Bounds on the sum of L1 influences
نویسندگان
چکیده
Let f : {−1, 1}n → [−1, 1] have degree d as a multilinear polynomial. It is well-known that the total influence of f is at most d. Aaronson and Ambainis asked whether the total L1 influence of f can also be bounded as a function of d. Bačkurs and Bavarian answered this question in the affirmative, providing a bound of O(d) for general functions and O(d) for homogeneous functions. We improve on their results by providing a bound of d for general functions and O(d log d) for homogeneous functions.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1404.3396 شماره
صفحات -
تاریخ انتشار 2014