arXiv research

Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix …

The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few t…

Novel algorithm speeds up log-determinant estimation for large matrices.

This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework o…

New method estimates log-determinant using trace powers, avoiding classical limitations.

In this article, we completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.

The study examines averages of Laplacian determinants over large genus moduli spaces.

DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.

Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify symplectically ruled log-symplectic $4$ manifolds (both orientable and non-orientab…

Survival strategies in a market with self-determined prices are closely tied to log-optimal investment.

New method computes affine normal directions efficiently for sparse polynomials.

A new algorithm improves sampling for graph learning models.

The paper extends risk measures to two-step approximations and studies log-concave distributions.

The paper connects complex normalizing flows to Kähler-Ricci flows using geometric and statistical perspectives.

Paper improves efficiency in matrix computations for Gaussian processes.

We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical thresh…

Let X be a complex manifold with strongly pseudoconvex boundary M. If u is a defining function for M, then -log u is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form s = i \del \delbar(-log u) is a symplectic structure on the complement of M in a neighborhood in X of M; it blows up along M. The Poiss…

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

A new method speeds up training of deep models by avoiding Jacobian determinant computation.

A new coordinate system for SPD matrices simplifies computations and generative modeling.

Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discret…

Abstract: Expresses zeta-determinant of Dirichlet-to-Neumann operator on forms.

Paper introduces VDE, a variance-reduced determinant estimator.

We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space, the collection of lower triangular matrices whose diagonal elements are all posi…

Develops interpolation methods for matrix functions in statistics and machine learning.

We compute the curvature of the determinant line bundle on a family of Dirac operators for a noncommutative two torus. Following Quillen's original construction for Riemann surfaces and using zeta regularized determinant of Laplacians, one can endow the determinant line bundle with a natural Hermitian metric. By using …

We show that the minimal number of colors for all effective $n$-colorings of a link with non-zero determinant is at least $1+\log_2 n$.

For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an $n \times n$ positive definite matrix, and its derivatives - leading to prohibitive $\mathcal{O}(n^3)$ computatio…

The Milnor fiber conjecture is proven for splice type singularities.

Develops a novel framework for pricing variance swaps in multi-asset stochastic volatility models.

Study uses renormalized area to determine metric expansion from minimal surfaces.

Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.

Improved Gaussian process regression with tighter log marginal likelihood bounds.

New algorithm speeds up sampling from log-concave distributions over polytopes.

The paper derives inequalities and formulas for generalized Ricci flow.

New algorithm for online portfolio selection with reduced runtime.

Differentially private log-location-scale regression models improve privacy in statistical analysis.

SGD's escape rate depends on log loss barrier, not linear loss barrier.

The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface $\Z$ over $\mathbb{C}\mathrm{P}^1$. We show that for the $\bar{\partial}$-operator along the fiber the logarithm of the regularized determinant $-1/2 \log \det' (\bar\partial^* \bar\partial)$ satisfies the anomaly equation of the …

The $\textit{volume density}$ of a hyperbolic link $K$ is defined to be the ratio of the hyperbolic volume of $K$ to the crossing number of $K$. We show that there are sequences of non-alternating links with volume density approaching $v_8$, where $v_8$ is the volume of the ideal hyperbolic octahedron. We show that the…

Data science predicts user interest for midwifery content.

Paper studies multiclass classifiers from binary classifiers, proving methods and demonstrating advantages.

New non-Kähler 3-folds constructed via log conifold transitions.

Bayesian inference and superstatistics model financial volatility dynamics across different timescales.

The paper improves support recovery in high-dimensional precision matrix estimation using meta learning.

A new method combines online and offline learning to tackle contextual bandits with missing action support.

This paper detects anomalies in cellular network traffic using hybrid methods.