2,428 research outputs found
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
Entity Personalized Talent Search Models with Tree Interaction Features
Talent Search systems aim to recommend potential candidates who are a good
match to the hiring needs of a recruiter expressed in terms of the recruiter's
search query or job posting. Past work in this domain has focused on linear and
nonlinear models which lack preference personalization in the user-level due to
being trained only with globally collected recruiter activity data. In this
paper, we propose an entity-personalized Talent Search model which utilizes a
combination of generalized linear mixed (GLMix) models and gradient boosted
decision tree (GBDT) models, and provides personalized talent recommendations
using nonlinear tree interaction features generated by the GBDT. We also
present the offline and online system architecture for the productionization of
this hybrid model approach in our Talent Search systems. Finally, we provide
offline and online experiment results benchmarking our entity-personalized
model with tree interaction features, which demonstrate significant
improvements in our precision metrics compared to globally trained
non-personalized models.Comment: This paper has been accepted for publication at ACM WWW 201
Quantitative toxicity prediction using topology based multi-task deep neural networks
The understanding of toxicity is of paramount importance to human health and
environmental protection. Quantitative toxicity analysis has become a new
standard in the field. This work introduces element specific persistent
homology (ESPH), an algebraic topology approach, for quantitative toxicity
prediction. ESPH retains crucial chemical information during the topological
abstraction of geometric complexity and provides a representation of small
molecules that cannot be obtained by any other method. To investigate the
representability and predictive power of ESPH for small molecules, ancillary
descriptors have also been developed based on physical models. Topological and
physical descriptors are paired with advanced machine learning algorithms, such
as deep neural network (DNN), random forest (RF) and gradient boosting decision
tree (GBDT), to facilitate their applications to quantitative toxicity
predictions. A topology based multi-task strategy is proposed to take the
advantage of the availability of large data sets while dealing with small data
sets. Four benchmark toxicity data sets that involve quantitative measurements
are used to validate the proposed approaches. Extensive numerical studies
indicate that the proposed topological learning methods are able to outperform
the state-of-the-art methods in the literature for quantitative toxicity
analysis. Our online server for computing element-specific topological
descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/Comment: arXiv admin note: substantial text overlap with arXiv:1703.1095
Interpretable Categorization of Heterogeneous Time Series Data
Understanding heterogeneous multivariate time series data is important in
many applications ranging from smart homes to aviation. Learning models of
heterogeneous multivariate time series that are also human-interpretable is
challenging and not adequately addressed by the existing literature. We propose
grammar-based decision trees (GBDTs) and an algorithm for learning them. GBDTs
extend decision trees with a grammar framework. Logical expressions derived
from a context-free grammar are used for branching in place of simple
thresholds on attributes. The added expressivity enables support for a wide
range of data types while retaining the interpretability of decision trees. In
particular, when a grammar based on temporal logic is used, we show that GBDTs
can be used for the interpretable classi cation of high-dimensional and
heterogeneous time series data. Furthermore, we show how GBDTs can also be used
for categorization, which is a combination of clustering and generating
interpretable explanations for each cluster. We apply GBDTs to analyze the
classic Australian Sign Language dataset as well as data on near mid-air
collisions (NMACs). The NMAC data comes from aircraft simulations used in the
development of the next-generation Airborne Collision Avoidance System (ACAS
X).Comment: 9 pages, 5 figures, 2 tables, SIAM International Conference on Data
Mining (SDM) 201
Robust Decision Trees Against Adversarial Examples
Although adversarial examples and model robustness have been extensively
studied in the context of linear models and neural networks, research on this
issue in tree-based models and how to make tree-based models robust against
adversarial examples is still limited. In this paper, we show that tree based
models are also vulnerable to adversarial examples and develop a novel
algorithm to learn robust trees. At its core, our method aims to optimize the
performance under the worst-case perturbation of input features, which leads to
a max-min saddle point problem. Incorporating this saddle point objective into
the decision tree building procedure is non-trivial due to the discrete nature
of trees --- a naive approach to finding the best split according to this
saddle point objective will take exponential time. To make our approach
practical and scalable, we propose efficient tree building algorithms by
approximating the inner minimizer in this saddle point problem, and present
efficient implementations for classical information gain based trees as well as
state-of-the-art tree boosting models such as XGBoost. Experimental results on
real world datasets demonstrate that the proposed algorithms can substantially
improve the robustness of tree-based models against adversarial examples
On the GBDT version of the B\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory
A general theorem on the GBDT version of the B\"acklund-Darboux
transformation for systems rationally depending on the spectral parameter is
treated and its applications to nonlinear equations are given. Explicit
solutions of direct and inverse problems for Dirac-type systems, including
systems with singularities, and for the system auxiliary to the -wave
equation are reviewed. New results on explicit construction of the wave
functions for radial Dirac equation are obtained
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