A novel class of non-reversible Markov chain Monte Carlo schemes relying on
continuous-time piecewise-deterministic Markov Processes has recently emerged.
In these algorithms, the state of the Markov process evolves according to a
deterministic dynamics which is modified using a Markov transition kernel at
random event times. These methods enjoy remarkable features including the
ability to update only a subset of the state components while other components
implicitly keep evolving and the ability to use an unbiased estimate of the
gradient of the log-target while preserving the target as invariant
distribution. However, they also suffer from important limitations. The
deterministic dynamics used so far do not exploit the structure of the target.
Moreover, exact simulation of the event times is feasible for an important yet
restricted class of problems and, even when it is, it is application specific.
This limits the applicability of these techniques and prevents the development
of a generic software implementation of them. We introduce novel MCMC methods
addressing these shortcomings. In particular, we introduce novel
continuous-time algorithms relying on exact Hamiltonian flows and novel
non-reversible discrete-time algorithms which can exploit complex dynamics such
as approximate Hamiltonian dynamics arising from symplectic integrators while
preserving the attractive features of continuous-time algorithms. We
demonstrate the performance of these schemes on a variety of applications.

本文介绍了一种新的基于非可逆马尔可夫链蒙特卡洛算法的类别，利用连续时间分段确定性马尔可夫过程。这些算法基于确定性动力学演化标记过程的状态，同时利用马尔可夫转移核来改变其状态。通过使用这些算法，只有子集状态被更新，导致其他组件的状态隐含不显，另外，利用无偏估计对数目标时，这些算法保持目标不变。本文提出新的 MCMC 方法来解决这些限制，并在多种应用中展示了这些方案的性能。

分段确定性马尔可夫链蒙特卡罗

Piecewise-Deterministic Markov Chain Monte Carlo

Randomized experiments have been used to assist decision-making in many
areas. They help people select the optimal treatment for the test population
with certain statistical guarantee. However, subjects can show significant
heterogeneity in response to treatments. The problem of customizing treatment
assignment based on subject characteristics is known as uplift modeling,
differential response analysis, or personalized treatment learning in
literature. A key feature for uplift modeling is that the data is unlabeled. It
is impossible to know whether the chosen treatment is optimal for an individual
subject because response under alternative treatments is unobserved. This
presents a challenge to both the training and the evaluation of uplift models.
In this paper we describe how to obtain an unbiased estimate of the key
performance metric of an uplift model, the expected response. We present a new
uplift algorithm which creates a forest of randomized trees. The trees are
built with a splitting criterion designed to directly optimize their uplift
performance based on the proposed evaluation method. Both the evaluation method
and the algorithm apply to arbitrary number of treatments and general response
types. Experimental results on synthetic data and industry-provided data show
that our algorithm leads to significant performance improvement over other
applicable methods.

本文提出了一种新型的 uplift 算法，通过随机森林进行建模，利用一种新颖的评估方法可以获取 uplift 模型中最重要的性能度量值 - 预期响应，解决了数据无法测量个体对不同治疗方式响应的问题，在合成数据和行业提供的数据上的实验结果表明，该算法在任意数量和不同响应类型的治疗方式上，性能显著优于其他可行方法。

多个处理和一般响应类型的提升建模

Uplift Modeling with Multiple Treatments and General Response Types

We propose a novel stochastic gradient method---semi-stochastic coordinate
descent (S2CD)---for the problem of minimizing a strongly convex function
represented as the average of a large number of smooth convex functions:
$f(x)=\tfrac{1}{n}\sum_i f_i(x)$. Our method first performs a deterministic
step (computation of the gradient of $f$ at the starting point), followed by a
large number of stochastic steps. The process is repeated a few times, with the
last stochastic iterate becoming the new starting point where the deterministic
step is taken. The novelty of our method is in how the stochastic steps are
performed. In each such step, we pick a random function $f_i$ and a random
coordinate $j$---both using nonuniform distributions---and update a single
coordinate of the decision vector only, based on the computation of the
$j^{th}$ partial derivative of $f_i$ at two different points. Each random step
of the method constitutes an unbiased estimate of the gradient of $f$ and
moreover, the squared norm of the steps goes to zero in expectation, meaning
that the stochastic estimate of the gradient progressively improves. The
complexity of the method is the sum of two terms: $O(n\log(1/\epsilon))$
evaluations of gradients $\nabla f_i$ and $O(\hat{\kappa}\log(1/\epsilon))$
evaluations of partial derivatives $\nabla_j f_i$, where $\hat{\kappa}$ is a
novel condition number.

提出了一种基于半随机坐标下降（S2CD）的新型随机梯度方法，用于最小化表示为大量平滑凸函数平均值的强凸函数，我们所提出的方法具有非常好的稳定性和计算复杂度。