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John McKay

Publications and source records attributed to John McKay.

At least 19 recordsLinked to original sources

Towards Multi-Objective Statistically Fair Federated Learning

Federated Learning (FL) has emerged as a result of data ownership and privacy concerns to prevent data from being shared between multiple parties included in a training procedure. Although issues, such as privacy, have gained significant attention in this domain, not much attention has been given to satisfying statistical fairness measures in the FL setting. With this goal in mind, we conduct studies to show that FL is able to satisfy different fairness metrics under different data regimes consisting of different types of clients. More specifically, uncooperative or adversarial clients might contaminate the global FL model by injecting biased or poisoned models due to existing biases in their training datasets. Those biases might be a result of imbalanced training set (Zhang and Zhou 2019), historical biases (Mehrabi et al. 2021a), or poisoned data-points from data poisoning attacks against fairness (Mehrabi et al. 2021b; Solans, Biggio, and Castillo 2020). Thus, we propose a new FL framework that is able to satisfy multiple objectives including various statistical fairness metrics. Through experimentation, we then show the effectiveness of this method comparing it with various baselines, its ability in satisfying different objectives collectively and individually, and its ability in identifying uncooperative or adversarial clients and down-weighing their effect

cs.LG

Kashiwa Lectures on "New Approaches to the Monster"

These notes stem from lectures given by the first author (JM) at the 2008 "Moonshine Conference in Kashiwa" and contain a number of new perspectives and observations on Monstrous Moonshine. Because many new points have not appeared anywhere in print, it is thought expedient to update, annotate and clarify them (as footnotes), an editorial task which the second author (YHH) is more than delighted to undertake. We hope the various puzzles and correspondences, delivered in a personal and casual manner, will serve as diversions intriguing to the community.

math.HO

Cusps, Congruence Groups and Monstrous Dessins

We study general properties of the dessins d'enfants associated with the Hecke congruence subgroups $Γ_0(N)$ of the modular group $\mathrm{PSL}_2(\mathbb{R})$. The definition of the $Γ_0(N)$ as the stabilisers of couples of projective lattices in a two-dimensional vector space gives an interpretation of the quotient set $Γ_0(N)\backslash\mathrm{PSL}_2(\mathbb{R})$ as the projective lattices $N$-hyperdistant from a reference one, and hence as the projective line over the ring $\mathbb{Z}/N\mathbb{Z}$. The natural action of $\mathrm{PSL}_2(\mathbb{R})$ on the lattices defines a dessin d'enfant structure, allowing for a combinatorial approach to features of the classical modular curves, such as the torsion points and the cusps. We tabulate the dessins d'enfants associated with the $15$ Hecke congruence subgroups of genus zero, which arise in Moonshine for the Monster sporadic group.

math.NT

Formal Groups, Witt vectors and Free Probability

We establish a link between free probability theory and Witt vectors, via the theory of formal groups. We derive an exponential isomorphism which expresses Voiculescu's free multiplicative convolution $\boxtimes$ as a function of the free additive convolution $\boxplus$. Subsequently we continue our previous discussion of the relation between complex cobordism and free probability. We show that the generic $n$th free cumulant corresponds to the cobordism class of the $(n-1)$-dimensional complex projective space. This permits us to relate several probability distributions from random matrix theory to known genera, and to build a dictionary. Finally, we discuss aspects of free probability and the asymptotic representation theory of the symmetric group from a conformal field theoretic perspective and show that every distribution with mean zero is embeddable into the Universal Grassmannian of Sato-Segal-Wilson.

math.OA

Thresholded Non-Uniform Fourier Frame-Based Reconstruction for Stripmap SAR

Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame reconstruction algorithm, extending the non-uniform fast Fourier transform, to stripmap SAR data. Further, we present an improved thresholded frame reconstruction algorithm for robust performance and improved computational efficiency. We demonstrate compelling results on real stripmap SAR data.

eess.SP

Coupling Rendering and Generative Adversarial Networks for Artificial SAS Image Generation

Acquisition of Synthetic Aperture Sonar (SAS) datasets is bottlenecked by the costly deployment of SAS imaging systems, and even when data acquisition is possible,the data is often skewed towards containing barren seafloor rather than objects of interest. We present a novel pipeline, called SAS GAN, which couples an optical renderer with a generative adversarial network (GAN) to synthesize realistic SAS images of targets on the seafloor. This coupling enables high levels of SAS image realism while enabling control over image geometry and parameters. We demonstrate qualitative results by presenting examples of images created with our pipeline. We also present quantitative results through the use of t-SNE and the Fréchet Inception Distance to argue that our generated SAS imagery potentially augments SAS datasets more effectively than an off-the-shelf GAN.

