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Title: Binary hidden Markov models and varieties, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2013, 2013
Description: This paper closely examines HMMs in which all the hidden random variables are...
Show moreThis paper closely examines HMMs in which all the hidden random variables are binary. Its main contributions are (1) a birational parametrization for every such HMM, with an explicit inverse for recovering the hidden parameters in terms of observables, (2) a semialgebraic model membership test for every such HMM, and (3) minimal dening equations for the 4-node fully binary model, comprising 21 quadrics and 29 cubics, which were computed using Grobner bases in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters in (1) are rationally identiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zariski closure is therefore a rational projective variety of dimension 5. Grobner basis computations for the model and its graph are found to be considerably faster using these parameters. In the case of two hidden states, item (2) supersedes a previous algorithm of Schonhuth which is only generically dened, and the dening equations (3) yield new invariants for HMMs of all lengths 4. Such invariants have been used successfully in model selection problems in phylogenetics, and one can hope for similar applications in the case of HMMs.
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Collection: Journal of Algebraic Statistics

Title: Learning Coefficient in Bayesian Estimation of Restricted Boltzmann Machine, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2013, 2013
Description: We consider the real log canonical threshold for the learning model in Bayesian estimation. This threshold corresponds to a learning...
Show moreWe consider the real log canonical threshold for the learning model in Bayesian estimation. This threshold corresponds to a learning coefficient of generalization error in Bayesian estimation, which serves to measure learning efficiency in hierarchical learning models [30, 31, 33]. In this paper, we clarify the ideal which gives the log canonical threshold of the restricted Boltzmann machine and consider the learning coefficients of this model.
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Collection: Journal of Algebraic Statistics

Title: The precision space of interpolatory cubature formulæ
Date: 2015, 2015-06-11
Description: Methods from Commutative Algebra and Numerical Analysis are combined to address a problem common to many disciplines: the estimation of the...
Show moreMethods from Commutative Algebra and Numerical Analysis are combined to address a problem common to many disciplines: the estimation of the expected value of a polynomial of a random vector using a linear combination of a finite number of its values. In this work we remark on the error estimation in cubature formulæ for polynomial functions and introduce the notion of a precision space for a cubature rule.
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Collection: Journal of Algebraic Statistics

Title: The degeneration of the Grassmannian into a toric variety and the calculation of the eigenspaces of a torus action
Date: 2015, 2015-06-11
Description: Using the method of degenerating a Grassmannian into a toric variety, we calculate formulas for the dimensions of the eigenspaces of the...
Show moreUsing the method of degenerating a Grassmannian into a toric variety, we calculate formulas for the dimensions of the eigenspaces of the action of an n-dimensional torus on a Grassmannian of planes in an n-dimensional space.
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Collection: Journal of Algebraic Statistics

Title: Varieties with maximum likelihood degree one
Date: 2014, 2014-04-30
Description: We show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under...
Show moreWe show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under monomial maps with finite fibers. The maximum likelihood estimator corresponding to such a variety is Kapranov’s Horn uniformization. This extends Kapranov’s characterization of A-discriminantal hypersurfaces to varieties of arbitrary codimension.
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Collection: Journal of Algebraic Statistics

Title: Maximum Likelihood for Matrices with Rank Constraints
Date: 2014, 2014-04-30
Description: Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded...
Show moreMaximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions. This led to the discovery of maximum likelihood duality between matrices of complementary ranks, a result proved subsequently by Draisma and Rodriguez.
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Collection: Journal of Algebraic Statistics

