arXiv research

Study Euler obstruction of 1-forms on determinantal singularities.

We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

The Poincaré-Hopf theorem is extended to projective varieties with isolated singularities.

Study characteristic classes of a specific type of determinantal varieties.

This paper improves signal reconstruction using determinantal sampling from random nodes.

Study curvature loci of 3-manifolds in R^6 and R^5.

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…

We use Donaldson's approximately holomorphic techniques to build embeddings of a closed symplectic manifold with symplectic form of integer class in the grassmannians Gr(r,N). We assure that these embeddings are asymptotically holomorphic in a precise sense. We study first the particular case of embeddings in the proje…

In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.

This paper proves all Pfaffian varieties are area-minimizing except hypersurfaces.

Paper proposes a simple estimator for DPP correlation kernels.

Given a fixed $n\times d$ matrix $\mathbf{X}$, where $n\gg d$, we study the complexity of sampling from a distribution over all subsets of rows where the probability of a subset is proportional to the squared volume of the parallelepiped spanned by the rows (a.k.a. a determinantal point process). In this task, it is im…

We calculate the free energy of Coulomb gas systems on Riemann surfaces.

Paper explores duality in DPPs using embedding structure analysis.

The determinantal variety $Σ_{pq}$ is defined to be the set of all $p\times q$ real matrices with $p\geq q$ whose ranks are strictly smaller than $q$. It is proved that $Σ_{pq}$ is a minimal cone in $\mathbb R^{pq}$ and all its strata are regular minimal submanifolds.

In the present paper and the companion paper [9] a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on a complex algebraic varieties X is introduced, by sampling "temperature deformed" determinantal point processes. The main new ingredient is a large deviation principle for Gibbs…

Determinantal consensus clustering improves clustering robustness.

The study examines determinantal point processes linked to a specific operator on Riemannian manifolds.

This research uses DPPs to improve semi-parametric regression models.

The study computes Bergman kernels and point process asymptotics on Kähler manifolds.

This work improves sampling efficiency on complex spaces using determinantal processes.

New algorithms for online MAP inference and learning for NDPPs.

The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.

The paper studies partition functions of point processes on Kähler manifolds, generalizing geometric functionals and relating to QHE.

We study the transverse Poisson structure to adjoint orbits in a complex semi-simple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen quasi-homogeneous coordinates the quasi-degree of the transverse Poisson structure is -2. In the particular case of {\emph…

The paper finds determinantal expressions for certain symmetric space integrals.

We study the complexity of sampling from a distribution over all index subsets of the set $\{1,...,n\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\mathbf{L}_S$ of some $n\times n$ p.s.d. matrix $\mathbf{L}$, where $\mathbf{L}_S$ corresponds to the entries of $\mathbf{L}$ ind…

Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models f…

New algorithm scales NDPP learning and inference to large item collections.

We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DP…

Paper explores how DPP sampling can implicitly regularize kernel regression.

DPP-BBO diversifies batched Bayesian optimization using DPPs.

Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the parameters of a DPP is still considered a difficult problem due to the non-convex nature…

The paper examines when real matrix Schubert varieties are minimal submanifolds.

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficie…

If E is a C^\infty complex vector bundle on an oriented C^\infty manifold Σ, diffeomorphic to a circle, then the space of sections of E has a canonical polarization in the sense of Pressley and Segal and so one has its determinantal gerbe with lien C^*, the group of nonzero complex numbers. If q:Σ-->B is a smooth famil…

We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, …

This work improves SGD minibatch sampling using determinantal point processes based on orthogonal polynomials.

Paper tests DPPs for diversity models, distinguishing them from other distributions.

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large problems is still limited due to the $\mathcal O(N^3)$ complexity of core tasks suc…

We propose a new class of structured methods for Monte Carlo (MC) sampling, called DPPMC, designed for high-dimensional nonisotropic distributions where samples are correlated to reduce the variance of the estimator via determinantal point processes. We successfully apply DPPMCs to problems involving nonisotropic distr…

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights. We introduce a natural distinction between pure critical points, which only depend on the functional space, and spurious critical points, …

Determinantal point processes (DPPs) have received significant attention in the recent years as an elegant model for a variety of machine learning tasks, due to their ability to elegantly model set diversity and item quality or popularity. Recent work has shown that DPPs can be effective models for product recommendati…

Study the limits of discrete DPPs to continuous DPPs as set size grows.

In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not equal the inverse of the sum. An example of this occurs in distributed Newton's…

Quantum machine learning boosts financial forecasting accuracy.

Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of…