我们考虑有限混合物（MFM）和Dirichlet工艺混合物（DPM）模型的贝叶斯混合物。最近的渐近理论已经确定，DPM高估了大型样本的聚类数量，并且两类模型的估计量对于不指定的群集的数量不一致，但是对有限样本分析的含义尚不清楚。拟合这些模型后的最终报告的估计通常是使用MCMC摘要技术获得的单个代表性聚类，但是尚不清楚这样的摘要估计簇的数量。在这里，我们通过模拟和对基因表达数据的应用进行了研究，发现（i）DPM甚至在有限样本中高估了簇数的数量，但仅在有限的程度上可以使用适当的摘要来纠正，并且（ii）（ii） ）错误指定会导致对DPM和MFM中集群数量的高估，但是结果通常仍然可以解释。我们提供了有关MCMC摘要的建议，并建议尽管MFM的渐近性能更具吸引力，这提供了强大的动力来偏爱它们，但使用MFMS和DPMS获得的结果通常在实践中非常相似。

潜在的DIRICHLET分配（LDA）广泛用于一组文档的无监督主题建模。模型中没有使用时间信息。但是，连续令牌的相应主题之间通常存在关系。在本文中，我们向LDA提供了一个扩展，该扩展名使用马尔可夫链来建模时间信息。我们将这种新模型从语音发现进行声学单元发现。作为输入令牌，该模型从具有512个代码的矢量定量（VQ）神经网络中对语音进行了离散的编码。然后，目标是将这512个VQ代码映射到50个类似电话的单元（主题），以使其更加类似于真实的电话。与基本LDA相反，该基础LDA仅考虑VQ代码在发声中的共同发生（文档），Markov链LDA还捕获了连续代码如何相互跟随。与基本LDA相比，这种扩展会导致集群质量和电话分割结果的提高。与最近学习50个单元的媒介量化神经网络方法相比，扩展的LDA模型在电话分割方面的性能较好，但在相互信息中的性能较差。

未知的非线性动力学通常会限制前馈控制的跟踪性能。本文的目的是开发一个可以使用通用函数近似器来补偿这些未知非线性动力学的前馈控制框架。前馈控制器被参数化为基于物理模型和神经网络的平行组合，在该组合中，两者都共享相同的线性自回旋（AR）动力学。该参数化允许通过Sanathanan-Koerner（SK）迭代进行有效的输出误差优化。在每个Sk-itteration中，神经网络的输出在基于物理模型的子空间中通过基于正交投影的正则化受到惩罚，从而使神经网络仅捕获未建模的动力学，从而产生可解释的模型。

尽管在文本，图像和视频上生成的对抗网络（GAN）取得了显着的成功，但由于一些独特的挑战，例如捕获不平衡数据中的依赖性，因此仍在开发中，生成高质量的表格数据仍在开发中，从而优化了合成患者数据的质量。保留隐私。在本文中，我们提出了DP-CGAN，这是一个由数据转换，采样，条件和网络培训组成的差异私有条件GAN框架，以生成现实且具有隐私性的表格数据。 DP-Cgans区分分类和连续变量，并将它们分别转换为潜在空间。然后，我们将条件矢量构建为附加输入，不仅在不平衡数据中介绍少数族裔类，还可以捕获变量之间的依赖性。我们将统计噪声注入DP-CGAN的网络训练过程中的梯度，以提供差异隐私保证。我们通过统计相似性，机器学习绩效和隐私测量值在三个公共数据集和两个现实世界中的个人健康数据集上使用最先进的生成模型广泛评估了我们的模型。我们证明，我们的模型优于其他可比模型，尤其是在捕获变量之间的依赖性时。最后，我们在合成数据生成中介绍了数据实用性与隐私之间的平衡，考虑到现实世界数据集的不同数据结构和特征，例如不平衡变量，异常分布和数据的稀疏性。

