"Despite the prevailing use of graphs as metaphors for communicating and reasoning about dependencies, the task of capturing informational dependencies by graphs is not at all trivial." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Network of Plausible, Inference", 1988)
"Probabilities are summaries of knowledge that is left behind when information is transferred to a higher level of abstraction." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Network of Plausible, Inference", 1988)
"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. […] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network."
"By a variable we will mean an attribute, measurement or inquiry
that may take on one of several possible outcomes, or values, from a specified
domain. If we have beliefs (i.e., probabilities) attached to the possible
values that a variable may attain, we will call that variable a random variable."
"Causality connotes law-like necessity, whereas probabilities
connote exceptionality, doubt, and lack of regularity."
"The ability of causal networks to predict the effects of
actions requires of course a stronger set of assumptions in the construction of
those networks, assumptions that rest on causal (not merely associational)
knowledge and that ensure the system would respond to interventions in
accordance with the principle of autonomy."
"The role of graphs in probabilistic and statistical modeling
is threefold: (1) to provide convenient means of expressing substantive
assumptions; (2) to facilitate economical representation of joint probability
functions; and (3) to facilitate efficient inferences from observations." (Judea
Pearl, "Causality: Models, Reasoning, and Inference", 2000)
"Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon." (Judea Pearl, "Causal inference in statistics: An overview", Statistics Surveys 3, 2009)
"Again, classical statistics only summarizes data, so it does not provide even a language for asking [a counterfactual] question. Causal inference provides a notation and, more importantly, offers a solution. As with predicting the effect of interventions [...], in many cases we can emulate human retrospective thinking with an algorithm that takes what we know about the observed world and produces an answer about the counterfactual world." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
"Deep learning has instead given us machines with truly impressive abilities but no intelligence. The difference is profound and lies in the absence of a model of reality." (Judea Pearl, "The Book of Why: The New Science of Cause and Effect", 2018)
"Just as they did thirty years ago, machine learning programs
(including those with deep neural networks) operate almost entirely in an
associational mode. They are driven by a stream of observations to which they
attempt to fit a function, in much the same way that a statistician tries to
fit a line to a collection of points. Deep neural networks have added many more
layers to the complexity of the fitted function, but raw data still drives the
fitting process. They continue to improve in accuracy as more data are fitted,
but they do not benefit from the 'super-evolutionary speedup'."
"Some scientists (e.g., econometricians) like to work with mathematical equations; others (e.g., hard-core statisticians) prefer a list of assumptions that ostensibly summarizes the structure of the diagram. Regardless of language, the model should depict, however qualitatively, the process that generates the data - in other words, the cause-effect forces that operate in the environment and shape the data generated." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
"The calculus of causation consists of two languages: causal diagrams, to express what we know, and a symbolic language, resembling algebra, to express what we want to know. The causal diagrams are simply dot-and-arrow pictures that summarize our existing scientific knowledge. The dots represent quantities of interest, called 'variables', and the arrows represent known or suspected causal relationships between those variables—namely, which variable 'listens' to which others." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
"The mental model is the arena where imagination takes place. It enables us to experiment with different scenarios by making local alterations to the model. […] To speak of causality, we must have a mental model of the real world. […] Our shared mental models bind us together into communities." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
"When the scientific question of interest involves retrospective thinking, we call on another type of expression unique to causal reasoning called a counterfactual. […] Counterfactuals are the building blocks of moral behavior as well as scientific thought. The ability to reflect on one’s past actions and envision alternative scenarios is the basis of free will and social responsibility. The algorithmization of counterfactuals invites thinking machines to benefit from this ability and participate in this (until now) uniquely human way of thinking about the world." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
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