arXiv research

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

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.

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…

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

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

Determinantal consensus clustering improves clustering robustness.

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…

DPP-BBO diversifies batched Bayesian optimization using DPPs.

Paper explores how DPP sampling can implicitly regularize kernel regression.

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.

New scalable MCMC sampling for nonsymmetric DPPs speeds up computations.

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

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…

Study characteristic classes of a specific type of determinantal varieties.

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

Improved uncertainty estimation through diverse sampling in neural networks.

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…

We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point Process (DPP). The DPP relies on a similarity measure between data points and g…

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on reg…

Determinantal Point Processes (DPPs) provide an elegant and versatile way to sample sets of items that balance the point-wise quality with the set-wise diversity of selected items. For this reason, they have gained prominence in many machine learning applications that rely on subset selection. However, sampling from a …

Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampl…

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.

Study Euler obstruction of 1-forms on determinantal singularities.

In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative correlation, i.e., ones that can generate a "diverse" sample from a set of items.…

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel $K$ that can be seen as a matrix storing the similarity between points. The diversity comes from the fact that the inclusion probability of a subset is equal to the determinan…

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…

Minimal cones defined by rank conditions in matrix spaces.

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…

Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from DPPs is a challenge and therefore we present DPPy, a Python toolbox that gathers kn…

Optimizes balanced treatment assignment for experiments.

Data collection and labeling is one of the main challenges in employing machine learning algorithms in a variety of real-world applications with limited data. While active learning methods attempt to tackle this issue by labeling only the data samples that give high information, they generally suffer from large computa…

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…

This work tackles scalable sampling for nonsymmetric DPPs.

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…

Sampling methods that choose a subset of the data proportional to its diversity in the feature space are popular for data summarization. However, recent studies have noted the occurrence of bias (under- or over-representation of a certain gender or race) in such data summarization methods. In this paper we initiate a s…

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

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

We study the Gibbs sampling algorithm for continuous determinantal point processes. We show that, given a warm start, the Gibbs sampler generates a random sample from a continuous $k$-DPP defined on a $d$-dimensional domain by only taking $\text{poly}(k)$ number of steps. As an application, we design an algorithm to ge…

Paper proposes a simple estimator for DPP correlation kernels.

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

Paper explores duality in DPPs using embedding structure analysis.

When faced with a data set too large to be processed all at once, an obvious solution is to retain only part of it. In practice this takes a wide variety of different forms, and among them "coresets" are especially appealing. A coreset is a (small) weighted sample of the original data that comes with the following guar…

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

Faster sampler reduces DPP sampling cost to O(nm + m^3 log m).

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