Noise-Tolerant Learning, the Parity Problem, and the Statistical Query Model

We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first O(log n log log n) bits of input. This is the first known instance of an efficient noise-tolerant algorithm for a concept class that is provably not learnable in the Statistical Query model of Kearns. Thus, we demonstrate that the set of problems learnable in the statistical query model is a strict subset of those problems learnable in the presence of noise in the PAC model. In coding-theory terms, what we give is a poly(n)-time algorithm for decoding linear k by n codes in the presence of random noise for the case of k = c log n loglog n for some c > 0. (The case of k = O(log n) is trivial since one can just individually check each of the 2^k possible messages and choose the one that yields the closest codeword.) A natural extension of the statistical query model is to allow queries about statistical properties that involve t-tuples of examples (as opposed to single examples). The second result of this paper is to show that any class of functions learnable (strongly or weakly) with t-wise queries for t = O(log n) is also weakly learnable with standard unary queries. Hence this natural extension to the statistical query model does not increase the set of weakly learnable functions

Neighborkeepers: Buddies for Better HealthAn Intervention to Improve Physical Activity Habits

Introduction: associated health complications have increased steadily across the United States. As a result, physical activity considerations have become a more significant focus of healthcare providers and government agencies. Recent studies suggest that social support network approaches, such as the buddy-system, improve participant adherence to physical activity regimens. To improve physical activity frequency and adherence, we implemented a buddy system approach with participants involved in a community outreach organization.https://scholarworks.uvm.edu/comphp_gallery/1014/thumbnail.jp

Standard CMOS Fabrication of a Sensitive Fully Depleted Electrolyte-Insulator-Semiconductor Field Effect Transistor for Biosensor Applications

Microfabricated semiconductor devices are becoming increasingly relevant for detection of biological and chemical components. The integration of active biological materials together with sensitive transducers offers the possibility of generating highly sensitive, specific, selective and reliable biosensors. This paper presents the fabrication of a sensitive, fully depleted (FD), electrolyte-insulator-semiconductor field-effect transistor (EISFET) made with a silicon-on-insulator (SOI) wafer of a thin 10-30 nm active SOI layer. Initial results are presented for device operation in solutions and for bio-sensing. Here we report the first step towards a high volume manufacturing of a CMOS-based biosensor that will enable various types of applications including medical and environmental sensing

Software Reliability via Run-Time Result-Checking

We review the eld of result-checking, discussing simple checkers and self-correctors. We argue that such checkers could protably be incorporated in software as an aid to ecient debug-ging and enhanced reliability. We consider how to modify traditional checking methodologies to make them more appropriate for use in real-time, real-number computer systems. In particular, we suggest that checkers should be allowed to use stored randomness: i.e., that they should be allowed to generate, preprocess, and store random bits prior to run-time, and then to use this information repeatedly in a series of run-time checks. In a case study of checking a gen-eral real-number linear transformation (for example, a Fourier Transform), we present a simple checker which uses stored randomness, and a self-corrector which is particularly ecient if store

Reconstructing Randomly Sampled Multivariate Polynomials From Highly Noisy Data

Sudan and others have considered the problem of reconstructing a bounded-degree polynomial f : F k ! F from n data-points, only t of which are guaranteed to be consistent with f . For t n=2, the solution may not be unique; but it may be possible to find a small set of candidates for f . Here we extend this work, proving results including the following: Pick ~x (1) ; : : : ; ~x (n) 2 u F k . Generate data-points (~x (1) ; f(~x (1) )); : : : ; (~x (n) ; f(~x (n) )), and allow an adversary to corrupt any n \Gamma t of them. We require t to be greater than a bound on the order of n k k+1 ; we also require a lower-bound on jF j. Then, with high probability, we may reconstruct from the corrupted data a small set of candidates for f . Our results improve on past research in several respects. First, our bound on t is lower. Second, we allow for weaker restrictions on the distribution of ~x (1) ; : : : ; ~x (n) : in particular, as in the previous paragraph, we allow fo..

Decoding algebraic geometric codes

The past few years have witnessed exciting discoveries in different areas of coding theory and computational number theory. The present monograph, which exhibits the author's "Habilitationsschrift," is a collection of five different topics dealing with these two important fields. We will start with a purely coding theoretic question and finish with a discussion of some problems from computational number theory. Along the way, we will gradually change our focus from coding theory to number theory. Our emphasis is almost entirely on the development of fast and practical algorithms for the problems involved. In many cases it turns out that having a view for both number theory and coding theory is a clear advantage. This is best demonstrated by Chapters 2 and 3, where we encounter most of the interrelations between coding and number theor

List decoding of algebraic geometric codes

We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed- Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields. For the latter problem we design a polynomial-time algorithm and show that the resulting overall list-decoding algorithm runs in polynomial time under some mild conditions. Several examples are include

Decoding Algebraic-Geometric Codes Beyond the Error-Correction Bound

Generalizing the high-noise decoding methods of [1, 19] to the class of algebraic-geometric codes, we design the first polynomialtime algorithms to decode algebraic-geometric codes significantly beyond the conventional error-correction bound. Applying our results to codes obtained from curves with many rational points, we construct arbitrarily long, constant-rate linear codes over a fixed field F q such that a codeword is efficiently, non-uniquely reconstructible after a majority of its letters have been arbitrarily corrupted. We also construct codes such that a codeword is uniquely and efficiently reconstructible after a majority of its letters have been corrupted by noise which is random in a specified sense. We summarize our results in terms of bounds on asymptotic parameters, giving a new characterization of decoding beyond the error-correction bound. 1 Introduction Error-correcting codes, originally designed to accommodate reliable transmission of information through unreliable ..