Center for Analysis and Design of Intelligent Agents

SYMBOLS, MODELS, CAUSALITY: Causation, Probabilities & More

Experience-Based Learning

What It Is	Learning is the acquisition of knowledge for particular purposes. When this acquisition happens via interaction with an environment it is experience-based.
Why It Is Important	Any environment which cannot be fully known a-priori requires experimentation of some sort, in the form of interaction with the world. This is what we call experience.
The Real World	The physical world we live in, often referred to as the “real world”, is highly complex, and rarely if ever do we have perfect models of how it behaves when we interact with it, whether it is to experiment with how it works or simply achieve some goal like buying bread.
Limited Time & Resources	An important limitation on any agent's ability to model the real world is its enormous state space, which vastly outdoes any known agent's memory capacity, even for relatively simple environments. Even if the models were sufficiently detailed, pre-computing everything beforehand is prohibited due to memory. On top of that, even if memory would suffice for pre-computing everything and anything necessary to go about our tasks, we would have to retrieve the pre-computed data in time when it's needed - the larger the state space the more demands on retrieval times this puts.
Why Experience-Based Learning is Relevant	Under LTE (limited time and energy) in a plentiful task-environment it is impossible to know everything all at once, including causal relations. Therefore, most of the time an intelligent agent capable of some reasoning will be working with uncertain assumptions where nothing is certain, only some things are more probable than others.

Probability

What It Is	Probability is a concept that is relevant to a situation where information is missing, which means it is a concept relevant to knowledge. A common conceptualization of probability is that it is a measure of the likelihood that an event will occur REF. If it is not know whether event <m>X</m> will be (or has been) observed in situation <m>Y</m> or not, the probability of <m>X</m> is the percentage of time <m>X</m> would be observed if the same situation <m>Y</m> occurred an infinite number of times.
Why It Is Important in AI	Probability enters into our knowledge of anything for which the knowledge is incomplete. As in, everything that humans do every day in every real-world environment. With incomplete knowledge it is in principle impossible to know what may happen. However, if we have very good models for some limited (small, simple) phenomenon, we can expect our prediction of what may happen to be pretty good, or at least practically useful. This is especially true for knowledge acquired through the scientific method, in which empirical evidence and human reason is systematically brought to bear on the validity of the models.
How To Compute Probabilities	Most common method is Bayesian networks, which encode the concept of probability in which probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief REF. Which makes it useful for representing an (intelligent) agent's knowledge of some environment, task or phenomenon.
How It Works	<m>P(a	b)={P(b	a)~P(a)}/{P(b)}</m>
Judea Pearl	Most Fervent Advocate (and self-proclaimed inventor) of Bayesian Networks in AI REF.

Causation

What It Is	A Platonic model for the relationship between two or more variables, whereby changes in one always precede changes in the other.
In More Detail	A causal relationship between variables <m>A,B</m> can be defined as a relationship such that changes in <m>A</m> always lead to a change in <m>B</m> and where the timing relationship is such that the former happens always before the latter, <m>forall delim{lbrace} A, B delim{rbrace}:~~t(A)~<~t(B)</m>. Example: A light switch is designed specifically to cause the light to turn on and off. In a causal analysis based on abduction one may reason that, given that light switches don't tend to flip randomly, a light that was off but is now on may indicate that someone or something flipped the light switch. (The inverse - a light that was on but is now off - has a larger set of reasonable causes, in addition to someone turning it off, a power outage or bulb burnout.)
Why It Is Important in Science	Causation is the foundation of empirical science. Without knowledge about causal relations it is impossible to get anything systematically done.
Why It Is Important in AI	The main purpose of intelligence is to figure out how to get new stuff done, given limited time and energy (LTE), i.e. to get stuff done cheaply but well. To get stuff done means knowing how to produce effects. In this case reliable methods for getting stuff done are worth more to an intelligence than unreliable ones. A relationship that approximates a Platonic cause-effect is worth more than one that does not.
History	David Hume (1711-1776) is one of the most influential philosophers addressing the topic. From the Encyclopedia of Philosophy: “…advocate[s] … that there are no innate ideas and that all knowledge comes from experience, Hume is known for applying this standard rigorously to causation and necessity.” REF This makes Hume an empiricist.
More Recent History	Causation has been cast by the wayside in statistics for the past 120 years, saying instead that all we can claim about the relationship of any variables is that they correlate. Needless to say this has lead to significant confusion as to what science can and cannot say about causal relationships, such as whether mobile phones cause cancer. Equally badly, the statistical stance has infected some scientific fields to view causation as “unscientific”.
Spurious Correlation	Non-zero correlation due to complete coincidence.
Causation & Correlation	What is the relation between causation and correlation? There is no (non-spurious) correlation without causation. There is no causation without correlation. However, causation between two variables does necessitate one of them to be the cause of the other: They can have a shared (possibly hidden) common cause.

