More than 200 years ago, Thomas Bayes came up with a brilliant idea that has helped shape the world today, called Bayes Theorem. This…
Prior Modeling
In Bayesian inference the prior model provides a valuable opportunity to incorporate domain expertise into our inferences. Unfortunately this opportunity often becomes a contentious issue in many fields, and this potential value is lost in the debate. In this case study I will discuss the challenges of building prior models that capture meaningful domain expertise and some practical strategies for ameliorating those challenges as much as possible.
Causality
Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence (AI) and systems from The Cognitive Science Society.
Useful Mental Model: Normal Distribution - Scott H Young
Some ideas are so powerful once you know them, you start to see them everywhere. Normal distributions are one of these ideas. Let's understand it!
The Periodic Table of Cognition
I’ve been studying the early history of electricity’s discovery as a map for our current discovery of artificial intelligence. The smartest people alive back then, including Isaac Newton, who may have been the smartest person who ever lived, had confident … Continue reading →
The Wisdom of Individuals: Exploring People's Knowledge About Everyday Events Using Iterated Learning
Abstract Determining the knowledge that guides human judgments is fundamental to understanding how people reason, make decisions, and form predictions. We use an experimental procedure called ‘‘iterated learning,’’ in which the responses that people give on one trial are used to generate the data they see on the next, to pinpoint the knowledge that informs people's predictions about everyday events (e.g., predicting the total box office gross of a movie from its current take). In particular, we use this method to discriminate between two models of human judgments: a simple Bayesian model ( Griffiths & Tenenbaum, 2006 ) and a recently proposed alternative model that assumes people store only a few instances of each type of event in memory (Min K ; Mozer, Pashler, & Homaei, 2008 ). Although testing these models using standard experimental procedures is difficult due to differences in the number of free parameters and the need to make assumptions about the knowledge of individual learners, we show that the two models make very different predictions about the outcome of iterated learning. The results of an experiment using this methodology provide a rich picture of how much people know about the distributions of everyday quantities, and they are inconsistent with the predictions of the Min K model. The results suggest that accurate predictions about everyday events reflect relatively sophisticated knowledge on the part of individuals.
The Past and Present of Computer-Augmented Hypothesis Generation
Don Swanson’s career started on a path familiar to many who read this blog.
AI That Evolves in the Wild | Edge.org
I’m interested not in domesticated AI—the stuff that people are trying to sell. I'm interested in wild AI—AI that evolves in the wild. I’m a naturalist, so that’s the interesting thing to me. Thirty-four years ago there was a meeting just like this in which Stanislaw Ulam said to everybody in the room—they’re all mathematicians—"What makes you so sure that mathematical logic corresponds to the way we think?" It’s a higher-level symptom. It’s not how the brain works. All those guys knew fully well that the brain was not fundamentally logical.
Terence Tao – Kepler, Newton, and the true nature of mathematical discovery
“And what those stories teach us about how AI will revolutionize math”
The Irrational Decision
How the computer revolution shaped our conception of rationality—and why human problems require solutions rooted in human intuition, morality, and judgment
A Bayesian Truth Serum for Subjective Data
Subjective judgments, an essential information source for science and policy, are problematic because there are no public criteria for assessing judgmental truthfulness. I present a scoring method for eliciting truthful subjective data in situations ...
Thinking—Fast, Slow, and Artificial: How AI is Reshaping Human Reasoning and the Rise of Cognitive Surrender
People increasingly consult generative artificial intelligence (AI) while reasoning. As AI becomes embedded in daily thought, what becomes of human judgment? We
Resource-rational belief revision can mitigate as well as amplify polarization
People's beliefs sometimes diverge after observing the same information, which has been interpreted as evidence of irrationality. This behaviour has been proposed to result from people's limited cognitive resources and motivated reasoning, but how belief revision differs across these explanations has not been formalized or compared to a rational norm. Further, while people may be biased relative to a normative ideal, they may still make optimal choices given their limited cognitive resources, or rationally balance the utility of holding accurate beliefs with the belief's intrinsic utility. Across two studies, we develop and test a unified computational account of belief polarization under these proposed mechanisms, showing that people's performance on a belief updating task best fits a limited-resource Bayesian model; external motivations may contribute to divergence (or convergence) by determining what pre-existing information people consider relevant to a situation, rather than by changing how people evaluate new information in isolation.
Mathematical methods and human thought in the age of AI
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the...
Thoughtful and relevant outside math. A partial summary: Gowers thinks it’s important to sustain a human mathematical culture, but is unconvinced by the Leiden Declaration’s attempt to do that by reaffirming human ownership of specific *discoveries*.
tachikoma
an interesting blog post by Timothy Gowers on the Leiden declaration (on AI and Math), on why he didn't sign. it gets to a subtler aspect of control over AI and our future.
