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1-Ch9.1-HT-INTRO-S15
1-Ch9.1-HT-INTRO-S15

Rectangles Are Nonnegative Juntas - Computer Science
Rectangles Are Nonnegative Juntas - Computer Science

Logarithmic Concave Measures and Related Topics
Logarithmic Concave Measures and Related Topics

... and f , g are non-negative Borel-measurable functions which implies the Lebesguemeasurability of r. (This is proved in 20] for the case of m = 1 and the same proof can be used for m  2. The formulation of Theorem 1 in 20] has to be corrected in such a way that we assume f and g to be Borel-measu ...
Draft: Coherent Risk Measures
Draft: Coherent Risk Measures

Introductory lecture notes on Markov chains and random walks
Introductory lecture notes on Markov chains and random walks

Chapter 5 - Pearson Higher Education
Chapter 5 - Pearson Higher Education

... “For even the most stupid of men, by some instinct of nature, by himself and without any instruction, is convinced that the more observations have been made, the less danger there is of wandering from one’s goal.” In probability, an experiment is any process with uncertain results that can be repeat ...
Random walks and electric networks
Random walks and electric networks

1-Pass Relative-Error Lp-Sampling with Applications
1-Pass Relative-Error Lp-Sampling with Applications

Possibility Theory and its Applications: Where Do we Stand
Possibility Theory and its Applications: Where Do we Stand

Integrated Common Sense Learning and Planning in POMDPs
Integrated Common Sense Learning and Planning in POMDPs

... i.e., with knowledge of o(1) , . . . , o(i) and a(1) , . . . , a(i−1) . We refer to the agent’s strategy for choosing such actions as a policy. One normally also fixes some kind of a reward (or loss) function over the states S to quantify how “good” or “bad” an agent’s policy for acting in the envir ...
How to model mutually exclusive events based on independent
How to model mutually exclusive events based on independent

sets of recurrence of z -actions and properties of sets of
sets of recurrence of z -actions and properties of sets of

Benchmarking real-valued acts
Benchmarking real-valued acts

... Of course, one can apply the existing axiomatizations for preference representation to the benchmarking procedure simply by expanding the primitive state space to Ω. This is a natural move and, in a well-known discussion about small worlds, Savage (1954) recommends that the state space be taken as l ...
Intelligent Environments
Intelligent Environments

Why Simple Hash Functions Work: Exploiting the Entropy in a Data
Why Simple Hash Functions Work: Exploiting the Entropy in a Data

Counting Stars and Other Small Subgraphs in Sublinear Time
Counting Stars and Other Small Subgraphs in Sublinear Time

كw = r v(Y(t))dt
كw = r v(Y(t))dt

Probability Theory
Probability Theory

Prior vs Likelihood vs Posterior Posterior Predictive Distribution
Prior vs Likelihood vs Posterior Posterior Predictive Distribution

AAAI Proceedings Template
AAAI Proceedings Template

Reachability is harder for directed than for undirected finite graphs
Reachability is harder for directed than for undirected finite graphs

A sharp threshold in proof complexity yields lower bounds for
A sharp threshold in proof complexity yields lower bounds for

Disjoint Paths in Expander Graphs via Random Walks
Disjoint Paths in Expander Graphs via Random Walks

The start of a script for the course
The start of a script for the course

Stable Beliefs and Conditional Probability Spaces
Stable Beliefs and Conditional Probability Spaces

< 1 ... 11 12 13 14 15 16 17 18 19 ... 262 >

Inductive probability

Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world.There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Only inference establishes new facts from data.The basis of inference is Bayes' theorem. But this theorem is sometimes hard to apply and understand. The simpler method to understand inference is in terms of quantities of information.Information describing the world is written in a language. For example a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements.Occam's razor says the ""simplest theory, consistent with the data is most likely to be correct"". The ""simplest theory"" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct.
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