The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference
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{"title"=>"The probabilistic convolution tree: Efficient exact Bayesian inference for faster LC-MS/MS protein inference", "type"=>"journal", "authors"=>[{"first_name"=>"Oliver", "last_name"=>"Serang", "scopus_author_id"=>"40762223400"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84898727906", "sgr"=>"84898727906", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0091507", "pmid"=>"24626234", "isbn"=>"1932-6203 (Linking)", "pui"=>"372786311"}, "id"=>"6f372505-ae6e-366f-beba-e80d7993fb9f", "abstract"=>"Abstract Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. ...", "link"=>"http://www.mendeley.com/research/probabilistic-convolution-tree-efficient-exact-bayesian-inference-faster-lcmsms-protein-inference", "reader_count"=>34, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Student > Doctoral Student"=>3, "Researcher"=>6, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>1, "Student > Master"=>6, "Other"=>2, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Student > Doctoral Student"=>3, "Researcher"=>6, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>1, "Student > Master"=>6, "Other"=>2, "Student > Bachelor"=>3, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Engineering"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>3, "Agricultural and Biological Sciences"=>16, "Computer Science"=>10}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>16}, "Computer Science"=>{"Computer Science"=>10}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>2}}, "reader_count_by_country"=>{"Austria"=>1, "United States"=>1, "Germany"=>1, "India"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1419513"], "description"=>"<p>The quadratic dynamic programming approach is illustrated using the digraph from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g003\" target=\"_blank\">figure 3:</a> One by one, each protein is added to the initially empty total number of present proteins, represented by the random variable . Thus, the probability distribution for each partial sum is computed and stored in the vector . Finally, the shared evidence is included, as it depends exclusively on the number of present proteins . Inference for a particular protein (<i>e.g.</i> protein ) could be performed easily by performing another forward pass with the constraint that , and all protein posteriors would thus be computed in cubic time with the number of proteins ( proteins steps per protein); however, a subsequent right-to-left pass could be used to compute all protein posteriors in time via the forward-backward algorithm.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "quadratic"], "article_id"=>961517, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g005", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_quadratic_dynamic_programming_approach_/961517", "title"=>"Illustration of the quadratic dynamic programming approach.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419512"], "description"=>"<p>(<b>a</b>) A dynamic programming approach to solving the problem from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g002\" target=\"_blank\">figure 2</a>. In this approach all values of , the information on which depends, are computed after successively including every next variable . This allows paths in the exponential tree generated by the power-set to be merged when they result in the same value , and thus allows a forward-backward algorithm to compute inference in quadratic time and space. (<b>b</b>) A general path graph can be constructed whenever the operation performed by the node , on which the shared data depends, can be decomposed as a series of consecutive operations that aggregate one at a time. This corresponds to operators with commutative and associative properties. The resulting transformation resembles Heckerman’s temporal transformation, which also uses quadratic time and space.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "quadratic"], "article_id"=>961516, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g004", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_quadratic_dynamic_programming_approach_and_its_generalization_/961516", "title"=>"A quadratic dynamic programming approach and its generalization.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419509"], "description"=>"<p>(<b>a</b>) Directed edges between proteins and spectral data represent causal statistical dependencies with spectra that can result from peptides in the adjacent protein. For simplicity, peptide-spectrum-matches (PSMs) are denoted simply using their spectral evidence, thereby producing a bipartite graph of proteins () to spectral data (). Proteins , , and share spectral data , because they share peptides that were matched to spectrum . : if the score of the PSM corresponding to spectrum is very high, it is tempting to award a high probability to protein ; however, proteins and compete for this shared evidence, and thereby have a chance to reduce the probability of . This process (called “explaining away” to describe the fact that the contribution of evidence to a single hypothesis is reduced by competing hypotheses) introduces new dependencies between all pairs of proteins sharing that evidence. (<b>b</b>) These shared spectral data introduce new non-causal dependencies between proteins with shared successors in (a). These dependencies are visualized in the undirected moral graph. When multiple proteins share spectral evidence, these undirected edges connect all pairs of predecessors, creating a clique in the moral graph . (<b>c</b>) The tree decomposition (sometimes called the “junction tree” or “clique tree”) merges the moral graph from (b) without loss of dependencies, so that inference can be performed using Pearl’s belief propagation algorithm. Belief propagation starts at the top clique, which only shares variable with its neighbor. Therefore, the top clique can perform inference while leaving as a symbolic, unknown quantity, so that it can be used to send information from the cliques below ( is an information bottleneck, through which the cliques below can influence the top clique). Likewise, the variables and can be marginalized out before sending any relevant information to considering the middle clique. This procedure can significantly reduce the runtime by allowing inference to be performed on the cliques rather than on all nodes in the tree; however, each clique represents an inseparable multidimensional distribution over several variables, and thus the cost of processing a single clique is more than exponential in the number of variables. When many proteins share common evidence (<i>i.e.