arXiv subjects

L. Crow

Publications and source records attributed to L. Crow.

5 recordsLinked to original sources

arXiv2024

An information theoretic limit to data amplification

In recent years generative artificial intelligence has been used to create data to support science analysis. For example, Generative Adversarial Networks (GANs) have been trained using Monte Carlo simulated input and then used to generate data for the same problem. This has the advantage that a GAN creates data in a significantly reduced computing time. N training events for a GAN can result in GN generated events with the gain factor, G, being more than one. This appears to violate the principle that one cannot get information for free. This is not the only way to amplify data so this process will be referred to as data amplification which is studied using information theoretic concepts. It is shown that a gain of greater than one is possible whilst keeping the information content of the data unchanged. This leads to a mathematical bound which only depends on the number of generated and training events. This study determines conditions on both the underlying and reconstructed probability distributions to ensure this bound. In particular, the resolution of variables in amplified data is not improved by the process but the increase in sample size can still improve statistical significance. The bound is confirmed using computer simulation and analysis of GAN generated data from the literature.

stat.ML↗

arXiv2024

Limits to classification performance by relating Kullback-Leibler divergence to Cohen's Kappa

The performance of machine learning classification algorithms are evaluated by estimating metrics, often from the confusion matrix, using training data and cross-validation. However, these do not prove that the best possible performance has been achieved. Fundamental limits to error rates can be estimated using information distance measures. To this end, the confusion matrix has been formulated to comply with the Chernoff-Stein Lemma. This links the error rates to the Kullback-Leibler divergences between the probability density functions describing the two classes. This leads to a key result that relates Cohen's Kappa to the Resistor Average Distance which is the parallel resistor combination of the two Kullback-Leibler divergences. The Resistor Average Distance has units of bits and is estimated from the same training data used by the classification algorithm, using kNN estimates of the KullBack-Leibler divergences. The classification algorithm gives the confusion matrix and Kappa. Theory and methods are discussed in detail and then applied to Monte Carlo data and real datasets. Four very different real datasets - Breast Cancer, Coronary Heart Disease, Bankruptcy, and Particle Identification - are analysed, with both continuous and discrete values, and their classification performance compared to the expected theoretical limit. In all cases this analysis shows that the algorithms could not have performed any better due to the underlying probability density functions for the two classes. Important lessons are learnt on how to predict the performance of algorithms for imbalanced data using training datasets that are approximately balanced. Machine learning is very powerful but classification performance ultimately depends on the quality of the data and the relevance of the variables to the problem.

stat.ML↗

arXiv2019

Big Variates: Visualizing and identifying key variables in a multivariate world

Big Data involves both a large number of events but also many variables. This paper will concentrate on the challenge presented by the large number of variables in a Big Dataset. It will start with a brief review of exploratory data visualisation for large dimensional datasets and the use of parallel coordinates. This motivates the use of information theoretic ideas to understand multivariate data. Two key information-theoretic statistics (Similarity Index and Class Distance Indicator) will be described which are used to identify the key variables and then guide the user in a subsequent machine learning analysis. Key to the approach is a novel algorithm to histogram data which quantifies the information content of the data. The Class Distance Indicator also sets a limit on the classification performance of machine learning algorithms for the specific dataset.

stat.AP↗

arXiv2017

New Search for Mirror Neutrons at HFIR

The theory of mirror matter predicts a hidden sector made up of a copy of the Standard Model particles and interactions but with opposite parity. If mirror matter interacts with ordinary matter, there could be experimentally accessible implications in the form of neutral particle oscillations. Direct searches for neutron oscillations into mirror neutrons in a controlled magnetic field have previously been performed using ultracold neutrons in storage/disappearance measurements, with some inconclusive results consistent with characteristic oscillation time of $\tau$$\sim$10~s. Here we describe a proposed disappearance and regeneration experiment in which the neutron oscillates to and from a mirror neutron state. An experiment performed using the existing General Purpose-Small Angle Neutron Scattering instrument at the High Flux Isotope Reactor at Oak Ridge National Laboratory could have the sensitivity to exclude up to $\tau$$<$15~s in 1 week of beamtime and at low cost.

hep-ex↗

arXiv2011

Tests of Modulated Intensity Small Angle Scattering in time of flight mode

We report results of tests of the MISANS technique at the CG-1D beamline at High Flux Isotope Reactor (HFIR), Oak Ridge National Laboratory (ORNL). A chopper at 40 Hz simulated a pulsed neutron source at the beamline. A compact turn-key MISANS module operating with the pulsed beam was installed and a well characterised MnSi sample was tested. The feasibility of application of high magnetic fields at the sample position was also explored. These tests demonstrate the great potential of this technique, in particular for examining magnetic and depolarizing samples, under extreme sample environments at pulsed sources, such as the Spallation Neutron Source (SNS) or the planned European Spallation Source (ESS).

physics.ins-det↗