From interpretability to inference: an estimation framework for
universal approximators
March 11, 2019
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Statistics
Computer Science
Economics
Machine Learning
Machine Learning
Econometrics
Machine Learning
Machine Learning
Econometrics
We present a novel framework for estimation and inference for the broad class
of universal approximators. Estimation is based on the decomposition of model
predictions into Shapley values. Inference relies on analyzing the bias and
variance...
A hybridizable discontinuous Galerkin method for the indefinite
time-harmonic Maxwell equations
March 11, 2019
| | | | |
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Numerical Analysis
Numerical Analysis
In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG)
method for the indefinite time-harmonic Maxwell equations with the perfectly
conducting boundary in the three-dimensional space. First, we derive the
wavenumber ex...
Picard groups, pull back and class groups
March 11, 2019
|
Mathematics
Algebraic Geometry
Number Theory
Let S be a certain affine algebraic surface over Q such that it
admits a regular map to A2/Q. We show that any non-trivial
torsion line bundle in the relative Picard group
Pic0(S/A2)...
Polyhedral products and features of their homotopy theory
March 10, 2019
| |
Mathematics
Algebraic Topology
Commutative Algebra
Combinatorics
History and Overview
A polyhedral product is a natural subspace of a Cartesian product that is
specified by a simplicial complex. The modern formalism arose as a
generalization of the spaces known as moment-angle complexes which were
developed within the nascen...
The twisted second moment of modular half integral weight L--functions
March 8, 2019
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Mathematics
Number Theory
Given a half-integral weight holomorphic Kohnen newform f on Γ0(4),
we prove an asymptotic formula for large primes p with power saving error
term for \begin{equation*} \sideset{}{^*} \sum_{\chi \hspace{-0.15cm} \pmod{p}}
| L(1/...
Ordinary and Prophet Planning under Uncertainty in Bernoulli Congestion
Games
March 8, 2019
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Computer Science
Mathematics
Computer Science and Game Theory
Probability
We consider an atomic congestion game in which each player i participates
in the game with an exogenous and known probability pi∈(0,1],
independently of everybody else, or stays out and incurs no cost. We compute
the parameterized ...
On the asymptotic normality of persistent Betti numbers
March 7, 2019
|
Mathematics
Statistics
Probability
Statistics Theory
Statistics Theory
Persistent Betti numbers are a major tool in persistent homology, a subfield
of topological data analysis. Many tools in persistent homology rely on the
properties of persistent Betti numbers considered as a two-dimensional
stochastic proce...
A face cover perspective to ℓ1 embeddings of planar graphs
March 7, 2019
Computer Science
Data Structures and Algorithms
Computational Geometry
It was conjectured by Gupta et al. [Combinatorica04] that every planar graph
can be embedded into ℓ1 with constant distortion. However, given an
n-vertex weighted planar graph, the best upper bound on the distortion is
only $O(\sqrt...
Infinitely many solutions for a Schrodinger equation with sign-changing
potential and nonlinear term
March 7, 2019
|
Mathematics
Functional Analysis
Analysis of PDEs
We propose a new variational approach to finding multiple critical points for
strongly indefinite problems without assuming the weak upper semicontinuity on
the variational functionals. By this approach, we obtain the existence of
infinitel...
On the Time-Range Dependency of the Beampatterns Produced by Arbitrary
Antenna Arrays: Discussions on the Misplaced Expectations from Frequency
Diverse Arrays
March 6, 2019
Physics
Classical Physics
In the recent years constructing time-invariant spatial-focusing beampatterns
by using frequency diverse arrays (FDAs) is conveyed in several papers. Further
than time-invariant spatial-focusing beampatterns, the unfeasibility of
constructi...