The most recent list can be found on on google scholar.
Brofos, James A; Brubaker, Marcus A; Lederman, Roy R
Manifold Density Estimation via Generalized Dequantization Technical Report
2021, (arXiv: 2102.07143).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Machine Learning, Density estimation, Manifolds, Statistics - Machine Learning
@techreport{brofos_manifold_2021,
title = {Manifold Density Estimation via Generalized Dequantization},
author = {James A Brofos and Marcus A Brubaker and Roy R Lederman},
url = {http://arxiv.org/abs/2102.07143},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-14},
abstract = {Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are not well-modeled by supposing that their underlying geometry is Euclidean. Instead, it can be useful to model such data as lying on a textbackslashit manifold with some known structure. For instance, some kinds of data may be known to lie on the surface of a sphere. We study the problem of estimating densities on manifolds. We propose a method, inspired by the literature on "dequantization," which we interpret through the lens of a coordinate transformation of an ambient Euclidean space and a smooth manifold of interest. Using methods from normalizing flows, we apply this method to the dequantization of smooth manifold structures in order to model densities on the sphere, tori, and the orthogonal group.},
note = {arXiv: 2102.07143},
keywords = {Algorithms, Computer Science - Machine Learning, Density estimation, Manifolds, Statistics - Machine Learning},
pubstate = {published},
tppubtype = {techreport}
}
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are not well-modeled by supposing that their underlying geometry is Euclidean. Instead, it can be useful to model such data as lying on a textbackslashit manifold with some known structure. For instance, some kinds of data may be known to lie on the surface of a sphere. We study the problem of estimating densities on manifolds. We propose a method, inspired by the literature on "dequantization," which we interpret through the lens of a coordinate transformation of an ambient Euclidean space and a smooth manifold of interest. Using methods from normalizing flows, we apply this method to the dequantization of smooth manifold structures in order to model densities on the sphere, tori, and the orthogonal group.
Brofos, James A; Lederman, Roy R
Magnetic Manifold Hamiltonian Monte Carlo Technical Report
2020, (arXiv: 2010.07753).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Machine Learning, HMC, Manifolds, MCMC, Statistics - Machine Learning
@techreport{brofos_magnetic_2020,
title = {Magnetic Manifold Hamiltonian Monte Carlo},
author = {James A Brofos and Roy R Lederman},
url = {http://arxiv.org/abs/2010.07753},
year = {2020},
date = {2020-10-01},
urldate = {2020-11-25},
abstract = {Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit improved mixing properties. The recently introduced magnetic HMC, a generalization of HMC motivated by the physics of particles influenced by magnetic field forces, has been demonstrated to improve the performance of HMC. In many applications, one wishes to sample from a distribution restricted to a constrained set, often manifested as an embedded manifold (for example, the surface of a sphere). We introduce magnetic manifold HMC, an HMC algorithm on embedded manifolds motivated by the physics of particles constrained to a manifold and moving under magnetic field forces. We discuss the theoretical properties of magnetic Hamiltonian dynamics on manifolds, and introduce a reversible and symplectic integrator for the HMC updates. We demonstrate that magnetic manifold HMC produces favorable sampling behaviors relative to the canonical variant of manifold-constrained HMC.},
note = {arXiv: 2010.07753},
keywords = {Algorithms, Computer Science - Machine Learning, HMC, Manifolds, MCMC, Statistics - Machine Learning},
pubstate = {published},
tppubtype = {techreport}
}
Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit improved mixing properties. The recently introduced magnetic HMC, a generalization of HMC motivated by the physics of particles influenced by magnetic field forces, has been demonstrated to improve the performance of HMC. In many applications, one wishes to sample from a distribution restricted to a constrained set, often manifested as an embedded manifold (for example, the surface of a sphere). We introduce magnetic manifold HMC, an HMC algorithm on embedded manifolds motivated by the physics of particles constrained to a manifold and moving under magnetic field forces. We discuss the theoretical properties of magnetic Hamiltonian dynamics on manifolds, and introduce a reversible and symplectic integrator for the HMC updates. We demonstrate that magnetic manifold HMC produces favorable sampling behaviors relative to the canonical variant of manifold-constrained HMC.
Bandeira, Afonso S; Chen, Yutong; Lederman, Roy R; Singer, Amit
Non-unique games over compact groups and orientation estimation in cryo-EM Journal Article
In: Inverse Problems, vol. 36, no. 6, pp. 064002, 2020, ISSN: 0266-5611, 1361-6420.
