Experience matters 1 Experience matters : Information acquisition optimizes probability gain
Experience matters 1 Experience matters : Information acquisition optimizes probability gain
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发表时间：
2009
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通讯作者：
Jonathan D. Nelson
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作者：
Jonathan D. Nelson
决定获取或关注哪条信息是感知、分类、医疗诊断和科学推理的基础。四个统计理论的信息价值-信息增益，Kullback-Liebler距离，概率增益（误差最小化），和影响-是同样符合人类信息获取的现有数据（纳尔逊，2005年; 2008年）。三个实验，通过计算机优化设计，最大限度地提供信息，测试这些理论最好地描述人类的信息搜索。实验1采用自然抽样和经验学习来表达环境概率，发现概率增益比其他统计理论或确定性启发式概率更好地解释了参与者的信息搜索。实验1和2发现，参与者的行为不同时，标准的口头呈现的汇总统计方法被用来传达环境的概率。实验3发现，参与者对概率增益的偏好是稳健的，这表明其他模型对参与者的搜索行为贡献很小。经验很重要3许多情况需要仔细选择信息。适当的医学检查可以改善诊断和治疗。精心设计的实验有助于在相互竞争的科学理论之间做出选择。视觉感知还需要仔细选择眼球运动到视觉场景的信息部分。直觉上，有用的实验是那些看似合理的竞争理论做出最矛盾的预测的实验。贝叶斯最优实验设计（Bayesian Optimal Experimental Design，OED）框架提供了一个数学方案，用于计算哪个查询（实验、医学测试或眼球运动）最有用。在数学上，它是贝叶斯决策理论的一个特例（Savage，1954）。请注意，在这个框架中测试的不是单个理论，而是多个理论。一个实验的有用性取决于所考虑的假设的概率、这些假设所需要的明确（也许是概率性的）预测以及所使用的效用函数。在不同的查询花费不同的金额，不同类型的错误有不同的成本的情况下，这些约束应该被用来确定最好的查询，而不是信息价值的通用标准。然而，这篇文章涉及的情况下，信息收集是唯一的目标。具体来说，我们专注于目标是通过选择有用的功能来查看对象进行分类的情况。查询一个特征，以获得关于刺激属于特定类别的概率的信息，相当于OED框架中的“实验”，并且通常会改变人们对刺激属于几个类别中的每一个的概率的信念。例如，在男性留胡子的比例高于女性的环境中，了解到某个特定的人留胡子会增加他们是男性的可能性。不同的OED模型在如何计算特定特征的有用性方面有所不同。所有的模型Experience matters 4都使用贝叶斯定理来更新关于每个类别ci的概率的信念，当观察到特定的特征值f时：
Deciding which piece of information to acquire or attend to is fundamental to perception, categorization, medical diagnosis, and scientific inference. Four statistical theories of the value of information—information gain, Kullback-Liebler distance, probability gain (error minimization), and impact—are equally consistent with extant data on human information acquisition (Nelson, 2005; 2008). Three experiments, designed via computer optimization to be maximally informative, tested which of these theories best describes human information search. Experiment 1, which used natural sampling and experience-based learning to convey environmental probabilities, found that probability gain explained participants’ information search better than the other statistical theories or the probability of certainty heuristic. Experiments 1 and 2 found that participants behaved differently when the standard method of verbally-presented summary statistics was used to convey environmental probabilities. Experiment 3 found that participants’ preference for probability gain is robust, suggesting that other models contribute little to participants’ search behavior. Experience matters 3 Many situations require careful selection of information. Appropriate medical tests can improve diagnosis and treatment. Carefully designed experiments can facilitate choosing between competing scientific theories. Visual perception also requires careful selection of eye movements to informative parts of a visual scene. Intuitively, useful experiments are those for which plausible competing theories make the most contradictory predictions. A Bayesian optimal experimental design (OED) framework provides a mathematical scheme for calculating which query (experiment, medical test, or eye movement) is expected to be most useful. Mathematically, it is a special case of Bayesian decision theory (Savage, 1954). Note that a single theory is not tested in this framework, but rather multiple theories. The usefulness of an experiment is a function of the probabilities of the hypotheses under consideration, the explicit (and perhaps probabilistic) predictions that those hypotheses entail, and which utility function is being used. In situations where different queries cost different amounts, and different kinds of mistakes have different costs, those constraints should be used to determine the best queries to make, rather than general purpose criteria for the value of information. This article, however, deals with situations where information gathering is the only goal. Specifically, we focus on situations in which the goal is to categorize an object by selecting useful features to view. Querying a feature, to obtain information about the probability of a stimulus belonging to a particular category, corresponds to an “experiment” in the OED framework, and will generally change one’s belief about the probability the stimulus belongs to each of several categories. For instance, in environments where a higher proportion of men than women have beards, learning that a particular individual has a beard increases the probability that they are male. The various OED models differ in terms of how they calculate the usefulness of looking at particular features. All of the models Experience matters 4 use Bayes’s theorem to update beliefs about the probability of each category ci when a particular feature value f is observed: