0
votes
0answers
39 views

Event probability prediction from multiple observations

I am programming some fuzzy logic for an application I'm developing, and I'm not sure how to "combine" multiple fuzzy boolean observations into a guess. Each of my fuzzy boolean observations describes ...
1
vote
3answers
178 views

Boolean algebra probability not coming out right

Assuming A,B,C,D are mutually independent. $P[(A\cup\overline{B}\cup C)\cap(A\cup C \cup \overline{D})]$ I get $(P(A) + 1 - P(B) + P(C))(P(A) + P(C) + 1 - P(D))$ But when I plug in the numbers, I ...
1
vote
1answer
67 views

The fraction of k-juntas with low influences in all of the coordinates

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...
4
votes
1answer
199 views

A Boolean function with total influence 1 must be a dictatorship

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...
3
votes
2answers
75 views

Parity is the only function with maximal influences

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...