eess.IV

Bridging the Gap: Simultaneous Fine Tuning for Data Re-Balancing

There are many real-world classification problems wherein the issue of data imbalance (the case when a data set contains substantially more samples for one/many classes than the rest) is unavoidable. While under-sampling the problematic classes is a common solution, this is not a compelling option when the large data class is itself diverse and/or the limited data class is especially small. We suggest a strategy based on recent work concerning limited data problems which utilizes a supplemental set of images with similar properties to the limited data class to aid in the training of a neural network. We show results for our model against other typical methods on a real-world synthetic aperture sonar data set. Code can be found at github.com/JohnMcKay/dataImbalance.

cs.CV

Erland Samuel Bring's "Transformation of Algebraic Equations"

We translate Erland Samuel Bring's treatise Meletemata quaedam Mathematica circa Transformationem Aequationum Alebraicarum (Some selected mathematics on the Transformation of Algebraic Equations) written as his Promotionschrift at the University of Lund in 1786, from its Latin into English, with modern mathematical notation. Bring (1736 - 98) made important contributions to algebraic equations and obtained the canonical form x^5+px+q = 0 for quintics before Jerrard, Ruffini and Abel. In due course, he realized the significance of the projective curve which now bears his name: the complete intersection of the homogeneous Fermat polynomials of degrees 1,2,3 in CP^4.

math.HO

Fast Stochastic Hierarchical Bayesian MAP for Tomographic Imaging

Any image recovery algorithm attempts to achieve the highest quality reconstruction in a timely manner. The former can be achieved in several ways, among which are by incorporating Bayesian priors that exploit natural image tendencies to cue in on relevant phenomena. The Hierarchical Bayesian MAP (HB-MAP) is one such approach which is known to produce compelling results albeit at a substantial computational cost. We look to provide further analysis and insights into what makes the HB-MAP work. While retaining the proficient nature of HB-MAP's Type-I estimation, we propose a stochastic approximation-based approach to Type-II estimation. The resulting algorithm, fast stochastic HB-MAP (fsHBMAP), takes dramatically fewer operations while retaining high reconstruction quality. We employ our fsHBMAP scheme towards the problem of tomographic imaging and demonstrate that fsHBMAP furnishes promising results when compared to many competing methods.

cs.CV

What's Mine is Yours: Pretrained CNNs for Limited Training Sonar ATR

Finding mines in Sonar imagery is a significant problem with a great deal of relevance for seafaring military and commercial endeavors. Unfortunately, the lack of enormous Sonar image data sets has prevented automatic target recognition (ATR) algorithms from some of the same advances seen in other computer vision fields. Namely, the boom in convolutional neural nets (CNNs) which have been able to achieve incredible results - even surpassing human actors - has not been an easily feasible route for many practitioners of Sonar ATR. We demonstrate the power of one avenue to incorporating CNNs into Sonar ATR: transfer learning. We first show how well a straightforward, flexible CNN feature-extraction strategy can be used to obtain impressive if not state-of-the-art results. Secondly, we propose a way to utilize the powerful transfer learning approach towards multiple instance target detection and identification within a provided synthetic aperture Sonar data set.

cs.CV

Using Frame Theoretic Convolutional Gridding for Robust Synthetic Aperture Sonar Imaging

Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent limitations to current SAS reconstruction methodology. In particular, popular and efficient Fourier domain SAS methods require a 2D interpolation which is often ill conditioned and inaccurate, inevitably reducing robustness with regard to speckle and inaccurate sound-speed estimation. To overcome these issues, we propose using the frame theoretic convolution gridding (FTCG) algorithm to handle the non-uniform Fourier data. FTCG extends upon non-uniform fast Fourier transform (NUFFT) algorithms by casting the NUFFT as an approximation problem given Fourier frame data. The FTCG has been show to yield improved accuracy at little more computational cost. Using simulated data, we outline how the FTCG can be used to enhance current SAS processing.

