一般来说,满足泊松分布的结果抽取叫泊松抽样(poisson sampling);同理有二项抽样(binomial sampling)。 针对以上两种分布或者说针对指数家族(exponential family)分布的函数,我们都可以根据实际数据获得log-似然函数(log-likelihood)然后去通过MLE获得其解析解或者数值解用于做参数估计和推断(inference)。不过这都是后话,是...
As well as exploring its theoretical properties, we introduce sampling methods for this distribution that are amenable to the reparameterization trick, and evaluate their performance. Lastly, we demonstrate that the continuous categorical outperforms standard choices empirically, across a simulation study, ...
Related work on prediction shift与预测偏移相关的工作 The shift of gradient conditional distribution g t (xk, yk) | xk was previously mentioned in papers on boosting [3, 13] but was not formally defined. Moreover, even the existence of non-zero shift was not proved theoretically. Based on ...
is based on the assumption that the conditional probability distribution of the next categorical value depends on the immediate preceding pattern [14,21,27,37,38]. For instance, given a sequenceS=s1s2…snof lengthncomposed of categorical values from the setΣand a set of sequences ...
The shift of gradient conditional distribution g t (xk, yk) | xk was previously mentioned in papers on boosting [3, 13] but was not formally defined. Moreover, even the existence of non-zero shift was not proved theoretically. Based on the out-of-bag estimation [2], Breiman proposed it...
The shift of gradient conditional distribution g t (xk, yk) | xk was previously mentioned in papers on boosting [3, 13] but was not formally defined. Moreover, even the existence of non-zero shift was not proved theoretically. Based on the out-of-bag estimation [2], Breiman proposed it...
1.6.3 The Poisson distribution 7 1.6.4 The normal distribution 7 1.6.5 The chisquared (X2) distribution 8 1.7 *The likelihood 9 2 Estimation and inference for categorical data 11 2.1 Goodness of fit 11 2.1.1 Pearson’s X2 goodness-of-fit statistic 11 2.1.2 * The link between X2 and...
Examples of differential exponential maps in the Cartesian differential category of real smooth functions include the exponential function, the complex exponential function, the split complex exponential function, and the dual numbers exponential function. As another source of interesting examples, we also ...
If ϑP,Q is a isomorphism for every pair of objects P, Q, then we say that F is cartesian-closed, or that F preserves exponentials. Note that the inverse image functor of a locally connected geometric morphism is always cartesian closed, by [25, Proposition C3.3.1], so that in ...
GLMs can be used to fit fixed effects models to certain types of non-normal data: those with a distribution from the exponential family. The chapter defines the Bernoulli, binomial and Poisson distributions. These distributions can all be described as 'one-parameter' distributions, that is using...