Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions …
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48 results for “Nonsymmetric DPP”
This work tackles scalable sampling for nonsymmetric DPPs.
problem Scalability issue in existing DPP sampling algorithms for nonsymmetric DPPs.
method Developed a linear-time algorithm for kernels with low-rank structure and a sublinear-time rejection sampling algorithm.
result Bounded rejection rate for kernels with structural constraints.
New scalable MCMC sampling for nonsymmetric DPPs speeds up computations.
problem Efficient sampling for nonsymmetric DPPs with low-rank kernels.
method Enhanced rejection sampling with efficient proposal distribution construction.
result Sublinear runtime for scalable MCMC sampling of -NDPPs.
New algorithm scales NDPP learning and inference to large item collections.
problem Memory and runtime limitations in existing NDPP learning and inference algorithms.
method Introduced a new NDPP kernel decomposition for learning and a linear-complexity MAP inference algorithm.
result Our algorithms scale linearly in , matching prior work's predictive performance.
From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximizationcs.LG
New algorithm approximates maximum of certain distributions on subsets.
problem Finding maximum of distributions on subsets.
method Connection between sampling and optimization via exchange inequalities and local random walks.
result Simple nearly-optimal approximation algorithm for MAP inference.
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and desc…
We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci …
Determinantal point processes (DPPs) have attracted significant attention as an elegant model that is able to capture the balance between quality and diversity within sets. DPPs are parameterized by a positive semi-definite kernel matrix. While DPPs have substantial expressive power, they are fundamentally limited by t…
We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distribut…
The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds with specific torsion conditions.
problem Tackles the Einstein connection in nonsymmetric pseudo-Riemannian manifolds with non-degenerate skew-symmetric tensor.
method Explicitly presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds with -torsion condition.
result Reduces to M.Prvanović's solution in the almost Hermitian case.
Paper tests DPPs for diversity models, distinguishing them from other distributions.
problem Testing whether a given distribution is a Determinantal Point Process (DPP) or far from any DPP.
method Proposes the first algorithm for DPP testing and establishes a lower bound on sample complexity.
result Establishes a matching lower bound on the sample complexity of DPP testing.
Analysis of DPPs and k-DPPs via spectral decomposition reveals identifiable parameters and non-identifiability gaps.
problem Identifying parameters of DPPs and k-DPPs through spectral decomposition.
method Spectral decomposition of the covariance matrix, analysis of invariances, and counting arguments.
result Identifiability of parameters changes fundamentally for k-DPPs, with specific invariances and non-identifiability gaps.
The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.
problem The challenge is to define the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.
method The approach involves using a weak almost contact structure and a linear connection with torsion.
result Explicit formulas for the Einstein connection are provided.
Kernel quadrature with DPPsstat.ML
We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the qua…
DPP-BBO diversifies batched Bayesian optimization using DPPs.
problem Efficiently proposing diverse and informative batches in batched Bayesian optimization.
method Introducing DPP-Batch Bayesian Optimization (DPP-BBO) with DPP-Thompson Sampling (DPP-TS).
result Novel Bayesian simple regret bounds for DPP-TS show improved performance over classical methods.
State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectivesstat.ML
New DPP kernels improve minibatch efficiency for large datasets.
problem Efficiently generating minibatches from large datasets.
method Wavelet-based DPPs and novel discrete conversion methods.
result Improved minibatch efficiency with low-rank decompositions.
Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things, since DPPs tend to select sets of points that are some distance apart (repulsion…
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…
Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in large-scale applications, which has triggered an effort towar…
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for Symmetric NMF is not as easy as for the nonsymmetric counterpart, the latter adm…
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…
DPPS uses DP priors for Bayesian non-parametric multi-arm bandits.
problem Optimizing multi-arm bandit environments with prior beliefs.
method Bayesian non-parametric algorithm based on Dirichlet Process priors.
result DPPS provides principled incorporation of prior beliefs and is optimal in Bayesian regret setup.
