uhhyunjoo
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2 years ago 3. Causation and Prediction : Axioms and Explications
Views about the nature of causation 은 나뉜다,
- causal influence 를 some sort of probablisitc relation 으로 분석하는 사람들
- causal influence 를 some sort of counterfactual relation 으로 분석하는 사람들
- 종종 a counterfactual relation 이 manipulations 나 interventions 에 대해 얘기하기도 한다.
- causation 에 대해 얘기하지 않는 것을 선호하는 사람들
이 챕터에서는, causal strcture 를 probability, counterfactuals, manipulations 와 연결하도록 가정하여 our usage 를 systematic 하게 만들 것이다.
3.1 Conditionsals
3.2 Causation
We understand causation to be a relation between particular events: something happens and causes something else to happen. Each cause is a particular event and each effect is a particular event. An event A can have more than one cause, none of which alone suffice to produce A. An event A can also be overdetermined: it can have more than one set of causes that suffice for A to occur.
우리는 인과관계가 특정한 사건들 사이의 관계라고 이해합니다: 어떤 일이 일어나고 다른 일이 일어나게 합니다. 각 원인은 특정 사건이고 각 효과는 특정 사건입니다. 사건 A에는 둘 이상의 원인이 있을 수 있으며, 그 중 어느 것도 A를 생성하기에 충분하지 않습니다. 이벤트 A는 또한 과도하게 결정될 수 있습니다. 이벤트 A가 발생하기에 충분한 두 개 이상의 원인 집합을 가질 수 있습니다.
- We assume that causation is transitive, irreflexive, and antisymmetric.
i) if A is a cause of B and B is a cause of C, then A is also a cause of C ii) an event A cannot cause itself iii) if A is a cause of B then B is not a cause of A.
The question of prediction has been equally unsettled—the question is:
if you know some causal relations, and you know some of the probability relations among some of the related variables, can you predict what will result if you intervene and alter the value of one or more of the variables.
So we have three problems:
first, the problem of clarifying the very idea of a causal system with sufficient precision for mathematical analysis and sufficient generality to capture a wide range of scientific practices;
second, the problem of understanding the possibilities and limitations for discovering such causal structures from various kinds of data;
and third, the problem of characterizing the probabilities predicted by a causal hypothesis given an intervention directly to force a value, or distribution of values, on one or more variables.
첫째, 수학적 분석을 위한 충분한 정밀도와 광범위한 과학적 관행을 포착하기에 충분한 일반성으로 인과 시스템의 아이디어를 명확히 하는 문제.
둘째, 다양한 종류의 데이터에서 그러한 인과 구조를 발견할 수 있는 가능성과 한계를 이해하는 문제.
셋째, 하나 이상의 변수에 값 또는 값의 분포를 강제하기 위한 개입이 주어졌을 때 인과 가설에 의해 예측된 확률을 특성화하는 문제.
This book attempts answers to all three of these questions.
We use a formalism—directed graphical models—that is not in the least original with us;
we claim some originality in explicitly stating the causal assumptions implicit in the causal interpretation of the graphs, and in extending the application of graphs to solving certain problems about manipulations.
The representation invokes two ideas about causation that are fundamental and ancient.
The first idea, which can be traced back at least to Bernoulli, is that the absence of causal relations is marked by independence in Introduction and Advertisement 3 Introduction and Advertisement 3 probability—in Bernoulli’s examples, if the outcome of one trial has no influence on the outcome of another trial, then the probability of both outcomes equals the product of each outcome separately.
The second idea, Bacon’s again, is that probability is associated with control: if variation of one feature, X, causes variation of another feature Y, then Y can be changed by an appropriate intervention that alters X. It turns out that the representation captures what is common to a wide variety of statistical models of causal relations—for example: regression models, logistic regression models, structural equation models, latent factor models, and many models of categorical data—and captures how these models may be used in prediction and control.
These axioms have implications for scientific discovery by experimental and nonexperimental means.
Our investigations require characterizing when two or alternative causal theories are, in various technical senses, indistinguishable by data, and characterizing when and which causal features are shared by all models indistinguishable from any particular model.
We evaluate the algorithms in terms of several different features.
(1) Are they computationally feasible on realistic problems?
(2) Are they reliable—do they in some sense converge to a description of features common to all models indistinguishable from the true model?
(3) Are they as informative as possible for the features of the data they use?
Our algorithmic results concern the discovery of causal structure in linear and nonlinear systems, systems with and without feedback, cases where there may, or may not, be unrecorded common causes of recorded variables, and cases in which membership in the observed sample is influenced by the variables under study.
The discovery of causal relations is only half of the story. The other half concerns the use in prediction of causal knowledge, even partial and incomplete causal knowledge.
인과관계 발견은 이야기의 절반에 불과하다. 나머지 절반은 인과적 지식, 심지어 부분적이고 불완전한 인과적 지식의 사용에 관한 것이다.
2.
This chapter introduces some mathematical concepts used throughout the book. The chapter is meant to provide mathematically explicit definitions (명확한 정의) of the formal apparatus (형식적 장치) we use.