113,445 research outputs found
Finding a Path is Harder than Finding a Tree
I consider the problem of learning an optimal path graphical model from data
and show the problem to be NP-hard for the maximum likelihood and minimum
description length approaches and a Bayesian approach. This hardness result
holds despite the fact that the problem is a restriction of the polynomially
solvable problem of finding the optimal tree graphical model
Out-sphere decoder for non-coherent ML SIMO detection and its expected complexity
In multi-antenna communication systems, channel information
is often not known at the receiver. To fully exploit
the bandwidth resources of the system and ensure the practical
feasibility of the receiver, the channel parameters are
often estimated and then employed in the design of signal
detection algorithms. However, sometimes communication
can occur in an environment where learning the channel coefficients
becomes infeasible. In this paper we consider the
problem of maximum-likelihood (ML)-detection in singleinput
multiple-output (SIMO) systems when the channel information
is completely unavailable at the receiver and when
the employed signalling at the transmitter is q-PSK. It is
well known that finding the solution to this optimization requires
solving an integer maximization of a quadratic form
and is, in general, an NP hard problem. To solve it, we propose
an exact algorithm based on the combination of branch
and bound tree search and semi-definite program (SDP) relaxation.
The algorithm resembles the standard sphere decoder
except that, since we are maximizing we need to construct
an upper bound at each level of the tree search. We
derive an analytical upper bound on the expected complexity
of the proposed algorithm
Advancing Divide-And-Conquer Phylogeny Estimation Using Robinson-Foulds Supertrees
One of the Grand Challenges in Science is the construction of the Tree of Life, an evolutionary tree containing several million species, spanning all life on earth. However, the construction of the Tree of Life is enormously computationally challenging, as all the current most accurate methods are either heuristics for NP-hard optimization problems or Bayesian MCMC methods that sample from tree space. One of the most promising approaches for improving scalability and accuracy for phylogeny estimation uses divide-and-conquer: a set of species is divided into overlapping subsets, trees are constructed on the subsets, and then merged together using a "supertree method". Here, we present Exact-RFS-2, the first polynomial-time algorithm to find an optimal supertree of two trees, using the Robinson-Foulds Supertree (RFS) criterion (a major approach in supertree estimation that is related to maximum likelihood supertrees), and we prove that finding the RFS of three input trees is NP-hard. We also present GreedyRFS (a greedy heuristic that operates by repeatedly using Exact-RFS-2 on pairs of trees, until all the trees are merged into a single supertree). We evaluate Exact-RFS-2 and GreedyRFS, and show that they have better accuracy than the current leading heuristic for RFS
Invited paper: An efficient H∞ estimation approach to speed up the sphere decoder
Maximum-likelihood (ML) decoding often reduces to solving an integer least-squares problem, which is NP hard in the worst-case. On the other hand, it has recently been shown that, over a wide range of dimensions and signal-to-noise ratios (SNR), the sphere decoding algorithm finds the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In this paper, we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoder. The search tree is pruned by computing lower bounds on the possible optimal solution as we proceed to go down the tree. Using ideas from H∞ estimation theory, we have developed a general framework to compute the lower bound on the integer least-squares. Several special cases of lower bounds were derived from this general framework. Clearly, the tighter the lower bound, the more branches can be eliminated from the tree. However, finding a tight lower bound requires significant computational effort that might diminish the savings obtained by additional pruning. In this paper, we propose the use of a lower bound which can be computed with only linear complexity. Its use for tree pruning results in significantly speeding up the basic sphere decoding algorithm
RAxML-NG: a fast, scalable and user-friendly tool for maximum likelihood phylogenetic inference
Motivation:
Phylogenies are important for fundamental biological research, but also have numerous applications in biotechnology, agriculture and medicine. Finding the optimal tree under the popular maximum likelihood (ML) criterion is known to be NP-hard. Thus, highly optimized and scalable codes are needed to analyze constantly growing empirical datasets. //
Results:
We present RAxML-NG, a from-scratch re-implementation of the established greedy tree search algorithm of RAxML/ExaML. RAxML-NG offers improved accuracy, flexibility, speed, scalability, and usability compared with RAxML/ExaML. On taxon-rich datasets, RAxML-NG typically finds higher-scoring trees than IQTree, an increasingly popular recent tool for ML-based phylogenetic inference (although IQ-Tree shows better stability). Finally, RAxML-NG introduces several new features, such as the detection of terraces in tree space and the recently introduced transfer bootstrap support metric. //
Availability and implementation:
The code is available under GNU GPL at https://github.com/amkozlov/raxml-ng. RAxML-NG web service (maintained by Vital-IT) is available at https://raxml-ng.vital-it.ch/
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
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