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…
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…
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to…
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix…
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…
New method samples DPPs efficiently without downsampling or low-rank approximations.
problem Efficient sampling from DPPs for diverse selections.
method Directly approximates distribution function of linear statistics using Laplace inversion.
result Scalable sampling for general DPPs, beyond symmetric kernels.
Higher-Order Generalization Bounds: Learning Deep Probabilistic Programs via PAC-Bayes Objectivescs.LG
Unified framework for learning flexible probabilistic programs using DPP and PAC-Bayes bounds.
problem Learning and generalizing from complex probabilistic models.
method Unified DPP representation and PAC-Bayes bounds for stochastic programs.
result Improved performance and generalization prediction using flexible DPP model representations and learned complexity measures.
This paper solves nonparametric estimation of continuous DPPs using kernel methods.
problem Estimating continuous Determinantal Point Processes (DPPs) without assuming a parametric form.
method Developed a fixed point algorithm based on a representer theorem for nonnegative functions in RKHS.
result Demonstrated a finite-dimensional problem for nonparametric MLE of continuous DPPs.
Faster sampler reduces DPP sampling cost to O(nm + m^3 log m).
problem High cost of sampling discrete DPPs.
method Uses rejection sampling and leverage score i.i.d. sampling.
result Reduces sampling cost from O(n^3) to O(nm + m^3 log m).
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the -Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together with a square integrable -form in the sense of \cite{giglinonsmooth}. This ex…
Adaptive algorithm samples items from a DPP without seeing all items.
problem Efficiently sample items from a DPP without preprocessing all items.
method Adaptive uniform sampling of a subset of data, followed by -DPP sampling on this subset.
result Produces a -DPP sample after observing only a small fraction of all elements, significantly faster than state-of-the-art.
Determinantal consensus clustering improves clustering robustness.
problem Robustness of clustering algorithms.
method Use of determinantal point processes (DPP) for random restart of clustering algorithms.
result Determinantal consensus clustering outperforms classical algorithms.
Paper explores duality in DPPs using embedding structure analysis.
problem Understanding the geometric structure of determinantal point processes.
method Analyzes the exponential family embedding of DPPs and uses the e-embedding curvature tensor.
result Discovers the duality between marginal and L-ensemble kernels.
This paper shows DPPs can outperform random coresets in machine learning tasks.
problem Building efficient coresets for machine learning models.
method Using determinantal point processes (DPPs) to construct coresets with provable improvements over random sampling.
result DPPs can provably outperform independently drawn coresets in terms of approximation of total loss.
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…
Paper explores how DPP sampling can implicitly regularize kernel regression.
problem Improving kernel regression by reducing redundancy in data.
method Using Determinantal Point Processes (DPPs) to sample subsets implicitly regularizes ridgeless Kernel Regression.
result Ensemble of ridgeless regressors can be effective for datasets with redundant information.
Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground set, they exhibit interesting properties such as negative correlation, and, unl…
New Einstein solvmanifolds constructed without using nilsolitons.
problem Constructing Einstein solvmanifolds not based on nilsolitons.
method Using nonsymmetric derivations and a computer algorithm to classify and find solutions up to dimension 9.
result Einstein solvmanifolds of dimensions ≤ 5 are not isometric to standard extensions of nilsolitons.
In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic l\infty-norm performance-loss bounds for DPP in the presence of approximation/estimation erro…
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 …
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…
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel . DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel through like…
Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGDstat.ML
This work improves SGD minibatch sampling using determinantal point processes based on orthogonal polynomials.
problem Improving variance reduction in stochastic gradient descent (SGD) for large datasets.
method Orthogonal polynomial-based determinantal point processes for sampling minibatches in SGD.
result DPP minibatches lead to a smaller mean square approximation error than uniform minibatches.
Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of 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 complexity of core tasks suc…
This research uses DPPs to improve semi-parametric regression models.
problem Improving comprehensibility in semi-parametric regression models without sacrificing accuracy.
method Introduced a novel representation of finite DPPs and used it to derive a key identity illustrating implicit regularization.
result Demonstrated the implicit regularization effect of determinantal sampling for semi-parametric regression.
Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. In this work we present a new method for learning th…