We consider the problem of inferring a latent function in a probabilistic
model of data. When dependencies of the latent function are specified by a
Gaussian process and the data likelihood is complex, efficient computation
often involve Markov chain Monte Carlo sampling with limited applicability to
large data sets. We extend some of these techniques to scale efficiently when
the problem exhibits a sequential structure. We propose an approximation that
enables sequential sampling of both latent variables and associated parameters.
We demonstrate strong performance in growing-data settings that would otherwise
be unfeasible with naive, non-sequential sampling.

本文研究在数据的概率模型中推断一个潜在函数的问题，并探究了基于马尔可夫链蒙特卡罗采样的高效计算方法在大型数据集上的可行性，提出了一种近似方法，使潜在变量和相关参数的顺序采样能够有效地处理增长数据设置，证明了其在无序、非顺序采样下不可行的情况下的强大性能。

高斯过程潜变量模型的连续采样

Sequential sampling of Gaussian process latent variable models

Bayesian optimization (BO) has emerged during the last few years as an
effective approach to optimizing black-box functions where direct queries of
the objective are expensive. In this paper we consider the case where direct
access to the function is not possible, but information about user preferences
is. Such scenarios arise in problems where human preferences are modeled, such
as A/B tests or recommender systems. We present a new framework for this
scenario that we call Preferential Bayesian Optimization (PBO) which allows us
to find the optimum of a latent function that can only be queried through
pairwise comparisons, the so-called duels. PBO extends the applicability of
standard BO ideas and generalizes previous discrete dueling approaches by
modeling the probability of the winner of each duel by means of a Gaussian
process model with a Bernoulli likelihood. The latent preference function is
used to define a family of acquisition functions that extend usual policies
used in BO. We illustrate the benefits of PBO in a variety of experiments,
showing that PBO needs drastically fewer comparisons for finding the optimum.
According to our experiments, the way of modeling correlations in PBO is key in
obtaining this advantage.

本文介绍了一种名为 PBO 的新框架，它扩展了标准 BO 的思想，并通过模型化 Bernoulli - 高斯过程模型来建模每个决斗的赢家概率，从而允许在仅通过两两比较的方式来查询隐函数，并且相对于以往方法，该方法在寻找最大值过程中需要极少的比较。