Title: Uncovering Proximity of Chromosome Territories using Classical Algebraic Statistics
Date: 2015, 2015-11-09
Description: Exchange type chromosome aberrations (ETCAs) are rearrangements of the genome that occur when chromosomes break and the resulting fragments...
Show moreExchange type chromosome aberrations (ETCAs) are rearrangements of the genome that occur when chromosomes break and the resulting fragments rejoin with fragments from other chromosomes or from other regions within the same chromosome. ETCAs are commonly observed in cancer cells and in cells exposed to radiation. The frequency of these chromosome rearrangements is correlated with their spatial proximity, therefore it can be used to infer the three dimensional organization of the genome. Extracting statistical significance of spatial proximity from cancer and radiation data has remained somewhat elusive because of the sparsity of the data. We here propose a new approach to study the three dimensional organization of the genome using algebraic statistics. We test our method on a published data set of irradiated human blood lymphocyte cells. We provide a rigorous method for testing the overall organization of the genome, and in agreement with previous results we find a random relative positioning of chromosomes with the exception of the chromosome pairs {1,22} and {13,14} that have a significantly larger number of ETCAs than the rest of the chromosome pairs suggesting their spatial proximity. We conclude that algebraic methods can successfully be used to analyze genetic data and have potential applications to larger and more complex data sets.
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Collection: Journal of Algebraic Statistics

Title: A linear-algebraic tool for conditional independence inference
Date: 2015, 2015-11-09
Description: In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is...
Show moreIn this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.
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Collection: Journal of Algebraic Statistics

Title: A Family of Quasisymmetry Models
Date: 2015, 2015-06-11
Description: We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its...
Show moreWe present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation.
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Collection: Journal of Algebraic Statistics

Title: Markov degree of configurations defined by fibers of a configuration
Date: 2015, 2015-11-09
Description: We consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is...
Show moreWe consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is bounded from above by the Markov complexity of the base configuration. As important examples of base configurations we consider incidence matrices of graphs and study the maximum Markov degree of configurations defined by fibers of the incidence matrices. In particular we give a proof that the Markov degree for two-way transportation polytopes is three.
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Collection: Journal of Algebraic Statistics

Title: On Polyhedral Approximations of Polytopes for Learning Bayesian Networks, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2013, 2013
Description: The motivation for this paper is the geometric approach to statistical learning Bayesiannetwork (BN) structures. We review three vector...
Show moreThe motivation for this paper is the geometric approach to statistical learning Bayesiannetwork (BN) structures. We review three vector encodings of BN structures. The first one has been used by Jaakkola et al. [9] and also by Cussens [4], the other two use special integral vectors formerly introduced, called imsets [18, 20]. The topic is the comparison of outer polyhedral approximations of the corresponding polytopes. We show how to transform the inequalities suggested by Jaakkola et al. [9] into the framework of imsets. The result of our comparison is the observation that the implicit polyhedral approximation of the standard imset polytope suggested in [21] gives a tighter approximation than the (transformed) explicit polyhedral approximation from [9]. As a consequence, we confirm a conjecture from [21] that the above-mentioned implicit polyhedral approximation of the standard imset polytope is an LP relaxation of that polytope. In the end, we review recent attempts to apply the methods of integer programming to learning BN structures and discuss the task of finding suitable explicit LP relaxation in the imset-based approach.
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Collection: Journal of Algebraic Statistics

Title: Higher Connectivity of Fiber Graphs of Gröbner Bases, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2013, 2013
Description: Fiber graphs of Gröbner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these...
Show moreFiber graphs of Gröbner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications on how fast the algorithm converges. In this paper, we study a class of ber graphs with elementary combinatorial techniques and provide results that support a recent conjecture of Engström: the connectivity is given by the minimum vertex degree.
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Collection: Journal of Algebraic Statistics

Title: Betti Numbers of Cut Ideals of Trees, AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Date: 2013, 2013
Description: Cut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions...
Show moreCut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions of cut ideals of tree graphs. By employing basic methods from topological combinatorics, we obtain upper bounds for the Betti numbers of this type of ideals. These take the form of simple formulas on the number of vertices, which arise from the enumeration of induced subgraphs of certain incomparability graphs associated to the edge sets of trees.
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Collection: Journal of Algebraic Statistics

