相关论文: Fast DPP Sampling for Nystr\"om with Application t…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

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…

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…

Discrete probabilistic programs (DPPs) provide a highly expressive formalism for compactly defining arbitrary finite probabilistic models. This expressivity comes at a price: DPP inference is PSPACE-hard. In this work, we show that DPP…

Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely,…

Subset selection is central to many wireless communication problems, including link scheduling, power allocation, and spectrum management. However, these problems are often NP-complete, because of which heuristic algorithms applied to solve…

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. The present paper proposes the use of…

The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This…

The Nystr\"om method is a popular low-rank approximation technique for large matrices that arise in kernel methods and convex optimization. Yet, when the data exhibits heavy-tailed spectral decay, the effective dimension of the problem…

Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…

Piecewise deterministic Markov processes (PDMPs) are a class of continuous-time Markov processes that were recently used to develop a new class of Markov chain Monte Carlo algorithms. However, the implementation of the processes is…

The Nystr\"om method is one of the most popular techniques for improving the scalability of kernel methods. However, it has not yet been derived for kernel PCA in line with classical PCA. In this paper we derive kernel PCA with the…

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures, whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. First we show…

We study Nystr\"om type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that…

Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…

Recently, the computer vision and machine learning community has been in favor of feature extraction pipelines that rely on a coding step followed by a linear classifier, due to their overall simplicity, well understood properties of linear…

We propose a novel diverse feature selection method based on determinantal point processes (DPPs). Our model enables one to flexibly define diversity based on the covariance of features (similar to orthogonal matching pursuit) or…

Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified…

This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the…

Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In…