Learning Talagrand DNF Formulas
نویسنده
چکیده
Consider the following version of Talagrand’s probabilistic construction of a monotone function f : {0, 1} n → {0, 1}. Let f be an n-term monotone DNF formula where each term is selected independently and uniformly at random (with replacement) from the set of all n log n) possible terms of length log(n) over the first log(n) variables. Let us call such a DNF formula a Talagrand DNF formula. This is a scaled-down version of the construction by Talagrand (1996) which is defined over all n variables and has subexponentially many terms. I am interested in the following problem:
منابع مشابه
Mansour's Conjecture is True for Random DNF Formulas
In 1994, Y. Mansour conjectured that for every DNF formula on n variables with t terms there exists a polynomial p with t non-zero coefficients such that Ex∈{0,1} [(p(x) − f(x))] ≤ ǫ. We make the first progress on this conjecture and show that it is true for randomly chosen DNF formulas and read-once DNF formulas. Our result yields the first polynomial-time query algorithm for agnostically lear...
متن کاملLearning DNF by Statistical and Proper Distance Queries Under the Uniform Distribution
We show that s-term DNF formulas can be learned under the uniform distribution in quasi-polynomial time with statistical queries of tolerance Ω(ε/s). The tolerance improves on the known tolerance Ω(ε/s) and is optimal with respect to its dependence on the error parameter ε. We further consider the related model of learning with proper distance queries and show that DNF formulas can be learned u...
متن کاملOn Learning Random DNF Formulas Under the Uniform Distribution
We study the average-case learnability of DNF formulas in the model of learning from uniformly distributed random examples. We define a natural model of random monotone DNF formulas and give an efficient algorithm which with high probability can learn, for any fixed constant γ > 0, a random t-term monotone DNF for any t = O(n2−γ). We also define a model of random non-monotone DNF and give an ef...
متن کاملA Query Algorithm for Agnostically Learning DNF?
Motivation: One of the most celebrated results in computational learning theory is Jackson’s query algorithm for PAC learning DNF formulas with respect to the uniform distribution [3]. A natural question is whether DNF formulas can be learned (even with queries and with respect to the uniform distribution) in a highly noisy setting, i.e., the wellknown agnostic framework of learning [5]. Additi...
متن کاملExtraction of Coverings as Monotone DNF Formulas
In this paper, we extend monotone monomials as large itemsets in association rule mining to monotone DNF formulas. First, we introduce not only the minimum support but also the maximum overlap, which is a new measure how much all pairs of two monomials in a monotone DNF formula commonly cover data. Next, we design the algorithm dnf cover to extract coverings as monotone DNF formulas satisfying ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010