Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance

Universal Interface of TAUOLA Technical and Physics Documentation

Because of their narrow width, tau decays can be well separated from their production process. Only spin degrees of freedom connect these two parts of the physics process of interest for high energy collision experiments. In the following, we present a Monte Carlo algorithm which is based on that property. The interface supplements events generated by other programs, with tau decays. Effects of spin, genuine weak corrections or of new physics may be taken into account at the time when a tau decay is generated and written into an event record.Comment: 1+44 pages, 17 eps figure

Supersymmetric Signatures at an eeγ\gamma Collider

High energy electron-photon colliders provide unique opportunities for probing physics beyond the standard model. We have studied the experimental signatures for two supersymmetric scenarios, with the lightest supersymmetric particle (LSP) being either the lightest neutralino or the gravitino. In the ``neutralino LSP'' scenario favored by the minimal supersymmetric standard model (MSSM), it is found that some basic parameters of the model, $\mu$, $\tan\beta$, $M_1$ and $M_2$, may be uniquely determined from the outgoing electron energy spectrum without assuming high scale unification of the masses or couplings. In the ``gravitino LSP'' scenario which occurs naturally in models of low energy dynamical supersymmetry breaking, it is possible to have background-free signatures if the next-to-lightest supersymmetric particle (NLSP) has a long decay length. In cases that the NLSP decays quickly, ways to distinguish among the experimental signatures of the two scenarios and of the standard model (SM) background are discussed.Comment: 14 pages, LaTex file, 3 figure

The Matrix Element Method and QCD Radiation

The matrix element method (MEM) has been extensively used for the analysis of top-quark and W-boson physics at the Tevatron, but in general without dedicated treatment of initial state QCD radiation. At the LHC, the increased center of mass energy leads to a significant increase in the amount of QCD radiation, which makes it mandatory to carefully account for its effects. We here present several methods for inclusion of QCD radiation effects in the MEM, and apply them to mass determination in the presence of multiple invisible particles in the final state. We demonstrate significantly improved results compared to the standard treatment.Comment: 15 pp; v2: references and some clarifications added; v3: discussion of NLO effects, version published in PR

How to Find More Supernovae with Less Work: Object Classification Techniques for Difference Imaging

We present the results of applying new object classification techniques to difference images in the context of the Nearby Supernova Factory supernova search. Most current supernova searches subtract reference images from new images, identify objects in these difference images, and apply simple threshold cuts on parameters such as statistical significance, shape, and motion to reject objects such as cosmic rays, asteroids, and subtraction artifacts. Although most static objects subtract cleanly, even a very low false positive detection rate can lead to hundreds of non-supernova candidates which must be vetted by human inspection before triggering additional followup. In comparison to simple threshold cuts, more sophisticated methods such as Boosted Decision Trees, Random Forests, and Support Vector Machines provide dramatically better object discrimination. At the Nearby Supernova Factory, we reduced the number of non-supernova candidates by a factor of 10 while increasing our supernova identification efficiency. Methods such as these will be crucial for maintaining a reasonable false positive rate in the automated transient alert pipelines of upcoming projects such as PanSTARRS and LSST.Comment: 25 pages; 6 figures; submitted to Ap

Directed Hamiltonicity and Out-Branchings via Generalized Laplacians

We are motivated by a tantalizing open question in exact algorithms: can we detect whether an $n$-vertex directed graph $G$ has a Hamiltonian cycle in time significantly less than $2^n$? We present new randomized algorithms that improve upon several previous works: 1. We show that for any constant $0<\lambda<1$ and prime $p$ we can count the Hamiltonian cycles modulo $p^{\lfloor (1-\lambda)\frac{n}{3p}\rfloor}$ in expected time less than $c^n$ for a constant $c<2$ that depends only on $p$ and $\lambda$. Such an algorithm was previously known only for the case of counting modulo two [Bj\"orklund and Husfeldt, FOCS 2013]. 2. We show that we can detect a Hamiltonian cycle in $O^*(3^{n-\alpha(G)})$ time and polynomial space, where $\alpha(G)$ is the size of the maximum independent set in $G$. In particular, this yields an $O^*(3^{n/2})$ time algorithm for bipartite directed graphs, which is faster than the exponential-space algorithm in [Cygan et al., STOC 2013]. Our algorithms are based on the algebraic combinatorics of "incidence assignments" that we can capture through evaluation of determinants of Laplacian-like matrices, inspired by the Matrix--Tree Theorem for directed graphs. In addition to the novel algorithms for directed Hamiltonicity, we use the Matrix--Tree Theorem to derive simple algebraic algorithms for detecting out-branchings. Specifically, we give an $O^*(2^k)$-time randomized algorithm for detecting out-branchings with at least $k$ internal vertices, improving upon the algorithms of [Zehavi, ESA 2015] and [Bj\"orklund et al., ICALP 2015]. We also present an algebraic algorithm for the directed $k$-Leaf problem, based on a non-standard monomial detection problem