Predicting human scanpaths when exploring panoramic videos is a challenging
task due to the spherical geometry and the multimodality of the input, and the
inherent uncertainty and diversity of the output. Most previous methods fail to
give a complete treatment of these characteristics, and thus are prone to
errors. In this paper, we present a simple new criterion for scanpath
prediction based on principles from lossy data compression. This criterion
suggests minimizing the expected code length of quantized scanpaths in a
training set, which corresponds to fitting a discrete conditional probability
model via maximum likelihood. Specifically, the probability model is
conditioned on two modalities: a viewport sequence as the deformation-reduced
visual input and a set of relative historical scanpaths projected onto
respective viewports as the aligned path input. The probability model is
parameterized by a product of discretized Gaussian mixture models to capture
the uncertainty and the diversity of scanpaths from different users. Most
importantly, the training of the probability model does not rely on the
specification of ``ground-truth'' scanpaths for imitation learning. We also
introduce a proportional-integral-derivative (PID) controller-based sampler to
generate realistic human-like scanpaths from the learned probability model.
Experimental results demonstrate that our method consistently produces better
quantitative scanpath results in terms of prediction accuracy (by comparing to
the assumed ``ground-truths'') and perceptual realism (through machine
discrimination) over a wide range of prediction horizons. We additionally
verify the perceptual realism improvement via a formal psychophysical
experiment and the generalization improvement on several unseen panoramic video
datasets.

本文提出了一种基于损失数据压缩实现扫描路径预测的简单新标准，该标准建议通过在训练集中量化扫描路径的期望代码长度来拟合离散条件概率模型，该概率模型以视口序列为条件，以适应不同用户生成的不确定性和多样性扫描路径， 并介绍了基于比例积分导数（PID）控制器的采样器来从学习的概率模型生成逼真的人类类似的扫描路径。该方法在广泛的预测时间范围内始终产生更好的定量扫描路径结果，并通过机器区分展现出较高的感知逼真度，同时在多个未见过的全景视频数据集上实现了普适性验证。

通过期望码长最小化预测全景视频的扫视路径

Scanpath Prediction in Panoramic Videos via Expected Code Length  Minimization

The goal of lossy data compression is to reduce the storage cost of a data
set $X$ while retaining as much information as possible about something ($Y$)
that you care about. For example, what aspects of an image $X$ contain the most
information about whether it depicts a cat? Mathematically, this corresponds to
finding a mapping $X\to Z\equiv f(X)$ that maximizes the mutual information
$I(Z,Y)$ while the entropy $H(Z)$ is kept below some fixed threshold. We
present a method for mapping out the Pareto frontier for classification tasks,
reflecting the tradeoff between retained entropy and class information. We
first show how a random variable $X$ (an image, say) drawn from a class
$Y\in\{1,...,n\}$ can be distilled into a vector $W=f(X)\in \mathbb{R}^{n-1}$
losslessly, so that $I(W,Y)=I(X,Y)$; for example, for a binary classification
task of cats and dogs, each image $X$ is mapped into a single real number $W$
retaining all information that helps distinguish cats from dogs. For the $n=2$
case of binary classification, we then show how $W$ can be further compressed
into a discrete variable $Z=g_\beta(W)\in\{1,...,m_\beta\}$ by binning $W$ into
$m_\beta$ bins, in such a way that varying the parameter $\beta$ sweeps out the
full Pareto frontier, solving a generalization of the Discrete Information
Bottleneck (DIB) problem. We argue that the most interesting points on this
frontier are "corners" maximizing $I(Z,Y)$ for a fixed number of bins
$m=2,3...$ which can be conveniently be found without multiobjective
optimization. We apply this method to the CIFAR-10, MNIST and Fashion-MNIST
datasets, illustrating how it can be interpreted as an
information-theoretically optimal image clustering algorithm.

该文提出了一种关于图像分类任务下的 Pareto frontier 映射和压缩的方法，通过找到相应的映射和压缩方法，分别最大化互信息和最小化熵，从而在保证信息完整性的同时，最大化信息与目标之间的相关性，而且该方法可以被解释为一种信息论优化的图像聚类算法。

二分类任务的 Pareto 最优数据压缩

Pareto-optimal data compression for binary classification tasks

Motivated by questions in lossy data compression and by theoretical
considerations, we examine the problem of estimating the rate-distortion
function of an unknown (not necessarily discrete-valued) source from empirical
data. Our focus is the behavior of the so-called "plug-in" estimator, which is
simply the rate-distortion function of the empirical distribution of the
observed data. Sufficient conditions are given for its consistency, and
examples are provided to demonstrate that in certain cases it fails to converge
to the true rate-distortion function. The analysis of its performance is
complicated by the fact that the rate-distortion function is not continuous in
the source distribution; the underlying mathematical problem is closely related
to the classical problem of establishing the consistency of maximum likelihood
estimators. General consistency results are given for the plug-in estimator
applied to a broad class of sources, including all stationary and ergodic ones.
A more general class of estimation problems is also considered, arising in the
context of lossy data compression when the allowed class of coding
distributions is restricted; analogous results are developed for the plug-in
estimator in that case. Finally, consistency theorems are formulated for
modified (e.g., penalized) versions of the plug-in, and for estimating the
optimal reproduction distribution.

本文引出自压缩领域和相关的理论问题，分析了通过实证数据来估计未知（并非必须是离散型的）信源的失真率 - 失真函数的问题。我们探讨了 “插件” 估计器的行为，给出了其一致性的充分条件，同时提供了某些情况下它失败的例子。针对一类广泛的信源，包括所有的平稳和符合渐进频率的信源，给出了 “插件” 估计器的一般一致性结果。最后，本文还提出了关于 “插件” 估计器的修正版本的一致性定理和最优重现分布估计的问题。