Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

Nielsen, Frank; Sun, Ke

doi:10.20944/preprints201610.0086.v1

Cited by 14 publications

(6 citation statements)

References 39 publications

(12 reference statements)

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“…Each code is given equal initial weighting, assuming there are approximately equal amounts of each code, and an initial covariance matrix (default sigma: 10 −5 ). The GMM returns the assigned code for each bead and the log probability and probability of this assignment (using the LogSumExp algorithm, see scikit-learn documentation and [ 38 ]). Confidence interval ellipses for each cluster are calculated from the computed eigenvalues (magnitude in each direction, e .…”

Section: Experimental Methodsmentioning

confidence: 99%

An open-source software analysis package for Microspheres with Ratiometric Barcode Lanthanide Encoding (MRBLEs)

et al. 2019

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Multiplexed bioassays, in which multiple analytes of interest are probed in parallel within a single small volume, have greatly accelerated the pace of biological discovery. Bead-based multiplexed bioassays have many technical advantages, including near solution-phase kinetics, small sample volume requirements, many within-assay replicates to reduce measurement error, and, for some bead materials, the ability to synthesize analytes directly on beads via solid-phase synthesis. To allow bead-based multiplexing, analytes can be synthesized on spectrally encoded beads with a 1:1 linkage between analyte identity and embedded codes. Bead-bound analyte libraries can then be pooled and incubated with a fluorescently-labeled macromolecule of interest, allowing downstream quantification of interactions between the macromolecule and all analytes simultaneously via imaging alone. Extracting quantitative binding data from these images poses several computational image processing challenges, requiring the ability to identify all beads in each image, quantify bound fluorescent material associated with each bead, and determine their embedded spectral code to reveal analyte identities. Here, we present a novel open-source Python software package (the mrbles analysis package) that provides the necessary tools to: (1) find encoded beads in a bright-field microscopy image; (2) quantify bound fluorescent material associated with bead perimeters; (3) identify embedded ratiometric spectral codes within beads; and (4) return data aggregated by embedded code and for each individual bead. We demonstrate the utility of this package by applying it towards analyzing data generated via multiplexed measurement of calcineurin protein binding to MRBLEs (Microspheres with Ratiometric Barcode Lanthanide Encoding) containing known and mutant binding peptide motifs. We anticipate that this flexible package should be applicable to a wide variety of assays, including simple bead or droplet finding analysis, quantification of binding to non-encoded beads, and analysis of multiplexed assays that use ratiometric, spectrally encoded beads.

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Section: Experimental Methodsmentioning

confidence: 99%

An open-source software analysis package for Microspheres with Ratiometric Barcode Lanthanide Encoding (MRBLEs)

et al. 2019

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“…Consider a set

of n w -mixtures [ 56 ]. Because

is the negative differential entropy of a mixture (not available in closed form [ 106 ]), we approximate the untractable F by another close tractable generator

. We use Monte Carlo stochastic sampling to get Monte-Carlo convex

for an independent and identically distributed sample

.…”

Section: Some Applications Of Information Geometrymentioning

confidence: 99%

An Elementary Introduction to Information Geometry

Nielsen

2020

Entropy

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126

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“…The Rényi

-weighted mean

can be rewritten as

where function

denotes the log-sum-exp (convex) function [ 41 , 42 ].…”

Section: Rényi Entropy and Divergence And Sibson Information Radiusmentioning

confidence: 99%

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

Nielsen

2021

Entropy

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We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.

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Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

Cited by 14 publications

References 39 publications

An open-source software analysis package for Microspheres with Ratiometric Barcode Lanthanide Encoding (MRBLEs)

An open-source software analysis package for Microspheres with Ratiometric Barcode Lanthanide Encoding (MRBLEs)

An Elementary Introduction to Information Geometry

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

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