arXiv subjects

Mark Hamilton

Publications and source records attributed to Mark Hamilton.

24 records · Page 2Linked to original sources

arXiv2019

MMLSpark: Unifying Machine Learning Ecosystems at Massive Scales

We introduce Microsoft Machine Learning for Apache Spark (MMLSpark), an ecosystem of enhancements that expand the Apache Spark distributed computing library to tackle problems in Deep Learning, Micro-Service Orchestration, Gradient Boosting, Model Interpretability, and other areas of modern computation. Furthermore, we present a novel system called Spark Serving that allows users to run any Apache Spark program as a distributed, sub-millisecond latency web service backed by their existing Spark Cluster. All MMLSpark contributions have the same API to enable simple composition across frameworks and usage across batch, streaming, and RESTful web serving scenarios on static, elastic, or serverless clusters. We showcase MMLSpark by creating a method for deep object detection capable of learning without human labeled data and demonstrate its effectiveness for Snow Leopard conservation.

cs.LG↗

arXiv2018

Semi-Supervised Translation with MMD Networks

This work aims to improve semi-supervised learning in a neural network architecture by introducing a hybrid supervised and unsupervised cost function. The unsupervised component is trained using a differentiable estimator of the Maximum Mean Discrepancy (MMD) distance between the network output and the target dataset. We introduce the notion of an $n$-channel network and several methods to improve performance of these nets based on supervised pre-initialization, and multi-scale kernels. This work investigates the effectiveness of these methods on language translation where very few quality translations are known \textit{a priori}. We also present a thorough investigation of the hyper-parameter space of this method on both synthetic data.

cs.LG↗

arXiv2018

Flexible and Scalable Deep Learning with MMLSpark

In this work we detail a novel open source library, called MMLSpark, that combines the flexible deep learning library Cognitive Toolkit, with the distributed computing framework Apache Spark. To achieve this, we have contributed Java Language bindings to the Cognitive Toolkit, and added several new components to the Spark ecosystem. In addition, we also integrate the popular image processing library OpenCV with Spark, and present a tool for the automated generation of PySpark wrappers from any SparkML estimator and use this tool to expose all work to the PySpark ecosystem. Finally, we provide a large library of tools for working and developing within the Spark ecosystem. We apply this work to the automated classification of Snow Leopards from camera trap images, and provide an end to end solution for the non-profit conservation organization, the Snow Leopard Trust.

cs.DC↗

arXiv2018

Convergence of polarizations, toric degenerations, and Newton-Okounkov bodies

Let $X$ be a smooth irreducible complex algebraic variety of dimension $n$ and $L$ a very ample line bundle on $X$. Given a toric degeneration of $(X,L)$ satisfying some natural technical hypotheses, we construct a deformation $\{J_s\}$ of the complex structure on $X$ and bases $\mathcal{B}_s$ of $H^0(X,L, J_s)$ so that $J_0$ is the standard complex structure and, in the limit as $s \to \infty$, the basis elements approach dirac-delta distributions centered at Bohr-Sommerfeld fibers of a moment map associated to $X$ and its toric degeneration. The theory of Newton-Okounkov bodies and its associated toric degenerations shows that the technical hypotheses mentioned above hold in some generality. Our results significantly generalize previous results in geometric quantization which prove "independence of polarization" between Kähler quantizations and real polarizations. As an example, in the case of general flag varieties $X=G/B$ and for certain choices of $λ$, our result geometrically constructs a continuous degeneration of the (dual) canonical basis of $V_λ^*$ to a collection of dirac delta functions supported at the Bohr-Sommerfeld fibres corresponding exactly to the lattice points of a Littelmann-Berenstein-Zelevinsky string polytope $Δ_{\underline{w}_0}(λ) \cap \mathbb{Z}^{\dim(G/B)}$.

math.SG↗

arXiv2017

AGN Populations in Large Volume X-ray Surveys: Photometric Redshifts and Population Types found in the Stripe 82X Survey

Multi-wavelength surveys covering large sky volumes are necessary to obtain an accurate census of rare objects such as high luminosity and/or high redshift active galactic nuclei (AGN). Stripe 82X is a 31.3 deg$^2$ X-ray survey with $Chandra$ and $XMM$-Newton observations overlapping the legacy Sloan Digital Sky Survey (SDSS) Stripe 82 field, which has a rich investment of multi-wavelength coverage from the ultraviolet to the radio. The wide-area nature of this survey presents new challenges for photometric redshifts for AGN compared to previous work on narrow-deep fields because it probes different populations of objects that need to be identified and represented in the library of templates. Here we present an updated X-ray plus multi-wavelength matched catalog, including $Spitzer$ counterparts, and estimated photometric redshifts for 5961 (96% of a total of 6181) X-ray sources, which have a normalized median absolute deviation, $σ_{\rm nmad}$ = 0.06 and an outlier fraction, $η$ = 13.7%. The populations found in this survey, and the template libraries used for photometric redshifts, provide important guiding principles for upcoming large-area surveys such as $eROSITA$ and 3$XMM$ (in X-ray) and the Large Synoptic Survey Telescope (LSST; optical).

astro-ph.GA↗

arXiv2005

Symplectic fibrations and Riemann-Roch numbers of reduced spaces

In this article we give formulas for the Riemann-Roch number of a symplectic quotient arising as the reduced space corresponding to a coadjoint orbit (for an orbit close to 0) as an evaluation of cohomology classes over the reduced space at 0. This formula exhibits the dependence of the Riemann-Roch number on the Lie algebra variable which specifies the orbit. We also express the formula as a sum over the components of the fixed point set of the maximal torus. Our proof applies to Hamiltonian G-manifolds even if they do not have a compatible Kahler structure, using the definition of quantisation in terms of the Spin-C Dirac operator.

math.SG↗