Large-Margin Determinantal Point Processes

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 a DPP's kernel matrix with multiple kernel functions, thus enhancing modeling flexibility. Second, we propose a novel parameter estimation technique based on the principle of large margin separation. In contrast to the state-of-the-art method of maximum likelihood estimation, our large-margin loss function explicitly models errors in selecting the target subsets, and it can be customized to trade off different types of errors (precision vs. recall). Extensive empirical studies validate our contributions, including applications on challenging document and video summarization, where flexibility in modeling the kernel matrix and balancing different errors is indispensable.Comment: 15 page

Approximate Inference in Continuous Determinantal Point Processes

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 the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required are not tractable in general. In this paper, we present two efficient DPP sampling schemes that apply to a wide range of kernel functions: one based on low rank approximations via Nystrom and random Fourier feature techniques and another based on Gibbs sampling. We demonstrate the utility of continuous DPPs in repulsive mixture modeling and synthesizing human poses spanning activity spaces

How Local is the Local Diversity? Reinforcing Sequential Determinantal Point Processes with Dynamic Ground Sets for Supervised Video Summarization

The large volume of video content and high viewing frequency demand automatic video summarization algorithms, of which a key property is the capability of modeling diversity. If videos are lengthy like hours-long egocentric videos, it is necessary to track the temporal structures of the videos and enforce local diversity. The local diversity refers to that the shots selected from a short time duration are diverse but visually similar shots are allowed to co-exist in the summary if they appear far apart in the video. In this paper, we propose a novel probabilistic model, built upon SeqDPP, to dynamically control the time span of a video segment upon which the local diversity is imposed. In particular, we enable SeqDPP to learn to automatically infer how local the local diversity is supposed to be from the input video. The resulting model is extremely involved to train by the hallmark maximum likelihood estimation (MLE), which further suffers from the exposure bias and non-differentiable evaluation metrics. To tackle these problems, we instead devise a reinforcement learning algorithm for training the proposed model. Extensive experiments verify the advantages of our model and the new learning algorithm over MLE-based methods

Graph Convolutional Neural Networks with Diverse Negative Samples via Decomposed Determinant Point Processes

Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates information from its first-order neighbour to update its representation. As a result, the representations of nodes with edges between them should be positively correlated and thus can be considered positive samples. However, there are more non-neighbour nodes in the whole graph, which provide diverse and useful information for the representation update. Two non-adjacent nodes usually have different representations, which can be seen as negative samples. Besides the node representations, the structural information of the graph is also crucial for learning. In this paper, we used quality-diversity decomposition in determinant point processes (DPP) to obtain diverse negative samples. When defining a distribution on diverse subsets of all non-neighbouring nodes, we incorporate both graph structure information and node representations. Since the DPP sampling process requires matrix eigenvalue decomposition, we propose a new shortest-path-base method to improve computational efficiency. Finally, we incorporate the obtained negative samples into the graph convolution operation. The ideas are evaluated empirically in experiments on node classification tasks. These experiments show that the newly proposed methods not only improve the overall performance of standard representation learning but also significantly alleviate over-smoothing problems.Comment: Accepted by IEEE TNNLS on 30-Aug-2023. arXiv admin note: text overlap with arXiv:2210.0072

Probabilistic Typology: Deep Generative Models of Vowel Inventories

Linguistic typology studies the range of structures present in human language. The main goal of the field is to discover which sets of possible phenomena are universal, and which are merely frequent. For ex- ample, all languages have vowels, while most—but not all—languages have an [u] sound. In this paper we present the first probabilistic treatment of a basic question in phonological typology: What makes a natural vowel inventory? We introduce a se- ries of deep stochastic point processes, and contrast them with previous computational, simulation-based approaches. We provide a comprehensive suite of experiments on over 200 distinct languages