Links | BibTeX | Tags: Algorithms, cryo-EM, Non-unique games, Representation Theory
@article{bandeira_non-unique_2020,
title = {Non-unique games over compact groups and orientation estimation in cryo-EM},
author = {Afonso S Bandeira and Yutong Chen and Roy R Lederman and Amit Singer},
url = {https://iopscience.iop.org/article/10.1088/1361-6420/ab7d2c},
doi = {10.1088/1361-6420/ab7d2c},
issn = {0266-5611, 1361-6420},
year = {2020},
date = {2020-01-01},
urldate = {2020-08-13},
journal = {Inverse Problems},
volume = {36},
number = {6},
pages = {064002},
keywords = {Algorithms, cryo-EM, Non-unique games, Representation Theory},
pubstate = {published},
tppubtype = {article}
}
Brofos, James A; Lederman, Roy R
Non-Canonical Hamiltonian Monte Carlo Technical Report
2020, (arXiv: 2008.08191).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Machine Learning, HMC, MCMC, Statistics - Machine Learning
@techreport{brofos_non-canonical_2020,
title = {Non-Canonical Hamiltonian Monte Carlo},
author = {James A Brofos and Roy R Lederman},
url = {http://arxiv.org/abs/2008.08191},
year = {2020},
date = {2020-01-01},
urldate = {2020-11-25},
abstract = {Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These non-canonical dynamics, motivated by examples in physics and symplectic geometry, correspond to techniques such as preconditioning which are routinely used to improve algorithmic performance. Indeed, recently, a special case of non-canonical structure, magnetic Hamiltonian Monte Carlo, was demonstrated to provide advantageous sampling properties. We present a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures. Our experimental results demonstrate sampling advantages associated to Hamiltonian Monte Carlo with non-canonical structure. To summarize our contributions: (i) we develop non-canonical HMC from foundations in symplectic geomtry; (ii) we construct an HMC procedure using implicit integration that satisfies the detailed balance; (iii) we propose to accelerate the sampling using an textbackslashem approximate explicit methodology; (iv) we study two novel, randomly-generated non-canonical structures: magnetic momentum and the coupled magnet structure, with implicit and explicit integration.},
note = {arXiv: 2008.08191},
keywords = {Algorithms, Computer Science - Machine Learning, HMC, MCMC, Statistics - Machine Learning},
pubstate = {published},
tppubtype = {techreport}
}
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These non-canonical dynamics, motivated by examples in physics and symplectic geometry, correspond to techniques such as preconditioning which are routinely used to improve algorithmic performance. Indeed, recently, a special case of non-canonical structure, magnetic Hamiltonian Monte Carlo, was demonstrated to provide advantageous sampling properties. We present a framework for Hamiltonian Monte Carlo using non-canonical symplectic structures. Our experimental results demonstrate sampling advantages associated to Hamiltonian Monte Carlo with non-canonical structure. To summarize our contributions: (i) we develop non-canonical HMC from foundations in symplectic geomtry; (ii) we construct an HMC procedure using implicit integration that satisfies the detailed balance; (iii) we propose to accelerate the sampling using an textbackslashem approximate explicit methodology; (iv) we study two novel, randomly-generated non-canonical structures: magnetic momentum and the coupled magnet structure, with implicit and explicit integration.
Lederman, Roy R; Singer, Amit
A representation theory perspective on simultaneous alignment and classification Journal Article
In: Applied and Computational Harmonic Analysis, vol. 49, no. 3, pp. 1001–1024, 2020, ISSN: 1063-5203.
Abstract | Links | BibTeX | Tags: Algorithms, Alignment, Classification, cryo-EM, Graph-cut, heterogeneity, Heterogeneous multireference alignment, Representation Theory, Rotation group, SDP, Synchronization
@article{lederman_representation_2020,
title = {A representation theory perspective on simultaneous alignment and classification},
author = {Roy R Lederman and Amit Singer},
url = {http://www.sciencedirect.com/science/article/pii/S1063520319301034},
doi = {10.1016/j.acha.2019.05.005},
issn = {1063-5203},
year = {2020},
date = {2020-01-01},
urldate = {2021-01-22},
journal = {Applied and Computational Harmonic Analysis},
volume = {49},
number = {3},
pages = {1001--1024},
abstract = {Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The problem of orientation assignment for the images motivated work on multireference alignment. The recent non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation with certificates of global optimality in some cases. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct conformations of molecules. Taking advantage of this opportunity presents an algorithmic challenge: determining both the class and orientation of each particle. We generalize multireference alignment to a problem of alignment and classification, and propose to extend non-unique games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying cryo-EM images and aligning them within their classes.},
keywords = {Algorithms, Alignment, Classification, cryo-EM, Graph-cut, heterogeneity, Heterogeneous multireference alignment, Representation Theory, Rotation group, SDP, Synchronization},
pubstate = {published},
tppubtype = {article}
}
Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The problem of orientation assignment for the images motivated work on multireference alignment. The recent non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation with certificates of global optimality in some cases. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct conformations of molecules. Taking advantage of this opportunity presents an algorithmic challenge: determining both the class and orientation of each particle. We generalize multireference alignment to a problem of alignment and classification, and propose to extend non-unique games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying cryo-EM images and aligning them within their classes.
