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Learning and Verifying Graphs using Queries with a Focus on Edge Counting
"... Abstract. We consider the problem of learning and verifying hidden graphs and their properties given query access to the graphs. We analyze various queries (edge detection, edge counting, shortest path), but we focus mainly on edge counting queries. We give an algorithm for learning graph partitions ..."
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Cited by 9 (4 self)
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Abstract. We consider the problem of learning and verifying hidden graphs and their properties given query access to the graphs. We analyze various queries (edge detection, edge counting, shortest path), but we focus mainly on edge counting queries. We give an algorithm for learning graph partitions using O(n log n) edge counting queries. We introduce a problem that has not been considered: verifying graphs with edge counting queries, and give a randomized algorithm with error ǫ for graph verification using O(log(1/ǫ)) edge counting queries. We examine the current state of the art and add some original results for edge detection and shortest path queries to give a more complete picture of the relative power of these queries to learn various graph classes. Finally, we relate our work to Freivalds ’ ‘fingerprinting technique ’ – a probabilistic method for verifying that two matrices are equal by multiplying them by random vectors. 1
Phylogenies without branch bounds: Contracting the short, pruning the deep
, 2009
"... We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is guaranteed to contain all edges that are: 1) sufficiently lo ..."
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Cited by 9 (2 self)
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We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is guaranteed to contain all edges that are: 1) sufficiently long and 2) sufficiently close to the leaves. How much of the true tree is recovered depends on the sequence length provided. The algorithm is distancebased and runs in polynomial time. 1
Network delay inference from additive metrics, Preprint. Available at Arxiv: math.PR/0604367
, 2006
"... We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicastbased delay inference, that is, the problem of reconstructing delay characteristics of a network from endtoend delay measurements on ..."
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Cited by 9 (1 self)
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We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicastbased delay inference, that is, the problem of reconstructing delay characteristics of a network from endtoend delay measurements on network paths. Our inference algorithm is based on additive metric techniques used in phylogenetics. It runs in polynomial time and requires a sample of size only poly(log n). We also show how to recover the topology of the routing tree. 1
AlignmentFree Phylogenetic Reconstruction
, 2009
"... We introduce the first polynomialtime phylogenetic reconstruction algorithm under a model of sequence evolution allowing insertions and deletions—or indels. Given appropriate assumptions, our algorithm requires sequence lengths growing polynomially in the number of leaf taxa. Our techniques are dis ..."
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Cited by 6 (1 self)
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We introduce the first polynomialtime phylogenetic reconstruction algorithm under a model of sequence evolution allowing insertions and deletions—or indels. Given appropriate assumptions, our algorithm requires sequence lengths growing polynomially in the number of leaf taxa. Our techniques are distancebased and largely bypass the problem of multiple alignment.
Fast and reliable reconstruction of phylogenetic trees with very short edges
 In SODA: ACMSIAM Symposium on Discrete Algorithms
, 2008
"... Phylogenetic reconstruction is the problem of reconstructing an evolutionary tree from sequences corresponding to leaves of that tree. A central goal in phylogenetic reconstruction is to be able to reconstruct the tree as accurately as possible from as short as possible input sequences. The sequence ..."
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Cited by 6 (2 self)
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Phylogenetic reconstruction is the problem of reconstructing an evolutionary tree from sequences corresponding to leaves of that tree. A central goal in phylogenetic reconstruction is to be able to reconstruct the tree as accurately as possible from as short as possible input sequences. The sequence length required for correct topological reconstruction depends on certain properties of the tree, such as its depth and minimal edgeweight. Fast converging reconstruction algorithms are considered stateof theart in this sense, as they require asymptotically minimal sequence length in order to guarantee (with high probability) correct topological reconstruction of the entire tree. However, when the original phylogenetic tree contains very short edges, this minimal sequencelength is still too long for practical purposes. Short
Article URL
, 2012
"... This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Towards a practical O(n log n) phylogeny algorithm ..."
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This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Towards a practical O(n log n) phylogeny algorithm
Active Learning of Interaction Networks
, 2009
"... From molecular arrangements to biological organisms, our world is composed of systems of small components interacting with and affecting each other. Scientists often learn the structure of such systems by tampering with them and making observations. In this thesis, we develop methods for automating ..."
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From molecular arrangements to biological organisms, our world is composed of systems of small components interacting with and affecting each other. Scientists often learn the structure of such systems by tampering with them and making observations. In this thesis, we develop methods for automating this process from an active learning perspective, a setting where the learner is not restricted to making passive observations, but can choose to query the data. First, we consider the setting of learning hidden graphs with queries. Each query type is motivated by a realworld problem, from genome sequencing to evolutionary tree reconstruction. We give new algorithms for learning graphs and also consider the problem of verifying the results of the learning task. Next, we turn to value injection queries, which model experiments used to identify gene regulatory networks. We analyze the complexity of learning large alphabet and analog circuits with value injection queries. We then apply this model to social networks, allowing the learner to activate and suppress agents in the network, and we give an optimal algorithm and matching lower bound for this problem. Finally, we examine the passive learner, who watches the output of agents in a social network and must deduce the most likely underlying network. Last, we consider a classical problem in query learning: learning finite automata, which themselves are networks of connected states. We introduce label queries as a generalization of the well studied membership queries. We give algorithms for learning automata using label queries and analyze other models for learning automata.
unknown title
, 2006
"... www.elsevier.com/locate/ipl On the longest path algorithm for reconstructing trees from distance matrices ..."
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www.elsevier.com/locate/ipl On the longest path algorithm for reconstructing trees from distance matrices
1 Largescale multiple sequence alignment and phylogeny estimation
"... With the advent of next generation sequencing technologies, alignment and phylogeny estimation of datasets with thousands of sequences is being attempted. To address these challenges, new algorithmic approaches have been developed that have been able to provide substantial improvements over standard ..."
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With the advent of next generation sequencing technologies, alignment and phylogeny estimation of datasets with thousands of sequences is being attempted. To address these challenges, new algorithmic approaches have been developed that have been able to provide substantial improvements over standard methods. This paper focuses on new approaches for ultralarge tree estimation, including methods for coestimation of alignments and trees, estimating trees without needing a full sequence alignment, and phylogenetic placement. While the main focus is on methods with empirical performance advantages, we also discuss the theoretical guarantees of methods under Markov models of evolution. Finally, we include a discussion of the future of largescale phylogenetic analysis. 1