arXiv subjects

Kenric Nelson

Publications and source records attributed to Kenric Nelson.

4 recordsLinked to original sources

arXiv2025

Variational Inference Optimized Using the Curved Geometry of Coupled Free Energy

We introduce an optimization framework for variational inference based on the coupled free energy, extending variational inference techniques to account for the curved geometry of the coupled exponential family. This family includes important heavy-tailed distributions such as the generalized Pareto and the Student's t. By leveraging the coupled free energy, which is equal to the coupled evidence lower bound (ELBO) of the inverted probabilities, we improve the accuracy and robustness of the learned model. The coupled generalization of Fisher Information metric and the affine connection. The method is applied to the design of a coupled variational autoencoder (CVAE). By using the coupling for both the distributions and cost functions, the reconstruction metric is derived to still be the mean-square average loss with modified constants. The novelty comes from sampling the heavy-tailed latent distribution with its associated coupled probability, which has faster decaying tails. The result is the ability to train a model robust against severe outliers, while assuring that the training process is stable. The Wasserstein-2 or Fr\'echet Inception Distance of the reconstructed CelebA images shows the CVAE has a 3\% improvement over the VAE after 5 epochs of training.

cs.LG↗

arXiv2025

Enhancing Decentralization in Blockchain Decision-Making Through Quadratic Voting and Its Generalization

This study explores the application of Quadratic Voting (QV) and its generalization to improve decentralization and effectiveness in blockchain governance systems. The conducted research identified three main types of quadratic (square root) voting. Two of them pertain to voting with a split stake, and one involves voting without splitting. In split stakes, Type 1 QV applies the square root to the total stake before distributing it among preferences, while Type 2 QV distributes the stake first and then applies the square root. In unsplit stakes (Type 3 QV), the square root of the total stake is allocated entirely to each preference. The presented formal proofs confirm that Types 2 and 3 QV, along with generalized models, enhance decentralization as measured by the Gini and Nakamoto coefficients. A pivotal discovery is the existence of a threshold stakeholder whose relative voting ratio increases under QV compared to linear voting, while smaller stakeholders also gain influence. The generalized QV model allows flexible adjustment of this threshold, enabling tailored decentralization levels. Maintaining fairness, QV ensures that stakeholders with higher stakes retain a proportionally greater voting ratio while redistributing influence to prevent excessive concentration. It is shown that to preserve fairness and robustness, QV must be implemented alongside privacy-preserving cryptographic voting protocols, as voters casting their ballots last could otherwise manipulate outcomes. The generalized QV model, proposed in this paper, enables algorithmic parametrization to achieve desired levels of decentralization for specific use cases. This flexibility makes it applicable across diverse domains, including user interaction with cryptocurrency platforms, facilitating community events and educational initiatives, and supporting charitable activities through decentralized decision-making.

cs.GT↗

arXiv2021

Generalized Box-Muller method for generating q-Gaussian random deviates

Addendum: The generalized Box-Müller algorithm provides a methodology for generating q-Gaussian random variates. The parameter $-\infty<q\leq3$ is related to the shape of the tail decay; $q<1$ for compact-support including parabola $(q=0)$; $1<q\leq3$ for heavy-tail including Cauchy $(q=2)$. This addendum clarifies the transformation $q'=((3q-1)/(q+1))$ within the algorithm is due to a difference in the dimensions d of the generalized logarithm and the generalized distribution. The transformation is clarified by the decomposition of $q=1+2κ/(1+dκ)$, where the shape parameter $-1<κ\leq\infty$ quantifies the magnitude of the deformation from exponential. A simpler specification for the generalized Box- Müller algorithm is provided using the shape of the tail decay. Original: The q-Gaussian distribution is known to be an attractor of certain correlated systems, and is the distribution which, under appropriate constraints, maximizes the entropy Sq, basis of nonextensive statistical mechanics. This theory is postulated as a natural extension of the standard (Boltzmann-Gibbs) statistical mechanics, and may explain the ubiquitous appearance of heavy-tailed distributions in both natural and man-made systems. The q-Gaussian distribution is also used as a numerical tool, for example as a visiting distribution in Generalized Simulated Annealing. We develop and present a simple, easy to implement numerical method for generating random deviates from a q-Gaussian distribution based upon a generalization of the well known Box-Muller method. Our method is suitable for a larger range of q values, q<3, than has previously appeared in the literature, and can generate deviates from q-Gaussian distributions of arbitrary width and center. MATLAB code showing a straightforward implementation is also included.

cond-mat.stat-mech↗

arXiv2013

Fractional nonlinear filtering problems and their associated fractional Zakai equations

In this paper we discuss fractional generalizations of the filtering problem. The "fractional" nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering problem emerges as the Riemann-Liouville fractional derivative in the associated Zakai equation. We discuss fractional generalizations of the filtering problem whose state and observation processes are driven by time-changed Brownian motion or/and Lévy process.

math.PR↗