Lederman, Roy R; Talmon, Ronen
Learning the geometry of common latent variables using alternating-diffusion Journal Article
In: Applied and Computational Harmonic Analysis, vol. 44, no. 3, pp. 509–536, 2018, ISSN: 1063-5203.
Abstract | Links | BibTeX | Tags: Algorithms, Alternating Diffusion, Alternating-diffusion, Common variable, diffusion maps, Diffusion-maps, Multi-view, multimodal, Multimodal analysis
@article{lederman_learning_2018,
title = {Learning the geometry of common latent variables using alternating-diffusion},
author = {Roy R Lederman and Ronen Talmon},
url = {http://www.sciencedirect.com/science/article/pii/S1063520315001190},
doi = {10.1016/j.acha.2015.09.002},
issn = {1063-5203},
year = {2018},
date = {2018-01-01},
urldate = {2020-08-13},
journal = {Applied and Computational Harmonic Analysis},
volume = {44},
number = {3},
pages = {509--536},
abstract = {One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a data-driven method based on alternating products of diffusion operators and show that it extracts the common source of variability. Moreover, we show that it extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.},
keywords = {Algorithms, Alternating Diffusion, Alternating-diffusion, Common variable, diffusion maps, Diffusion-maps, Multi-view, multimodal, Multimodal analysis},
pubstate = {published},
tppubtype = {article}
}
One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a data-driven method based on alternating products of diffusion operators and show that it extracts the common source of variability. Moreover, we show that it extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.
Lederman, Roy R
Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions Technical Report
2017.
Abstract | Links | BibTeX | Tags: Algorithms, cryo-EM, Fourier Transform, Numerical Analysis, Prolate, Slepian, Software
@techreport{lederman_numerical_2017,
title = {Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions},
author = {Roy R Lederman},
url = {https://arxiv.org/abs/1710.02874v1},
year = {2017},
date = {2017-10-01},
urldate = {2020-08-13},
abstract = {Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the
truncated Fourier transform, restricted to D-dimensional balls in the spatial
domain and frequency domain. Despite their useful properties in many
applications, GPSFs are often replaced by crude approximations. The purpose of
this paper is to review the elements of computing GPSFs and associated
eigenvalues. This paper is accompanied by open-source code.},
keywords = {Algorithms, cryo-EM, Fourier Transform, Numerical Analysis, Prolate, Slepian, Software},
pubstate = {published},
tppubtype = {techreport}
}
Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the
truncated Fourier transform, restricted to D-dimensional balls in the spatial
domain and frequency domain. Despite their useful properties in many
applications, GPSFs are often replaced by crude approximations. The purpose of
this paper is to review the elements of computing GPSFs and associated
eigenvalues. This paper is accompanied by open-source code.
truncated Fourier transform, restricted to D-dimensional balls in the spatial
domain and frequency domain. Despite their useful properties in many
applications, GPSFs are often replaced by crude approximations. The purpose of
this paper is to review the elements of computing GPSFs and associated
eigenvalues. This paper is accompanied by open-source code.
Lederman, Roy R; Singer, Amit
A Representation Theory Perspective on Simultaneous Alignment and Classification Technical Report
no. arXiv:1607.03464 [cs, math], 2016, (arXiv: 1607.03464).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Computer Vision and Pattern Recognition, cryo-EM, Mathematics - Optimization and Control, Representation Theory
@techreport{lederman_representation_2016,
title = {A Representation Theory Perspective on Simultaneous Alignment and Classification},
author = {Roy R Lederman and Amit Singer},
url = {http://arxiv.org/abs/1607.03464},
year = {2016},
date = {2016-07-01},
urldate = {2021-01-22},
number = {arXiv:1607.03464 [cs, math]},
abstract = {One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule. Many algorithms for the reconstruction of molecules from images in heterogeneous Cryo-EM experiments are based on iterative approximations of the molecules in a non-convex optimization that is prone to reaching suboptimal local minima. Other algorithms require an alignment in order to perform classification, or vice versa. The recently introduced Non-Unique Games framework provides a representation theoretic approach to studying problems of alignment over compact groups, and offers convex relaxations for alignment problems which are formulated as semidefinite programs (SDPs) with certificates of global optimality under certain circumstances. In this manuscript, we propose to extend Non-Unique Games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying Cryo-EM images and aligning them within their respective classes. Our proposed approach can also be extended to the case of continuous heterogeneity.},
note = {arXiv: 1607.03464},
keywords = {Algorithms, Computer Science - Computer Vision and Pattern Recognition, cryo-EM, Mathematics - Optimization and Control, Representation Theory},
pubstate = {published},
tppubtype = {techreport}
}
One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule. Many algorithms for the reconstruction of molecules from images in heterogeneous Cryo-EM experiments are based on iterative approximations of the molecules in a non-convex optimization that is prone to reaching suboptimal local minima. Other algorithms require an alignment in order to perform classification, or vice versa. The recently introduced Non-Unique Games framework provides a representation theoretic approach to studying problems of alignment over compact groups, and offers convex relaxations for alignment problems which are formulated as semidefinite programs (SDPs) with certificates of global optimality under certain circumstances. In this manuscript, we propose to extend Non-Unique Games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying Cryo-EM images and aligning them within their respective classes. Our proposed approach can also be extended to the case of continuous heterogeneity.
