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Bounded Independence Fools Halfspaces
 In Proc. 50th Annual Symposium on Foundations of Computer Science (FOCS), 2009
"... We show that any distribution on {−1, +1} n that is kwise independent fools any halfspace (a.k.a. linear threshold function) h: {−1, +1} n → {−1, +1}, i.e., any function of the form h(x) = sign ( ∑n i=1 wixi − θ) where the w1,..., wn, θ are arbitrary real numbers, with error ɛ for k = O(ɛ−2 log 2 ..."
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Cited by 43 (17 self)
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We show that any distribution on {−1, +1} n that is kwise independent fools any halfspace (a.k.a. linear threshold function) h: {−1, +1} n → {−1, +1}, i.e., any function of the form h(x) = sign ( ∑n i=1 wixi − θ) where the w1,..., wn, θ are arbitrary real numbers, with error ɛ for k = O(ɛ−2 log 2
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
The strength of weak learnability
 Machine Learning
, 1990
"... Abstract. This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with h ..."
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Cited by 861 (24 self)
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well. In addition, the construction has some interesting theoretical consequences, including a set of general upper bounds on the complexity of any strong learning algorithm as a function of the allowed error e.
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Dynamic taint analysis for automatic detection, analysis, and signature generation of exploits on commodity software
 In Network and Distributed Systems Security Symposium
, 2005
"... Software vulnerabilities have had a devastating effect on the Internet. Worms such as CodeRed and Slammer can compromise hundreds of thousands of hosts within hours or even minutes, and cause millions of dollars of damage [32, 51]. To successfully combat these fast automatic Internet attacks, we nee ..."
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Cited by 634 (30 self)
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Software vulnerabilities have had a devastating effect on the Internet. Worms such as CodeRed and Slammer can compromise hundreds of thousands of hosts within hours or even minutes, and cause millions of dollars of damage [32, 51]. To successfully combat these fast automatic Internet attacks, we need fast automatic attack detection and filtering mechanisms. In this paper we propose dynamic taint analysis for automatic detection and analysis of overwrite attacks, which include most types of exploits. This approach does not need source code or special compilation for the monitored program, and hence works on commodity software. To demonstrate this idea, we have implemented TaintCheck, a mechanism that can perform dynamic taint analysis by performing binary rewriting at run time. We show that TaintCheck reliably detects most types of exploits. We found that TaintCheck produced no false positives for any of the many different programs that we tested. Further, we show how we can use a twotiered approach to build a hybrid exploit detector that enjoys the same accuracy as TaintCheck but have extremely low performance overhead. Finally, we propose a new type of automatic signature generation—semanticanalysis based signature generation. We show that by backtracing the chain of tainted data structure rooted at the detection point, TaintCheck can automatically identify which original flow and which part of the original flow have caused the attack and identify important invariants of the payload that can be used as signatures. Semanticanalysis based signature generation can be more accurate, resilient against polymorphic worms, and robust to attacks exploiting polymorphism than the patternextraction based signature generation methods.
Comparison of parametric representations for monosyllabic word recognition in continuously spoken sentences
 ACOUSTICS, SPEECH AND SIGNAL PROCESSING, IEEE TRANSACTIONS ON
, 1980
"... Several parametric representations of the acoustic signal were compared as to word recognition performance in a syllableoriented continuous speech recognition system. The vocabulary included many phonetically similar monosyllabic words, therefore the emphasis was on ability to retain phonetically ..."
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Cited by 1089 (2 self)
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Several parametric representations of the acoustic signal were compared as to word recognition performance in a syllableoriented continuous speech recognition system. The vocabulary included many phonetically similar monosyllabic words, therefore the emphasis was on ability to retain phonetically significant acoustic information in the face of syntactic and duration variations. For each ~ arameter set (based on a melfrequency cepstrum, a linear frequency cepstrum, a linear prediction cepstrum, a linear prediction spectrum, or a set of reflection coefficients), word templates were generated using an efficient dynamic method, and test data were time registered wi th the templates. A set of ten melfrequency cepstrum coefficients computed every 6 " 4 ms resulted in the best performance, namely 96.. 5 % and 9500 % recognition with each of two speakers.. The superior performance of the melfrequency cepstrum coefficients may be attributed to the fact that they better represent the perceptually relevant aspects of the shortterm speech spectrum.
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique and maximum stable set problems in perfect graphs, the maximum k partite subgraph problem in graphs, and va...
Automatic Discovery of Linear Restraints Among Variables of a Program
, 1978
"... The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs. ..."
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Cited by 733 (47 self)
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The model of abstract interpretation of programs developed by Cousot and Cousot [2nd ISOP, 1976], Cousot and Cousot [POPL 1977] and Cousot [PhD thesis 1978] is applied to the static determination of linear equality or inequality invariant relations among numerical variables of programs.
Agile ApplicationAware Adaptation for Mobility
 SOSP16
, 1997
"... In this paper we show that applicationaware adaptation, a collaborative partnership between the operating system and applications, offers the most general and effective approach to mobile information access. We describe the design of Odyssey, a prototype implementing this approach, and show how it ..."
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Cited by 503 (31 self)
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In this paper we show that applicationaware adaptation, a collaborative partnership between the operating system and applications, offers the most general and effective approach to mobile information access. We describe the design of Odyssey, a prototype implementing this approach, and show how it supports concurrent execution of diverse mobile applications. We identify agility as a key attribute of adaptive systems, and describe how to quantify and measure it. We present the results of our evaluation of Odyssey, indicating performance improvements up to a factor of 5 on a benchmark of three applications concurrently using remote services over a network with highly variable bandwidth.
Results 1  10
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