arXiv research

Defines and proves properties of weighted renormalized volume coefficients.

Diffusion models adapt to low-dimensional data regardless of coefficient choices.

This paper presents an infinite variational autoencoder (VAE) whose capacity adapts to suit the input data. This is achieved using a mixture model where the mixing coefficients are modeled by a Dirichlet process, allowing us to integrate over the coefficients when performing inference. Critically, this then allows us t…

Generalizes underlap coefficient for multivariate group separation.

This work addresses unstable MeanFlow training by optimizing a coefficient in the loss function.

We study the cross-correlation matrix $C_{ij}$ of inventory variations of the most active individual and institutional investors in an emerging market to understand the dynamics of inventory variations. We find that the distribution of cross-correlation coefficient $C_{ij}$ has a power-law form in the bulk followed by …

Privacy amplification improved through contraction coefficients and $E_γ$-divergence.

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

Bayesian variational inference improves medical image segmentation confidence.

Researchers calculate entropy of heat kernel on manifolds for very small times.

Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…

The abstract discusses nonuniqueness results for specific Riemannian invariants.

Neural GARCH models financial time series with time-varying coefficients.

MeanFlow training is unstable due to misusing conditional velocity, leading to variance issues.

A framework for disentangling class-related and class-independent factors in data.

CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.

Estimates Markov chain mixing time from a single trajectory.

Paper proposes a new method for feature importance in model selection.

This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our …

Optimizes diffusion processes for target distributions.

The speed of convergence of the Expectation Maximization (EM) algorithm for Gaussian mixture model fitting is known to be dependent on the amount of overlap among the mixture components. In this paper, we study the impact of mixing coefficients on the convergence of EM. We show that when the mixture components exhibit …

The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…

The flat trace of geodesic Koopman operators varies with negatively curved surfaces.

We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient $v_3$ in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated $\mathcal{W}$-functional.

Efficiently identifies important variables in binary outcomes using variational Bayes.

Homological stability proved for handlebody mapping class groups.

The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of self-adjoint elliptic differential operators. $\H(r;g)$ is a non-Laplace-type perturbation …

Method learns latent SDEs from high-dimensional time series.

VarGrad reduces variance in ELBO gradient estimation for variational inference.

CAVI speeds up Bayesian MIDAS regression by 107x-1,772x with similar accuracy.

Emulator speeds up landslide run-out modeling sensitivity analysis.

A conformally invariant generalization of the Willmore energy for compact immersed submanifolds of even dimension in a Riemannian manifold is derived and studied. The energy arises as the coefficient of the log term in the renormalized area expansion of a minimal submanifold in a Poincare-Einstein space with prescribed…

Study measures inequality in social-economic systems using Fokker-Planck equations and Lotka-Volterra dynamics.

Proves solution uniqueness for biomembrane shape prediction.

This paper carries out a renormalization of the volume of the Loewner-Nirenberg singular Yamabe metric in a given conformal class on a compact manifold-with-boundary. This generalizes the usual volume renormalization for Poincare-Einstein metrics. The coefficient of the log term in the volume expansion defines a confor…

New method for ancestral inference in branching processes with random environments.

The Duffing oscillator's parameters are identified online using variational message passing.

Efficiently selects important variables in high-dimensional logistic regression.

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised learning in a continuous-domain hybrid search space with gTV regu…

The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural networks, where the activation function is represented as a linear c…

We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …

Non-negative matrix factorization (NMF) is a knowledge discovery method that is used in many fields. Variational inference and Gibbs sampling methods for it are also wellknown. However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution us…

New method calibrates asynchronous, error-prone covariates for longitudinal data.

A new method for Bayesian inference in high dimensions using projected Stein variational gradient descent.

Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted networks. This paper builds a new framework to cope with this problem. The key idea i…

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…

A novel non-supervised method detects anomalies in multivariate time series.

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that…