Private vs. common random bits in communication complexity
Information Processing Letters
Elements of information theory
Elements of information theory
Journal of Computer and System Sciences
Lower bounds for sampling algorithms for estimating the average
Information Processing Letters
Clustering in large graphs and matrices
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Sampling algorithms: lower bounds and applications
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Competitive recommendation systems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Testing that distributions are close
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Three Theorems Regarding Testing Graph Properties
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The complexity of massive data set computations
The complexity of massive data set computations
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
Fast monte-carlo algorithms for finding low-rank approximations
Journal of the ACM (JACM)
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Matrix approximation and projective clustering via volume sampling
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms
Random Structures & Algorithms
Bound for the L2 Norm of Random Matrix and Succinct Matrix Approximation
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Optimal sampling from sliding windows
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Teaching dimension and the complexity of active learning
COLT'07 Proceedings of the 20th annual conference on Learning theory
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal sampling from sliding windows
Journal of Computer and System Sciences
Sampling sub-problems of heterogeneous max-cut problems and approximation algorithms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Adaptive sampling and fast low-rank matrix approximation
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Space-efficient estimation of statistics over sub-sampled streams
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Activized learning: transforming passive to active with improved label complexity
The Journal of Machine Learning Research
| Hi-index | 0.00 |
We present a novel technique, based on the Jensen-Shannon divergence from information theory, to prove lower bounds on the query complexity of sampling algorithms that approximate functions over arbitrary domain and range. Unlike previous methods, our technique does not use a reduction from a decision promise problem. As a result, it gives stronger bounds for functions that possess a large set of inputs, each two of which exhibit a gap in the function value.We demonstrate the technique with new query complexity lower bounds for three fundamental problems: (1) the "election problem", for which we obtain a quadratic improvement over previous bounds, (2) low rank matrix approximation, for which we prove the first lower bounds, showing that the algorithms given for this problem are almost optimal, and (3) matrix reconstruction.In addition, we introduce a new method for proving lower bounds on the expected query complexity of functions, using the Kullback-Leibler divergence. We demonstrate its use by a simple query complexity lower bound for the mean.