211 research outputs found
Inference for determinantal point processes without spectral knowledge
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 likelihood-based inference is not straightforward. First, the kernel
that appears in the likelihood is not , but another kernel related to
through an often intractable spectral decomposition. This issue is
typically bypassed in machine learning by directly parametrizing the kernel
, at the price of some interpretability of the model parameters. We follow
this approach here. Second, the likelihood has an intractable normalizing
constant, which takes the form of a large determinant in the case of a DPP over
a finite set of objects, and the form of a Fredholm determinant in the case of
a DPP over a continuous domain. Our main contribution is to derive bounds on
the likelihood of a DPP, both for finite and continuous domains. Unlike
previous work, our bounds are cheap to evaluate since they do not rely on
approximating the spectrum of a large matrix or an operator. Through usual
arguments, these bounds thus yield cheap variational inference and moderately
expensive exact Markov chain Monte Carlo inference methods for DPPs
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
Improving Sequential Determinantal Point Processes for Supervised Video Summarization
It is now much easier than ever before to produce videos. While the
ubiquitous video data is a great source for information discovery and
extraction, the computational challenges are unparalleled. Automatically
summarizing the videos has become a substantial need for browsing, searching,
and indexing visual content. This paper is in the vein of supervised video
summarization using sequential determinantal point process (SeqDPP), which
models diversity by a probabilistic distribution. We improve this model in two
folds. In terms of learning, we propose a large-margin algorithm to address the
exposure bias problem in SeqDPP. In terms of modeling, we design a new
probabilistic distribution such that, when it is integrated into SeqDPP, the
resulting model accepts user input about the expected length of the summary.
Moreover, we also significantly extend a popular video summarization dataset by
1) more egocentric videos, 2) dense user annotations, and 3) a refined
evaluation scheme. We conduct extensive experiments on this dataset (about 60
hours of videos in total) and compare our approach to several competitive
baselines
- …