An official website of the United States government
Abstract Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The transform is defined by computing the optimal transport of each distribution to a fixed reference distribution and has a number of benefits when it comes to speed of computation and to determining classification boundaries. In this paper, we characterize a number of settings in which LOT embeds families of distributions into a space in which they are linearly separable. This is true in arbitrary dimension, and for families of distributions generated through perturbations of shifts and scalings of a fixed distribution. We also prove conditions under which the $L^2$ distance of the LOT embedding between two distributions in arbitrary dimension is nearly isometric to Wasserstein-2 distance between those distributions. This is of significant computational benefit, as one must only compute $$N$$ optimal transport maps to define the $N^2$ pairwise distances between $$N$$ distributions. We demonstrate the benefits of LOT on a number of distribution classification problems.
more »
« less
Better Input Modeling via Model Averaging
Rather than the standard practice of selecting a single “best-fit” distribution from a candidate set, frequentist model averaging (FMA) forms a mixture distribution that is a weighted average of the candidate distributions with the weights tuned by cross-validation. In previous work we showed theoretically and empirically that FMA in the probability space leads to higher fidelity input distributions. In this paper we show that FMA can also be implemented in the quantile space, leading to fits that emphasize tail behavior. We also describe an R package for FMA that is easy to use and available for download.
more »
« less
- Award ID(s):
- 1634982
- PAR ID:
- 10122981
- Date Published:
- Journal Name:
- Proceedings of the 2018 Winter Simulation Conference
- Page Range / eLocation ID:
- 1575-1586
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The majority of state-of-the-art deep learning methods are discriminative approaches, which model the conditional distribution of labels given inputs features. The success of such approaches heavily depends on high-quality labeled instances, which are not easy to obtain, especially as the number of candidate classes increases. In this paper, we study the complementary learning problem. Unlike ordinary labels, complementary labels are easy to obtain because an annotator only needs to provide a yes/no answer to a randomly chosen candidate class for each instance. We propose a generative-discriminative complementary learning method that estimates the ordinary labels by modeling both the conditional (discriminative) and instance (generative) distributions. Our method, we call Complementary Conditional GAN (CCGAN), improves the accuracy of predicting ordinary labels and is able to generate high-quality instances in spite of weak supervision. In addition to the extensive empirical studies, we also theoretically show that our model can retrieve the true conditional distribution from the complementarily-labeled data.more » « less
-
Random values from discrete distributions are typically generated from uniformly-random samples. A common technique is to use a cumulative distribution table (CDT) lookup for inversion sampling, but it is also possible to use Boolean functions to map a uniformly-random bit sequence into a value from a discrete distribution. This work presents a methodology for deriving such functions for any discrete distribution, encoding them in VHDL for implementation in combinational hardware, and (for moderate precision and sample space size) confirming the correctness of the produced distribution. The process is demonstrated using a discrete Gaussian distribution with a small sample space, but it is applicable to any discrete distribution with fixed parameters. Results are presented for sampling schemes from several submissions to the NIST PQC standardization process, comparing this method to CDT lookups on a Xilinx Artix-7 FPGA. The process produces compact solutions for distributions up to moderate size and precision.more » « less
-
ABSTRACT We present new Large Binocular Telescope, Hubble Space Telescope, and Spitzer Space Telescope data for the failed supernova candidate N6946-BH1. We also report an unsuccessful attempt to detect the candidate with Chandra. The ∼300 000 $$\, \mathrm{L}_\odot$$ red supergiant progenitor underwent an outburst in 2009 and has since disappeared in the optical. In the LBT data from 2008 May through 2019 October, the upper limit on any increase in the R-band luminosity of the source is $$2000 \, \mathrm{L}_\odot$$. HST and Spitzer observations show that the source continued to fade in the near-IR and mid-IR, fading by approximately a factor of 2 between 2015 October and 2017 September to 2900 $$\, \mathrm{L}_\odot$$ at Hband (F160W). Models of the spectral energy distribution are inconsistent with a surviving star obscured either by an ongoing wind or dust formed in the transient. The disappearance of N6946-BH1 remains consistent with a failed supernova, but the post-failure phenomenology requires further theoretical study.more » « less
-
Failure time data of fielded systems are usually obtained from the actual users of the systems. Due to various operational preferences and/or technical obstacles, a large proportion of field data are collected as aggregate data instead of the exact failure times of individual units. The challenge of using such data is that the obtained information is more concise but less precise in comparison to using individual failure times. The most significant needs in modeling aggregate failure time data are the selection of an appropriate probability distribution and the development of a statistical inference procedure capable of handling data aggregation. Although some probability distributions, such as the Gamma and Inverse Gaussian distributions, have well-known closed-form expressions for the probability density function for aggregate data, the use of such distributions limits the applications in field reliability estimation. For reliability practitioners, it would be invaluable to use a robust approach to handle aggregate failure time data without being limited to a small number of probability distributions. This paper studies the application of phase-type (PH) distribution as a candidate for modeling aggregate failure time data. An expectation-maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters, and the confidence interval for the reliability estimate is also obtained. The simulation and numerical studies show that the robust approach is quite powerful because of the high capability of PH distribution in mimicking a variety of probability distributions. In the area of reliability engineering, there is limited work on modeling aggregate data for field reliability estimation. The analytical and statistical inference methods described in this work provide a robust tool for analyzing aggregate failure time data for the first time.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
