The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Dynamic multidimensional histograms
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A spectral algorithm for learning mixture models
Journal of Computer and System Sciences - Special issue on FOCS 2002
On Learning Mixtures of Heavy-Tailed Distributions
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Streaming and sublinear approximation of entropy and information distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The space complexity of pass-efficient algorithms for clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
The spectral method for general mixture models
COLT'05 Proceedings of the 18th annual conference on Learning Theory
| Hi-index | 5.24 |
We present a multiple pass streaming algorithm for learning the density function of a mixture of k uniform distributions over rectangles in R^d, for any d0. Our learning model is: samples drawn according to the mixture are placed in arbitrary order in a data stream that may only be accessed sequentially by an algorithm with a very limited random access memory space. Our algorithm makes 2@?+2 passes, for any @?0, and requires memory at most O@?(@e^-^2^/^@?k^2d^4+(4k)^d), where @e is the tolerable error of the algorithm. This exhibits a strong memory-pass tradeoff in terms of @e: a few more passes significantly lower its memory requirements, thus trading one of the two most important resources in streaming computation for the other. Chang and Kannan first considered this problem for d=1,2. Our learning algorithm is especially appropriate for situations where massive data sets of samples are available, but computation with such large inputs requires very restricted models of computation.