer in this research study of the probability density
function of a continuous random variable. Where we have to
reached to results that show the oneness of the general shape of
this function when it is linear or quadratic, as we came up to
the general formula for this function for each of the above two
cases. It was clarified the necessary and sufficient conditions of
a linear and quadratic function to be, a continuous probability
density function.
