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But it's often more helpful to think of softmax the first way: exponentiating its inputs and then normalizing them. The exponentiation means that one more unit of evidence increases the weight given to any hypothesis multiplicatively.

from sklearn.base import TransformerMixin class DataFrameImputer(TransformerMixin): def fit(self, X, y=None): self.fill = pd.Series([X[c].value_counts().index[0] if X[c].dtype == np.dtype('O') else X[c].median() for c in X], index=X.columns) return self def transform(self, X, y=None): return X.fillna(self.fill)

A 95% confidence interval does not mean that for a given realised interval calculated from sample data there is a 95% probability the population parameter lies within the interval, nor that there is a 95% probability that the interval covers the population parameter.^{[11]} Once an experiment is done and an interval calculated, this interval either covers the parameter value or it does not, it is no longer a matter of probability. The 95% probability relates to the reliability of the estimation procedure, not to a specific calculated interval.^{[12]} Neyman himself (the original proponent of confidence intervals) made this point in his original paper:^{[3]}

If repeated samples were taken and the 95% confidence interval computed for each sample, 95% of the intervals would contain the population mean. Naturally, 5% of the intervals would not contain the population mean.
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