Inference与predicting的区别

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Inference与predicting的区别

文献阅读：The GPML Toolbox version 4.2

文献原文：

Likelihood functionality is needed both during inference and while predicting.

1. 英文词义

Inference n. 推理；推论；推断
Predicting n.预测

2. 在问题 What is the difference between prediction and inference? 中获赞最高的答案对这两个词的解释

回答1：

Inference: Given a set of data you want to infer how the output is generated as a function of the data.
Prediction: Given a new measurement, you want to use an existing data set to build a model that reliably chooses the correct identifier from a set of outcomes.

回答2：

同时给出了更直白的解释
Inference: You want to find out what the effect of Age, Passenger Class and, Gender has on surviving the Titanic Disaster. You can put up a logistic regression and infer the effect each passenger characteristic has on survival rates.
Prediction: Given some information on a Titanic passenger, you want to choose from the set {lives,dies} and be correct as often as possible.

Prediction doesn’t revolve around establishing the most accurate relation between the input and the output , accurate prediction cares about putting new observations into the right class as often as possible.

So the “practical example” crudely boils down to the following difference: Given a set of passenger data for a single passenger the inference approach gives you a probability of surviving, the classifier gives you a choice between lives or dies.

Tuning classifiers is a very interesting and crucial topic in the same way that correctly interpreting p-values and confidence intervals is.

回答3：

…Whereas prediction is about predicting outcomes, inference is about understanding the relationship of the inputs to the outcome: which input has such a relationship, and how can we distinguish a “true” relationship from random covariation

回答4：

Generally when doing data analysis we imagine that there is some kind of “data generating process” which gives rise to the data, and inference refers to learning about the structure of this process while prediction means being able to actually forecast the data that come from it. Oftentimes the two go together, but not always.

An example where the two go hand in hand would be the simple linear regression model
Y i = β 0 x i 0 + β 1 x i 1 + ϵ Y_i = \beta_0 x_{i0}+\beta_1 x_{i1} +\epsilon Yi​=β0​xi0​+β1​xi1​+ϵ

Inference in this case would mean estimating the parameters of the model β 0 , β 1 \beta_0 , \beta_1 β0​,β1​ and the predictions would just be computed from the estimates of these parameters. But there are other types of models where one is able to make sensible predictions, but the model doesn’t necessarily lead to meaningful insights about what is happening behind the scenes.

Some examples of these kinds of models would be complicated ensemble methods which can lead to good predictions but are sometimes difficult or impossible to understand.
(这里说有些模型可能其预测效果很好，但是模型内部的的可解释性就不那么强。或者其模型内部的参数没有实际物理意义。)

回答5：

Here’s the paragraph from the book: An Introduction to Statistical Learning. In page 20 of the book, the authors provide a beautiful example which made me understand the difference.

For example, in a real estate setting, one may seek to relate values of homes to inputs such as crime rate, zoning, distance from a river, air quality, schools, income level of community, size of houses, and so forth. In this case one might be interested in how the individual input variables affect the prices–that is ,how much extra will a house be worth if it has a view of the river? This is a inference problem. Alternatively, one may simply be interested in predicting the value of a home given its characteristics: is this house under- or over-valued? This is a prediction problem

3. 总结

综合上面的解释，
Inference 是探索过程的本质，以及造成这样输出的原因，对于一个系统来说，也就是要学习、估计系统的参数。
Prediction 更为纯粹，在prediction时，不考虑系统内部的因果关系，只针对当前输入进行预测。

本文标签： 区别Inferencepredicting