Title: Tying Up Loose Strands: Defining Equations of the Strand Symmetric Model
Date: 2015, 2015-06-11
Description: The strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show...
Show moreThe strand symmetric model is a phylogenetic model designed to reflect the symmetry inherent in the double-stranded structure of DNA. We show that the set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal. This knowledge allows one to determine the vanishing ideal of the general strand symmetric model of any trivalent tree. Our proof of the main result is computational. We use the fact that the Zariski closure of the strand symmetric model is the secant variety of a toric variety to compute the dimension of the variety. We then show that the known equations generate a prime ideal of the correct dimension using elimination theory.
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Collection: Journal of Algebraic Statistics

Title: The maximum likelihood degree of Fermat hypersurfaces
Date: 2015, 2015-11-09
Description: We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in...
Show moreWe study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likelihood estimation. The number of critical points over a projective variety is a topological invariant of the variety and is called maximum likelihood degree. We provide closed formulas for the maximum likelihood degree of any Fermat curve in the projective plane and of Fermat hypersurfaces of degree 2 in any projective space. Algorithmic methods to compute the ML degree of a generic Fermat hypersurface are developed throughout the paper. Such algorithms heavily exploit the symmetries of the varieties we are considering. A computational comparison of the different methods and a list of the maximum likelihood degrees of several Fermat hypersurfaces are available in the last section.
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Collection: Journal of Algebraic Statistics

Title: On the Connectivity of Fiber Graphs
Date: 2015, 2015-06-11
Description: We consider the connectivity of fiber graphs with respect to Gröbner basis and Graver basis moves. First, we present a sequence of fiber...
Show moreWe consider the connectivity of fiber graphs with respect to Gröbner basis and Graver basis moves. First, we present a sequence of fiber graphs using moves from a Gröbner basis and prove that their edge-connectivity is lowest possible and can have an arbitrarily large distance from the minimal degree. We then show that graph-theoretic properties of fiber graphs do not depend on the size of the right-hand side. This provides a counterexample to a conjecture of Engström on the node-connectivity of fiber graphs. Our main result shows that the edge-connectivity in all fiber graphs of this counterexample is best possible if we use moves from Graver basis instead.
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Collection: Journal of Algebraic Statistics

