Center for Analysis and Design of Intelligent Agents

T-720-ATAI-2018

Lecture Notes, W11: Probabilities, Causation & Experience-Based Learning

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.

Probability

What It Is	Probability is the measure of the likelihood that an event will occur REF.
Why It Is Important	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 phenomenon, we can expect our prediction of what may happen to be pretty good. 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 Do It	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 ideal for representing an (intelligent) agent's knowledge of some environment, task or phenomenon lecture_notes_experience-based_learning.
How It Works	<m>P(a	b)={P(b	a)P(a)}/{P(b)}</m>
Judea Pearl	Most Fervent Advocate of Bayesian Networks in AI REF.

Causation

What It Is	A causal variable can (informally) be defined as a variable whose relationship with another variable is such that when changed it will change the other variable. 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	Causation is the foundation of empirical science. Without knowledge about causal relations it is impossible to get anything done.
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”. c.f. BAYESIANISM AND CAUSALITY, OR, WHY I AM ONLY A HALF-BAYESIAN by J. Pearl
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.
Correlation Supports Prediction	While correlation is sufficient for prediction (if A and B correlate highly, then it does not matter if we see an A OR a B, we can predict that the other is likely on the scent.
Causation Supports Action	We may know that A and B correlate, but if we want B to disappear we don't know whether to do that by modifying A or B, because we don't know if B is a result of A or vice versa. Example: The position of the light switch and the state of the lightbulb 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.
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.

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Table of Contents

T-720-ATAI-2018

Lecture Notes, W11: Probabilities, Causation & Experience-Based Learning

Experience-Based Learning

Probability

Causation