Matthias G. Mayer

The linked paper introduces the key concept of factored spaced models / finite factored sets, structural independence, in a fully general setting using families of random elements. The key contribution is a general definition of the history object and a theorem that the history fully characterizes the semantic implications of...

I present the fundamental theorem for all finitely factored measurable spaces. The fundamental theorem is that two events are orthogonal if and only if they are independent in all product probability distributions. It tells us that the definition of orthogonality really captures the essence of structural independence by the following...

PDF This is a technical post researching infinite factor spaces In a factor space F=⨉i∈IFi, for a measurable Z:F→Z(F), a Z-measurable index function J:F→{0,1}I is generating X:F→X(F), if X depends only on those arguments (xi), where J(x)i is 1, and Z. In this post, we show that there is an...

PDF This is a technical post researching infinite factor spaces I define a general measurable factor space that shows that the history can't be straightforwardly generalized to the infinite case. The example shows the following: * Unlike in the finite setting, the condition ∀P∈▲∗(F):πJ⫫Pπ¯J | Z in the definition of...

I present my bachelor's thesis that reformulates Finite Factored Sets: Causality with Deterministic Relationships Abstract: We present a reformulation of Finite Factored Sets that uses functions and cartesian products instead of partitions and factorizations. In the new setting, we motivate assuming conditional orthogonality from observed conditional independence and show that...

This short post is about how to write something like ×i∈IVi and ×i∈IVi MathJax doesn't allow picture environments so we can't define a new command that draws a cross. The solution is simple: Enlarge the normal \times command. Paste this in a math environment at the top of the document:...

This post was written in the SERI MATS program under John Wentworth. In our quest to find steering mechanisms in computational systems, we first have to find the right framework to look at the internals of such a system. This framework should naturally express the systems we normally associate with...