</i> share at least one peptide identified by spectral evidence), a large clique is formed in the moral graph and inference becomes intractable in the general case.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "graphical"], "article_id"=>961513, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g001", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mass_spectrometry_a_graphical_view_/961513", "title"=>"Mass spectrometry: a graphical view.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419531"], "description"=>"<p>(<b>a</b>) Distribution of log runtimes for different connected subgraphs (24 fractions). A HUGIN-based junction tree implementation is compared to a probabilistic convolution tree-based junction tree implementation. The cost of inference will be dominated by a few outlier graphs, which do not decompose effectively using the junction tree. As a result, some connected subgraphs would require an impractical number of steps when using the HUGIN algorithm. This runtime can be improved by using probabilistic convolution trees, while still achieving the exact result. (<b>b</b>) One difficult connected subgraph from panel (a). Proteins are shown as red squares, probabilistic adders are shown as blue inverted triangles (these are the nodes can make use of probabilistic convolution trees), spectral evidence is shown as green circles. This subgraph would require steps using the HUGIN junction tree. In contrast, the probabilistic convolution can solve this same subgraph in steps (and achieve an exact result).</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "convolution", "tree-based", "junction", "hugin-based", "hela"], "article_id"=>961524, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g010", "stats"=>{"downloads"=>3, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Runtime_benefit_of_convolution_tree_based_junction_tree_over_HUGIN_based_junction_tree_on_HeLa_data_/961524", "title"=>"Runtime benefit of convolution tree-based junction tree over HUGIN-based junction tree on HeLa data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419528"], "description"=>"<p>(<b>a</b>) A comparison of power-set enumeration and the quadratic dynamic programming approach on small problems of the form from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g002\" target=\"_blank\">figure 2</a>. Note that axes are log-scaled, and so a widening gap between the curves indicates a super-linear speedup for the algorithm producing the lower curve. (<b>b</b>) A comparison of quadratic dynamic programming and the convolution tree approach on larger problems of this form. The convolution tree achieves a super-linear speedup and a super-linear reduction in memory consumption, making it applicable to much larger problems than either the quadratic dynamic programming approach or power-set enumeration. On very small problems (requiring substantially less than one second of runtime), the more sophisticated dynamic programming approaches have higher overhead, and are therefore slightly slower.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods"], "article_id"=>961521, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g008", "stats"=>{"downloads"=>5, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Runtime_comparison_between_the_algorithms_/961521", "title"=>"Runtime comparison between the algorithms.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419516"], "description"=>"<p>(<b>a</b>) An alternate transformation for efficiently computing posteriors for all proteins. Instead of unrolling the commutative and associative operator one protein at a time as performed by the quadratic dynamic programming algorithm, variables are paired successively, resulting in a tree with depth (when is a power of ). (<b>b</b>) Inference on this tree can be performed by solving a minimal ternary node structure and then proceeding inductively: all nodes (except for the proteins themselves) have two parent subtrees, and , and one child. The parent subtrees connect the node of interest to all data reachable through the parents above (partitioned into and , respectively), and the child subtree connects to all data reachable below, (denoted ). The joint probability with all data above can be passed as messages from parents to children, and the likelihoods given data below (that is, all data reachable through a downward edge out of a given node) can be passed upward from child to parents. Each of these three messages turns out to be a convolutions (shown in inset). For example, all ways that can be computed by a shifted and reflected dot product, which finds all and with a sum of . Thus the prior probability for can be seen as a vector equal to the convolution of the prior probabilities of prior probabilities for and . These convolutions can be performed with fast Fourier transform (FFT) in time (where is the size of the possible state space of ). If the vectors are very sparse, then a standard discrete Fourier transform-based (DFT) convolution may be faster.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "convolution"], "article_id"=>961519, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g006", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Faster_dynamic_programming_using_the_convolution_tree_/961519", "title"=>"Faster dynamic programming using the convolution tree.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419526"], "description"=>"<p>The convolution tree is illustrated using the digraph from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g003\" target=\"_blank\">figure 3</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g005\" target=\"_blank\">figure 5:</a> Messages are passed down the tree (via step 1). A subsequent pass would send messages up the tree (step 2), computing the protein posteriors in sub-quadratic time. Note that the normalized vector is equivalent to the distribution , and is identical to the normalized vector of the same name computed by the quadratic algorithm illustrated in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091507#pone-0091507-g005\" target=\"_blank\">figure 5</a>.