Title: Engineering Escherichia coli to produce and secrete colicins for rapid and selective biofilm cell killing
Date: 2021
Description: Bacterial biofilms are associated with chronic infectious diseases and are highly resistant to conventional...
Show moreBacterial biofilms are associated with chronic infectious diseases and are highly resistant to conventional antibiotics. Antimicrobial bacteriocins are alternatives to conventional antibiotics and are characterized by unique cell-killing mechanisms, including pore formation on cell membranes, nuclease activity, and cell wall synthesis inhibition. Here, we used cell-free protein synthesis to rapidly evaluate the antibiofilm activities of colicins E1, E2, and E3. We found that E2 (with DNase activity) most effectively killed target biofilm cells (i.e., the K361 strain) while leaving nontargeted biofilms intact. We then engineered probiotic Escherichia coli microorganisms with genetic circuits to controllably synthesize and secrete colicin E2, which successfully inhibited biofilms and killed preformed indicator biofilms. Our findings suggest that colicins rapidly and selectively kill target biofilm cells in multispecies biofilms and demonstrate the potential of using microorganisms engineered to produce antimicrobial colicin proteins as live therapeutic strategies to treat biofilm-associated infections.
Sponsorship: NIH-R15AI130988
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Title: Empirical Modeling of Public Safety to Voice Traffic to Aid Emergency Capacity
Creator: Taher, Tanim, Bacchus, Roger
Date: 2012-04-18, 2012-04-18
Description: An RF measurement system with high time resolution is implemented to determine the statistical characteristics of...
Show moreAn RF measurement system with high time resolution is implemented to determine the statistical characteristics of various channels in the Land Mobile Radio bands. The applicability of simple statistical models to the observed data is investigated, as well as their validity over short and long periods of time. The results show that the statistics of the idle and holding times of communication on these channels vary significantly over time and demonstrate daily periodicity, requiring non-stationary models to accurately represent them. Over short durations of time however, conventional distributions such as the exponential and lognormal may adequately characterize the properties of these quantities, allowing convenient and compact representations of the data. Results based on empirical data are presented to quantify the probability of stationarity for voice traffic within a time span of given length. The findings are useful for network planning or streamlining, network simulation and modeling, and investigation of dynamic spectrum access.
Sponsorship: National Science Foundation, Federal Communications Commission, Motorola, Cleversafe, Roberson & Associates LLC
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Title: Replacement as a Problem for Justification of Preventative Detention
Creator: Davis, Michael
Date: 2011, 2011-04
Publisher: John Jay College of Criminal Justice of The City University of New Yor
Description: What makes Don E. Scheid’s article on indefinite detention interesting is that he thinks through many of the moral...
Show moreWhat makes Don E. Scheid’s article on indefinite detention interesting is that he thinks through many of the moral issues inherent in attempting to prevent (or, rather, keep to a minimum) certain kinds of violent crime, an attempt we have come to call (however unwisely) ‘‘the war on terror.’’ Scheid takes ‘‘war’’ as literally as possible, while making the reasonable assumption that this war, unlike wars generally, is not a temporary expedient responding to a moral emergency but an institution that must operate at full power for a long time, decades at least. Scheid’s argument yields a long list of preconditions for justified indefinite preventive detention: a high standard of dangerousness (‘‘mega-terrorism’’), a reasonable standard of proof of dangerousness, as good an investigation as conditions will allow, adequate resources for the defense, a hearing before a fair and independent tribunal, detention under the most comfortable conditions practical, and periodic review of the detainee’s supposed dangerousness. To these preconditions one more should be added: that detaining the persons in question will reduce the danger posed. I take this additional precondition to follow from Scheid’s own defense of indefinite detention, not from an independent argument. Scheid limits his argument to megaterrorists because the scale of destruction they have already achieved (for example, destruction of the World Trade Center) shows them to be dangerous on a scale ordinary crime is not and so to invite measures of prevention beyond what seems necessary (or proper) for ordinary criminals. Scheid explicitly declines to consider the non-consequentialist argument that preventive detention is what a mega-terrorist deserves for his character or for what he has already done. Scheid’s argument for preventive detention is consequentialist throughout: we may, and should, detain to prevent (or at least substantially reduce the probability of) the large-scale destruction of life that mega-terrorists aim at. We may justifiably deny a few, including some innocent persons, their freedom because, and only because, it makes the rest of us, the great majority, considerably safer. My additional precondition can be defended in the same way: where there is no danger posed, any detention is (all else equal) a net loss in happiness, well being, or whatever reasonable measure of consequences we adopt. A precondition of preventative detention must be a net reduction in danger posed. Where what is proposed is an institution of preventative detention, the institution must have that effect overall. What I shall argue here is that preventive detention generally fails to satisfy this condition and Scheid’s indefinite preventive detention of mega-terrorists always does. An institution to prevent terrorism by detaining terrorists cannot, in practice, significantly reduce the danger terrorism poses.
Criminal Justice Ethics. Vol. 30, No. 1, April 2011, 90-97.
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Title: Learning the Lingo? Gender, Prestige and Linguistic Adaptation in Review Communities
Creator: Hemphill, Libby, Otterbacher, Jahna
Date: 2011-11-19, 2012-02
Publisher: ACM Press
Description: Women and men communicate differently in both face-to- face and computer-mediated environments. We study linguistic...
Show moreWomen and men communicate differently in both face-to- face and computer-mediated environments. We study linguistic patterns considered gendered in reviews contributed to the Internet Movie Database. IMDb has been described as a male-majority community, in which females contribute fewer reviews and enjoy less prestige than males. Analyzing reviews posted by prolific males and females, we hypothesize that females adjust their communication styles to be in sync with their male counterparts. We find evidence that while certain characteristics of “female language” persevere over time (e.g., frequent use of pronouns) others (e.g., hedging) decrease with time. Surprisingly, we also find that males often increase their use of “female” features. Our results indicate, that even when they resemble men’s reviews linguistically, women’s reviews still enjoy less prestige and smaller audiences.
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