In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Ex Input:
Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as pseudorandom generators for halfspaces. In this work, we investigate the limits of these techniques by proving inapproximability results for the sign function. Firstly, the "polynomial regression" algorithm of Kalai et al. (SIAM J. Comput. 2008) shows that halfspaces can be learned with respect to log-concave distributions on Rn in the challenging agnostic learning model. The power of this algorithm relies on the fact that under log-concave distributions, halfspaces can be approximated arbitrarily well by low-degree polynomials. We ask whether this technique can be extended beyond log-concave distributions, and establish a negative result. We show that polynomials of any degree cannot approximate the sign function to within arbitrarily low error for a large class of non-log-concave distributions on the real line, including those with densities proportional to exp(|x|0.99). This impossibility result extends to multivariate distributions, and thus gives a strong limitation on the power of the polynomial regression algorithm for halfspaces. Secondly, we investigate the derandomization of Chernoff-type concentration inequalities. Chernoff-type tail bounds on sums of independent random variables have pervasive applications in theoretical computer science. Schmidt et al. (SIAM J. Discrete Math. 1995) showed that these inequalities can be established for sums of random variables with only O(log(1/))-wise independence, for a tail probability of . We show that their results are tight up to constant factors. These results rely on techniques from weighted approximation theory, which studies how well functions on the real line can be approximated by polynomials under various distributions. We believe that these techniques will have further applications in other areas of theoretical computer science. Harvard University, School of Engineering and Applied Sciences. Supported by an NDSEG Fellowship and NSF grant CNS-1237235. Harvard University, School of Engineering and Applied Sciences. Supported by NSF grant CCF-1116616 and the Lord Rutherford Memorial Research Fellowship.

Ex Output:
Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness

Ex Input:
An important use of machine learning is to learn what people value. What posts or photos should a user be shown? Which jobs or activities would a person find rewarding? In each case, observations of people's past choices can inform our inferences about their likes and preferences. If we assume that choices are approximately optimal according to some utility function, we can treat preference inference as Bayesian inverse planning. That is, given a prior on utility functions and some observed choices, we invert an optimal decision-making process to infer a posterior distribution on utility functions. However, people often deviate from approximate optimality. They have false beliefs, their planning is sub-optimal, and their choices may be temporally inconsistent due to hyperbolic discounting and other biases. We demonstrate how to incorporate these deviations into algorithms for preference inference by constructing generative models of planning for agents who are subject to false beliefs and time inconsistency. We explore the inferences these models make about preferences, beliefs, and biases. We present a behavioral experiment in which human subjects perform preference inference given the same observations of choices as our model. Results show that human subjects (like our model) explain choices in terms of systematic deviations from optimal behavior and suggest that they take such deviations into account when inferring preferences.

Ex Output:
Learning the Preferences of Ignorant, Inconsistent Agents

Ex Input:
As mobile devices have become indispensable in modern life, mobile security is becoming much more important. Traditional password or PIN-like point-of-entry security measures score low on usability and are vulnerable to brute force and other types of attacks. In order to improve mobile security, an adaptive neuro-fuzzy inference system(ANFIS)-based implicit authentication system is proposed in this paper to provide authentication in a continuous and transparent manner. To illustrate the applicability and capability of ANFIS in our implicit authentication system, experiments were conducted on behavioural data collected for up to 12 weeks from different Android users. The ability of the ANFIS-based system to detect an adversary is also tested with scenarios involving an attacker with varying levels of knowledge. The results demonstrate that ANFIS is a feasible and efficient approach for implicit authentication with an average of 95% user recognition rate. Moreover, the use of ANFIS-based system for implicit authentication significantly reduces manual tuning and configuration tasks due to its selflearning capability.

Ex Output:
Continuous Implicit Authentication for Mobile Devices based on Adaptive Neuro-Fuzzy Inference System