29,531 research outputs found
Nonparametric likelihood based estimation of linear filters for point processes
We consider models for multivariate point processes where the intensity is
given nonparametrically in terms of functions in a reproducing kernel Hilbert
space. The likelihood function involves a time integral and is consequently not
given in terms of a finite number of kernel evaluations. The main result is a
representation of the gradient of the log-likelihood, which we use to derive
computable approximations of the log-likelihood and the gradient by time
discretization. These approximations are then used to minimize the approximate
penalized log-likelihood. For time and memory efficiency the implementation
relies crucially on the use of sparse matrices. As an illustration we consider
neuron network modeling, and we use this example to investigate how the
computational costs of the approximations depend on the resolution of the time
discretization. The implementation is available in the R package ppstat.Comment: 10 pages, 3 figure
A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates
We present an accurate and efficient method to calculate the gravitational
potential of an isolated system in three-dimensional Cartesian and cylindrical
coordinates subject to vacuum (open) boundary conditions. Our method consists
of two parts: an interior solver and a boundary solver. The interior solver
adopts an eigenfunction expansion method together with a tridiagonal matrix
solver to solve the Poisson equation subject to the zero boundary condition.
The boundary solver employs James's method to calculate the boundary potential
due to the screening charges required to keep the zero boundary condition for
the interior solver. A full computation of gravitational potential requires
running the interior solver twice and the boundary solver once. We develop a
method to compute the discrete Green's function in cylindrical coordinates,
which is an integral part of the James algorithm to maintain second-order
accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics
code, and perform various tests to check that our solver is second-order
accurate and exhibits good parallel performance.Comment: 24 pages, 13 figures; accepted for publication in ApJ
Balanced Quantization: An Effective and Efficient Approach to Quantized Neural Networks
Quantized Neural Networks (QNNs), which use low bitwidth numbers for
representing parameters and performing computations, have been proposed to
reduce the computation complexity, storage size and memory usage. In QNNs,
parameters and activations are uniformly quantized, such that the
multiplications and additions can be accelerated by bitwise operations.
However, distributions of parameters in Neural Networks are often imbalanced,
such that the uniform quantization determined from extremal values may under
utilize available bitwidth. In this paper, we propose a novel quantization
method that can ensure the balance of distributions of quantized values. Our
method first recursively partitions the parameters by percentiles into balanced
bins, and then applies uniform quantization. We also introduce computationally
cheaper approximations of percentiles to reduce the computation overhead
introduced. Overall, our method improves the prediction accuracies of QNNs
without introducing extra computation during inference, has negligible impact
on training speed, and is applicable to both Convolutional Neural Networks and
Recurrent Neural Networks. Experiments on standard datasets including ImageNet
and Penn Treebank confirm the effectiveness of our method. On ImageNet, the
top-5 error rate of our 4-bit quantized GoogLeNet model is 12.7\%, which is
superior to the state-of-the-arts of QNNs
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