This paper improves video summarization using a new algorithm and dataset.
problem Efficiently summarizing videos for browsing and searching.
method Improves sequential determinantal point process (SeqDPP) with a large-margin algorithm and a new probabilistic distribution.
result Significantly improved video summarization model with better user input integration and diversity.
dHMM improves sequential labeling by encouraging diversity.
problem Improving performance of HMM in real-world sequential labeling tasks.
method dHMM incorporates a diversity-encouraging prior over state-transition probabilities.
result dHMM outperforms state-of-the-art methods on benchmark datasets for PoS tagging and OCR.
New method optimizes Gaussian process allocation for BO.
problem Existing methods for inducing point allocation in BO hinder performance.
method Proposes a new allocation strategy using quality-diversity decomposition.
result Demonstrates improved BO performance through local high-fidelity modeling.
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…
New algorithm speeds up determinantal point process sampling.
problem Efficiently sampling from determinantal point processes with minimal preprocessing and sampling costs.
method Introducing a Poisson random variable to control subset probabilities, reducing the number of rows to poly(d) for sampling.
result The new algorithm achieves poly(d) sampling time, independent of n, without distorting probabilities.
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 improves signal reconstruction using determinantal sampling from random nodes.
problem Approximating square-integrable functions from random node evaluations.
method Combines determinantal point processes and mixtures thereof for RKHS-adapted approximations.
result Proves mean-square guarantees in L2 norm and shows faster convergence rates. 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…
Paper proposes a simple estimator for DPP correlation kernels.
problem Estimating the correlation kernel matrix of DPPs.
method Closed-form estimator for correlation kernel, easy to implement.
result Consistency and asymptotic normality of the estimator proved.
The study computes Bergman kernels and point process asymptotics on Kähler manifolds.
problem Computing asymptotics of Bergman kernels and point process distributions on Kähler manifolds.
method Equivariant and partial Bergman kernels, determinantal point processes, asymptotic analysis.
result The distribution of linear statistics converges to a centered normal variable with specific variances.
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.
The study examines determinantal point processes linked to a specific operator on Riemannian manifolds.
problem Understanding the spectral properties and associated point processes of the Bochner-Schrödinger operator.
method Analysis of the Bochner-Schrödinger operator on tensor powers of Hermitian line bundles, focusing on large p asymptotics. result The asymptotic behavior of determinantal point processes associated with the operator's spectral projection is computed, leading to the law of large numbers and central limit theorem.
New algorithm samples determinantal point processes with sublinear preprocessing time.
problem Sampling from determinantal point processes efficiently with small expected subset size.
method Proposes an algorithm with sublinear preprocessing and independent sampling cost.
result Achieves sublinear preprocessing time and independent sampling cost.
The paper studies partition functions of point processes on Kähler manifolds, generalizing geometric functionals and relating to QHE.
problem Analyzing partition functions of determinantal point processes on Kähler manifolds.
method Using geometric functionals and TYZ expansion coefficients of the Bergman kernel.
result The coefficients of the partition function expansion are geometric functionals on Kähler metrics.
New algorithms for online MAP inference and learning for NDPPs.
problem Online inference and learning for nonsymmetric determinantal point processes.
method Single-pass algorithms with sub-linear memory usage.
result Comparable performance to offline algorithms with multiple passes.
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.
The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.
problem Sampling from strongly Rayleigh distributions efficiently.
method Optimal sublinear sampling algorithms for random spanning trees and determinantal point processes.
result Achieves optimal sublinear sampling for strongly Rayleigh distributions.
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.
New sampling method reduces variance in correlated high-dimensional distributions.
problem Reducing variance in Monte Carlo estimators for correlated high-dimensional distributions.
method DPPMC (Determinantal Point Processes Monte Carlo) method for structured sampling.
result DPPMCs improve state-of-the-art in various optimization and machine learning problems.
A new point process for clustering distributions with repulsion.
problem Clustering distributions with repulsion.
method Distributional Determinantal Point Process (dDPP) with sliced Wasserstein kernel.
result Validated dDPP as a well-defined point process and applied to gene expression and epilepsy data.
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.
Optimal transport kernels improve neural architecture search efficiency.
problem Comparing complex neural architectures similarity using Euclidean metric fails.
method Developed a novel discrepancy using tree-Wasserstein (TW) for neural architectures.
result TW-based approaches outperform other methods in sequential and parallel NAS.
New method improves scalability of Gaussian processes for discrete data.
problem Scalability issue in Gaussian processes for discrete domains.
method Simulated annealing for selecting inducing points.
result Simulated annealing outperforms SVM and full GP on DNA sequence data.
Study the limits of discrete DPPs to continuous DPPs as set size grows.
problem Characterize the behavior of discrete DPPs as they approach continuous DPPs.
method Non-asymptotic characterization of the limit in terms of weak coherency.
result Sufficient conditions for weak coherency are identified.
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 M, matching prior work's predictive performance. 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.
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 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…
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…
Researchers derive Markov properties of discrete DPPs.
problem Lack of statistical properties exploration for discrete DPPs.
method Derive Markov properties using graphical models.
result Markov properties of discrete DPPs can be expressed.
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…
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…
Existing MAP inference algorithms for determinantal point processes (DPPs) need to calculate determinants or conduct eigenvalue decomposition generally at the scale of the full kernel, which presents a great challenge for real-world applications. In this paper, we introduce a class of DPPs, called BwDPPs, that are char…
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.
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.
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 O(N3) complexity of core tasks suc…
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) 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…
Optimizes balanced treatment assignment for experiments.
problem Balancing treatment groups in experiments for optimal results.
method Optimization of a two-sample test, using minimum spanning tree test.
result Optimal assignment algorithm with polynomial time complexity.
Proposes landmark selection for kernel methods.
problem Selecting important landmarks from large training sets.
method Deterministic and randomized adaptive algorithm for landmark selection.
result Landmarks are related to the minima of kernelized Christoffel functions.
Quantum machine learning boosts financial forecasting accuracy.
problem Churn prediction and credit risk assessment in finance.
method Used quantum and classical Determinantal Point Processes for churn prediction, and quantum neural networks for credit risk assessment.
result Significant improvement in precision for churn prediction (6% increase). Quantum models match classical performance with fewer parameters.
New algorithms improve experimental design efficiency and approximation quality.
problem Finding optimal subset of vectors for expensive measurements.
method Bayesian experimental design using determinantal point processes.
result Developed efficient algorithms for optimal design under multiple criteria.
This work improves sampling efficiency on complex spaces using determinantal processes.
problem Efficient sampling from large-scale datasets with general spaces.
method Determinantal point processes on general spaces and diffusion geometry.
result Improved sampling rates for determinantal processes on Riemannian manifolds and networks.
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 k-NDPPs. Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize…
Improved uncertainty estimation through diverse sampling in neural networks.
problem Enhancing uncertainty estimation for machine learning models.
method Data-driven correlations and determinantal point processes-based sampling for dropout layers.
result State-of-the-art results in uncertainty estimation for regression and classification tasks.
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…
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.…