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Electronic Colloquium on Computational Complexity

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Reports tagged with Linear Threshold Functions:
TR01-098 | 19th November 2001
Ke Yang

On Learning Correlated Boolean Functions Using Statistical Query

In this paper, we study the problem of using statistical
query (SQ) to learn highly correlated boolean functions, namely, a
class of functions where any
pair agree on significantly more than a fraction 1/2 of the inputs.
We give a limit on how well ... more >>>

TR07-128 | 10th November 2007
Kevin Matulef, Ryan O'Donnell, Ronitt Rubinfeld, Rocco Servedio

Testing Halfspaces

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x)=sgn(w ⋅ x - θ). We consider halfspaces over the continuous domain R^n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube {-1,1}^n ... more >>>

TR13-096 | 25th June 2013
Dana Ron, Rocco Servedio

Exponentially improved algorithms and lower bounds for testing signed majorities

A signed majority function is a linear threshold function $f : \{+1,1\}^n \to \{+1,1\}$ of the form
$f(x)={\rm sign}(\sum_{i=1}^n \sigma_i x_i)$ where each $\sigma_i \in \{+1,-1\}.$ Signed majority functions are a highly symmetrical subclass of the class of all linear threshold functions, which are functions of the form ${\rm ... more >>>

TR22-068 | 5th May 2022
Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, Madhu Sudan, Santhoshini Velusamy

Sketching Approximability of (Weak) Monarchy Predicates

Revisions: 1

We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In particular, we explore the approximability of monarchy-like functions where the value of the function is determined by a weighted combination of the vote of the first ... more >>>

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