Lederman, Roy R; Rokhlin, V
On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II Journal Article
In: SIAM Journal on Numerical Analysis, vol. 54, no. 2, pp. 665–687, 2016, ISSN: 0036-1429, 1095-7170.
Links | BibTeX | Tags: Algorithms, Laplace Transform, Numerical Analysis
@article{lederman_analytical_2016,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II},
author = {Roy R Lederman and V Rokhlin},
url = {http://epubs.siam.org/doi/10.1137/15M1028583},
doi = {10.1137/15M1028583},
issn = {0036-1429, 1095-7170},
year = {2016},
date = {2016-01-01},
urldate = {2020-08-13},
journal = {SIAM Journal on Numerical Analysis},
volume = {54},
number = {2},
pages = {665--687},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}
Lederman, Roy R; Rokhlin, V
On the Analytical and Numerical Properties of the Truncated Laplace Transform I. Journal Article
In: SIAM Journal on Numerical Analysis, vol. 53, no. 3, pp. 1214–1235, 2015, ISSN: 0036-1429, 1095-7170.
Links | BibTeX | Tags: Algorithms, Laplace Transform, Numerical Analysis
@article{lederman_analytical_2015,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform I.},
author = {Roy R Lederman and V Rokhlin},
url = {http://epubs.siam.org/doi/10.1137/140990681},
doi = {10.1137/140990681},
issn = {0036-1429, 1095-7170},
year = {2015},
date = {2015-01-01},
urldate = {2020-08-13},
journal = {SIAM Journal on Numerical Analysis},
volume = {53},
number = {3},
pages = {1214--1235},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}
Lederman, Roy R; Talmon, Ronen
Common Manifold Learning Using Alternating-Diffusion Technical Report
Yale CS no. YALEU/DCS/TR-1497, 2014.
Links | BibTeX | Tags: AD, Algorithms, Alternating Diffusion, Manifold Learning
@techreport{lederman_common_2014,
title = {Common Manifold Learning Using Alternating-Diffusion},
author = {Roy R Lederman and Ronen Talmon},
url = {https://cpsc.yale.edu/sites/default/files/files/tr1497.pdf},
year = {2014},
date = {2014-01-01},
number = {YALEU/DCS/TR-1497},
pages = {42},
institution = {Yale CS},
keywords = {AD, Algorithms, Alternating Diffusion, Manifold Learning},
pubstate = {published},
tppubtype = {techreport}
}
Lederman, Roy R
On the Analytical and Numerical Properties of the Truncated Laplace Transform PhD Thesis
Yale University, 2014, (YALEU/DCS/TR-1490).
BibTeX | Tags: Algorithms, Laplace Transform, Numerical Analysis
@phdthesis{lederman_analytical_2014,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform},
author = {Roy R Lederman},
year = {2014},
date = {2014-01-01},
school = {Yale University},
note = {YALEU/DCS/TR-1490},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {phdthesis}
}
Lederman, Roy R
A permutations-based algorithm for fast alignment of long paired-end reads Technical Report
Yale CS no. YALEU/DCS/TR-1474, 2013.
BibTeX | Tags: Algorithms, DNA sequencing, Fast algorithms, Randomized algorithms, Sequencing
@techreport{lederman_permutations-based_2013,
title = {A permutations-based algorithm for fast alignment of long paired-end reads},
author = {Roy R Lederman},
year = {2013},
date = {2013-04-01},
number = {YALEU/DCS/TR-1474},
pages = {11},
institution = {Yale CS},
keywords = {Algorithms, DNA sequencing, Fast algorithms, Randomized algorithms, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}
Lederman, Roy R
Homopolymer Length Filters Technical Report
Yale CS no. YALEU/DCS/TR-1465, 2012.
BibTeX | Tags: Algorithms, DNA sequencing, Sequence Alignment, Sequencing
@techreport{lederman_homopolymer_2012,
title = {Homopolymer Length Filters},
author = {Roy R Lederman},
year = {2012},
date = {2012-10-01},
number = {YALEU/DCS/TR-1465},
pages = {12},
institution = {Yale CS},
keywords = {Algorithms, DNA sequencing, Sequence Alignment, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}