math.NA

Robust Sonar ATR Through Bayesian Pose Corrected Sparse Classification

Sonar imaging has seen vast improvements over the last few decades due in part to advances in synthetic aperture Sonar (SAS). Sophisticated classification techniques can now be used in Sonar automatic target recognition (ATR) to locate mines and other threatening objects. Among the most promising of these methods is sparse reconstruction-based classification (SRC) which has shown an impressive resiliency to noise, blur, and occlusion. We present a coherent strategy for expanding upon SRC for Sonar ATR that retains SRC's robustness while also being able to handle targets with diverse geometric arrangements, bothersome Rayleigh noise, and unavoidable background clutter. Our method, pose corrected sparsity (PCS), incorporates a novel interpretation of a spike and slab probability distribution towards use as a Bayesian prior for class-specific discrimination in combination with a dictionary learning scheme for localized patch extractions. Additionally, PCS offers the potential for anomaly detection in order to avoid false identifications of tested objects from outside the training set with no additional training required. Compelling results are shown using a database provided by the United States Naval Surface Warfare Center.

cs.CV

Localized Dictionary design for Geometrically Robust Sonar ATR

Advancements in Sonar image capture have opened the door to powerful classification schemes for automatic target recognition (ATR. Recent work has particularly seen the application of sparse reconstruction-based classification (SRC) to sonar ATR, which provides compelling accuracy rates even in the presence of noise and blur. Existing sparsity based sonar ATR techniques however assume that the test images exhibit geometric pose that is consistent with respect to the training set. This work addresses the outstanding open challenge of handling inconsistently posed test sonar images relative to training. We develop a new localized block-based dictionary design that can enable geometric, i.e. pose robustness. Further, a dictionary learning method is incorporated to increase performance and efficiency. The proposed SRC with Localized Pose Management (LPM), is shown to outperform the state of the art SIFT feature and SVM approach, due to its power to discern background clutter in Sonar images.

cs.CV

Discriminative Sparsity for Sonar ATR

Advancements in Sonar image capture have enabled researchers to apply sophisticated object identification algorithms in order to locate targets of interest in images such as mines. Despite progress in this field, modern sonar automatic target recognition (ATR) approaches lack robustness to the amount of noise one would expect in real-world scenarios, the capability to handle blurring incurred from the physics of image capture, and the ability to excel with relatively few training samples. We address these challenges by adapting modern sparsity-based techniques with dictionaries comprising of training from each class. We develop new discriminative (as opposed to generative) sparse representations which can help automatically classify targets in Sonar imaging. Using a simulated SAS data set from the Naval Surface Warfare Center (NSWC), we obtained compelling classification rates for multi-class problems even in cases with considerable noise and sparsity in training samples.

cs.CV

Homogeneous Lie Groups and Quantum Probability

Here we extend the algebro-geometric approach to free probability, started in~\cite{FMcK4,F14}, to general (non)-commutative probability theories. We show that any universal convolution product of moments of independent (non)-commutative random variables defined on a graded connected dual semi-group is given by a pro-unipotent group scheme. We show that moment-cumulant formulae have a natural interpretation within the theory of homogeneous Lie groups, which we generalise for the present purpose, and are given by the log and exp map, respectively. Finally, we briefly discuss the universal role of the shuffle Hopf algebra.

math.RT

Sporadic and Exceptional

We study the web of correspondences linking the exceptional Lie algebras $E_{8,7,6}$ and the sporadic simple groups Monster, Baby and the largest Fischer group. This is done via the investigation of classical enumerative problems on del Pezzo surfaces in relation to the cusps of certain subgroups of $PSL(2,R)$ for the relevant McKay-Thompson series in Generalized Moonshine. We also study Conway's sporadic group, as well as its association with the Horrocks-Mumford bundle.

math.AG

Moonshine and the Meaning of Life

With a jocund air, we present an observation on the first 24 coefficients of the modular invariant and of the modular discriminant. The observation is purely for the sake of entertainment and could be of some diversion to a mathematical audience.

math.NT

The Dynamics of Offensive Messages in the World of Social Media: the Control of Cyberbullying on Twitter

The 21st century has redefined the way we communicate, our concept of individual and group privacy, and the dynamics of acceptable behavioral norms. The messaging dynamics on Twitter, an internet social network, has opened new ways/modes of spreading information. As a result cyberbullying or in general, the spread of offensive messages, is a prevalent problem. The aim of this report is to identify and evaluate conditions that would dampen the role of cyberbullying dynamics on Twitter. We present a discrete-time non-linear compartmental model to explore how the introduction of a Quarantine class may help to hinder the spread of offensive messages. We based the parameters of this model on recent Twitter data related to a topic that communities would deem most offensive, and found that for Twitter a level of quarantine can always be achieved that will immediately suppress the spread of offensive messages, and that this level of quarantine is independent of the number of offenders spreading the message. We hope that the analysis of this dynamic model will shed some insights into the viability of new models of methods for reducing cyberbullying in public social networks.

cs.SI