Causation & AI

Correlation Supports Prediction	Correlation is sufficient for simple prediction (if <m>A</m> and <m>B</m> correlate highly, then it does not matter if we see an <m>A</m> OR a <m>B</m>, we can predict that the other is likely on the scene).
Knowledge of Causation Supports Action	We may know that <m>A</m> and <m>B</m> correlate, but if we don't know whether <m>B</m> is a result of <m>A</m> or vice versa, and we want <m>B</m> to disappear, we don't know whether it will suffice to modify <m>A</m>. Example: The position of the light switch and the state of the light bulb correlate. Only by knowing that the light switch controls the bulb can we go directly to the switch if we want the light to turn on.
Causal Models Are Necessary To Guide Action	While correlation gives us indication of causation, the direction of the “causal arrow” is critically necessary for guiding action. Luckily, knowing which way the arrows point in any large set of correlated variables is usually not too hard to find out, by empirical experimentation.
Judea Pearl	Most Fervent Advocate of causality in AI, and the inventor of the Do Calculus. C.f. BAYESIANISM AND CAUSALITY, OR, WHY I AM ONLY A HALF-BAYESIAN.
State Of The Art	Recent work by Judea Pearl demonstrates clearly the fallaciousness of the statistical stance, and fixes some important gaps in our knowledge on this subject which hopefully will rectify the situation in the coming years. YouTube lecture by J. Pearl on causation.

Controlled Experiment

What is it?	A fairly recent research method, historically speaking, for testing hypotheses / theories
Why is it Important?	The most reliable way humanity has found to create reliable sharable knowledge.
Why is it Relevant Here?	Like individual learning, it involves dealing with new phenomena and figuring them out.
Are the Methods Identical?	Very similar. Science is a systematized, organized approach to what individuals do when they learn. This involves: - Exploring - Hypothesizing - Trying out - Recording results - Unifying and consolidating related information - Creating coherent stories about what has been found (theorizing)
Bottom line	The most powerful mechanism for generating reliable knowledge known to mankind has a lot in common with A(G)I.

Explanation & Explainability

What It Is	The ability (of anyone or anything) to explain, after the fact or before, why something happened the way it did, how it could have happened differently but didn't (in general and/or this time).
In AI	The ability of a controller to explain, after the fact or before, why it did something or intends to do it.
Explanation Depends On Causation	It is impossible to explain anything in any useful way without referring to general causal relations.
Why It Is Important	If a controller does something we don't want it to repeat - e.g. crash an airplane full of people (in simulation mode, hopefully!) - it needs to be able to explain why it did what it did. If it can't, it means it - and we - can never be sure of why it did what it did, whether it had any other choice, or under what conditions it might do it again.
Explanation Depends on Causation	No explanation is without reference to causes; discernible causal structure is a prerequisite for explainability.
Bottom Line for Human-Level AI	To grow and learn and self-inspect an AI must be able to sort out causal chains. If it can't it will not only be incapable of explaining to others why it is like it is, it will be incapable of explaining to itself why things are the way they are, and thus, it will be incapable of sorting out whether something it did is better for its own growth than something else. Explanation is the big black hole of ANNs: In principle ANNs are black boxes, and thus they are in principle unexplainable - whether to themselves or others. One way to address this is by encapsulating knowledge as hierarchical models that are built up over time, and can be de-constructed at any time (like AERA does).

Table of Contents

SYMBOLS, MODELS, CAUSALITY: Causation, Probabilities & More

Experience-Based Learning

Probability

Causation

Causation & AI

Controlled Experiment

Explanation & Explainability