Related papers: Resolving the induction problem: Can we state with…
We show that Skilling's method of induction leads to a unique general theory of inductive inference, the method of Maximum relative Entropy (ME). The main tool for updating probabilities is the logarithmic relative entropy; other entropies…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on finite inference of recursive functions, since…
Specialized intelligent systems can be found everywhere: finger print, handwriting, speech, and face recognition, spam filtering, chess and other game programs, robots, et al. This decade the first presumably complete mathematical theory of…
Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One…
How to form priors that do not seem artificial or arbitrary is a central question in Bayesian statistics. The case of forming a prior on the truth of a proposition for which there is no evidence, and the definte evidence that the event can…
Correlated proportions arise in longitudinal (panel) studies. A typical example is the ``opinion swing'' problem: ``Has the proportion of people favoring a politician changed after his recent speech to the nation on TV?''. Since the same…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently,…
I review the works of G\"ardenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by…
In this thesis we start by providing some detail regarding how we arrived at our present understanding of probabilities and how we manipulate them - the product and addition rules by Cox. We also discuss the modern view of entropy and how…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…
Many Question-Answering (QA) datasets contain unanswerable questions, but their treatment in QA systems remains primitive. Our analysis of the Natural Questions (Kwiatkowski et al. 2019) dataset reveals that a substantial portion of…