On associative algebras of minimal rank
Proceedings of the 2nd international conference, AAECC-2 on Applied algebra, algorithmics and error-correcting codes
Lectures on the complexity of bilinear problems
Lectures on the complexity of bilinear problems
A lower bound for matrix multiplication
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Lower bounds for the multiplicative complexity of matrix multiplication
Computational Complexity
Algebraic Complexity Theory
Better methods for solving parsimony and compatibility
RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Obtaining highly accurate topology estimates of evolutionary trees from very short sequences
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Efficient algorithms for inverting evolution
Journal of the ACM (JACM)
Lower bounds for matrix product, in bounded depth circuits with arbitrary gates
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the complexity of matrix product
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Combining polynomial running time and fast convergence for the disk-covering method
Journal of Computer and System Sciences - Computational biology 2002
A (5/2)n2-Lower Bound for the Multiplicative Complexity of n×n-Matrix Multiplication
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
On the complexity of the multiplication of matrices of small formats
Journal of Complexity
Learning nonsingular phylogenies and hidden Markov models
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Beyond the Alder-Strassen bound
Theoretical Computer Science - Automata, languages and programming
Hierarchical mixture models: a probabilistic analysis
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
ACM SIGACT News
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Geometric complexity theory and tensor rank
Proceedings of the forty-third annual ACM symposium on Theory of computing
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Evolution is often modeled as a stochastic process which modifies DNA. One of the most popular and successful such processes are the Cavender-Farris (CF) trees, which are represented as edge weighted trees. The Phylogeny Construction Problem is that of, given /spl kappa/ samples drawn from a CF tree, output a CF tree which is close to the original. Each CF tree naturally defines a random variable, and the gold standard for reconstructing such trees is the maximum likelihood estimator of this variable. This approach is notoriously computationally expensive. We show that a very simple algorithm, which is a variant on one of the most popular algorithms used by practitioners, converges on the true tree at a rate which differs from the optimum by a constant. We do this by analyzing upper and lower bounds for the convergence rate of learning very simple CF trees, and then show that the learnability of each CF tree is sandwiched between two such simpler trees. Our results rely on the fact that, if the right metric is used, the likelihood space of CF trees is smooth.