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "probabilistic", "convolution"], "article_id"=>961520, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g007", "stats"=>{"downloads"=>2, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_probabilistic_convolution_tree_/961520", "title"=>"Illustration of the probabilistic convolution tree.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419511"], "description"=>"<p>Super-exponential enumeration is illustrated using a simple digraph. The protein prior for protein is denoted using the vector (written using Python dictionary notation), where and . Likelihoods due to unique evidence for protein are denoted , and the likelihood due to shared evidence is shown using , both using the same notation. The scores populating the and vectors comes from the peptide-level likelihoods indicating the quality of the match between the peptide and any matching spectra (<i>i.e.</i> these scores come from the conditionally independent product of PSM scores for that peptide). For example, the prior probability on protein is 0.8, and a unique peptide corresponding to protein has the score 0.35 (indicating the relative likelihoods are 0.35 versus 0.65 for the respective hypotheses that the peptide matching spectrum is created by protein versus the hypothesis that the peptide is not created by protein ). The inset shows the table produced by enumerating all distinct protein configurations, and the resulting joint probability with all data (both unique and shared). This computational cost of this enumeration is in for proteins.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "enumeration"], "article_id"=>961515, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g003", "stats"=>{"downloads"=>2, "page_views"=>18, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_enumeration_approach_/961515", "title"=>"Illustration of the enumeration approach.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419536"], "description"=>"<p>(<b>a</b>) A probabilistic demixing (a problem highly related to deconvolution) problem from mass spectrometry. An observed chimeric spectrum with data is composed of a linear combination of four different compounds and with unknown relative abundances , which we want to infer. Three values that can receive contributions from multiple compounds are labeled with the background colors red, green, and blue. (<b>b</b>) The resulting cascaded graph of probabilistic adder nodes. The variables are discretized into relative abundances of interest. Conditional probabilities individually treat each intensity as proportional to the abundance of the compound that produces it. Data unique to each compound are labeled , and are conditionally independent given . Shared evidence nodes are colored to correspond to the background colors from (a). Probabilistic adder nodes are cascaded to build a tree for probabilistic inference, enabling the computation of a posterior distribution for the relative abundance of each compound.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "constituent"], "article_id"=>961529, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g011", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Decomposition_of_a_spectrum_into_its_constituent_compounds_/961529", "title"=>"Decomposition of a spectrum into its constituent compounds.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419510"], "description"=>"<p>Several proteins matching unique and shared peptide-level evidence. The peptide-level evidence, is partitioned into unique peptide-level evidence () as well as a collection of shared peptide level evidence shared by all proteins (). Graphs of this form are typical when searching mass spectra against protein databases containing substantial redundancy (<i>e.g.</i> databases with many splice variants or close homologs), because these types of proteins share core similarities but also have unique regions that distinguish them from one another. Inference on this type of graph cannot be performed efficiently through protein clustering, protein pruning, or junction tree decomposition; to date, exact Bayesian protein inference on such splice variant graphs has only been performed in super-exponential time.</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "spectrometry-based", "splice"], "article_id"=>961514, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g002", "stats"=>{"downloads"=>5, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Difficult_inference_mass_spectrometry_based_identification_of_splice_variants_/961514", "title"=>"Difficult inference: mass spectrometry-based identification of splice variants.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/1419529"], "description"=>"<p>(<b>a</b>) A Bayesian network with probabilistic adder nodes and . (<b>b</b>) The resulting cascaded graph of probabilistic adder nodes transforms the graph into an equivalent Bayesian network that can be solved efficiently as a convolution tree. Graphs that do not cascade into polytrees (<i>i.e.</i> graphs that have loops even after cascading nodes as shown here) can be solved with a slightly modified junction tree inference algorithm: junction tree clique nodes that consist of a single probabilistic adder node and its inputs can pass messages through convolution tree nodes (without realizing the full conditional probability distribution).</p>", "links"=>[], "tags"=>["Computational biology", "proteomics", "Spectrometric identification of proteins", "algorithms", "Applied mathematics", "Probability theory", "Bayes theorem", "statistics", "Statistical methods", "graph", "cascaded"], "article_id"=>961522, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Oliver Serang"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0091507.g009", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_graph_and_its_cascaded_equivalent_/961522", "title"=>"A graph and its cascaded equivalent.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-03-13 10:02:45"}

PMC Usage Stats | Further Information

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Relative Metric

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