了解深度神经网络的结果是朝着更广泛接受深度学习算法的重要步骤。许多方法解决了解释人工神经网络的问题，但通常提供不同的解释。此外，不同的解释方法的超级公路可能导致互相冲突。在本文中，我们提出了一种使用受限制的Boltzmann机器（RBMS）来聚合不同解释算法的特征归属的技术，以实现对深神经网络的更可靠和坚固的解释。关于现实世界数据集的几个具有挑战性的实验表明，所提出的RBM方法优于流行的特征归因方法和基本集合技术。

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns meta-knowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bi-level optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned meta-knowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a Neural Gauge to "measure" the physical parameters of an unseen system with observed trajectories. We test the validity of the iMODE method on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: a) it allows for online real-time monitoring of a dynamical system; b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; c) it is computationally fast and less intensive than the popular Extended Dynamic Mode Decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

We introduce PRISM, a method for real-time filtering in a probabilistic generative model of agent motion and visual perception. Previous approaches either lack uncertainty estimates for the map and agent state, do not run in real-time, do not have a dense scene representation or do not model agent dynamics. Our solution reconciles all of these aspects. We start from a predefined state-space model which combines differentiable rendering and 6-DoF dynamics. Probabilistic inference in this model amounts to simultaneous localisation and mapping (SLAM) and is intractable. We use a series of approximations to Bayesian inference to arrive at probabilistic map and state estimates. We take advantage of well-established methods and closed-form updates, preserving accuracy and enabling real-time capability. The proposed solution runs at 10Hz real-time and is similarly accurate to state-of-the-art SLAM in small to medium-sized indoor environments, with high-speed UAV and handheld camera agents (Blackbird, EuRoC and TUM-RGBD).

Strategic test allocation plays a major role in the control of both emerging and existing pandemics (e.g., COVID-19, HIV). Widespread testing supports effective epidemic control by (1) reducing transmission via identifying cases, and (2) tracking outbreak dynamics to inform targeted interventions. However, infectious disease surveillance presents unique statistical challenges. For instance, the true outcome of interest - one's positive infectious status, is often a latent variable. In addition, presence of both network and temporal dependence reduces the data to a single observation. As testing entire populations regularly is neither efficient nor feasible, standard approaches to testing recommend simple rule-based testing strategies (e.g., symptom based, contact tracing), without taking into account individual risk. In this work, we study an adaptive sequential design involving n individuals over a period of {\tau} time-steps, which allows for unspecified dependence among individuals and across time. Our causal target parameter is the mean latent outcome we would have obtained after one time-step, if, starting at time t given the observed past, we had carried out a stochastic intervention that maximizes the outcome under a resource constraint. We propose an Online Super Learner for adaptive sequential surveillance that learns the optimal choice of tests strategies over time while adapting to the current state of the outbreak. Relying on a series of working models, the proposed method learns across samples, through time, or both: based on the underlying (unknown) structure in the data. We present an identification result for the latent outcome in terms of the observed data, and demonstrate the superior performance of the proposed strategy in a simulation modeling a residential university environment during the COVID-19 pandemic.

Causal deep learning (CDL) is a new and important research area in the larger field of machine learning. With CDL, researchers aim to structure and encode causal knowledge in the extremely flexible representation space of deep learning models. Doing so will lead to more informed, robust, and general predictions and inference -- which is important! However, CDL is still in its infancy. For example, it is not clear how we ought to compare different methods as they are so different in their output, the way they encode causal knowledge, or even how they represent this knowledge. This is a living paper that categorises methods in causal deep learning beyond Pearl's ladder of causation. We refine the rungs in Pearl's ladder, while also adding a separate dimension that categorises the parametric assumptions of both input and representation, arriving at the map of causal deep learning. Our map covers machine learning disciplines such as supervised learning, reinforcement learning, generative modelling and beyond. Our paradigm is a tool which helps researchers to: find benchmarks, compare methods, and most importantly: identify research gaps. With this work we aim to structure the avalanche of papers being published on causal deep learning. While papers on the topic are being published daily, our map remains fixed. We open-source our map for others to use as they see fit: perhaps to offer guidance in a related works section, or to better highlight the contribution of their paper.