摘要翻译：
我们考虑随机过程的马尔可夫模型，其中下一阶条件分布是由核密度估计器(KDE)定义的，类似于马尔可夫预测密度和某些时间序列bootstrap方案。我们讨论的KDE Markov模型（KDE-MMs）是平稳过程的非线性、非参数、完全概率表示，基于具有强渐近相合性质的技术。该模型通过将训练数据序列中的点以上下文敏感的方式连接起来生成新的数据，并加入一些加性驱动噪声。提出了一种新的EM型最大似然算法，用于KDE-MMS中的数据驱动带宽选择。此外，我们用隐藏状态增强了KDE-MMs，生成了一个新的模型类KDE-HMMS。添加的状态变量捕获非马尔可夫长记忆和信号结构（例如，慢振荡），补充由马尔可夫过程描述的短程依赖性。由此产生的联合马尔可夫和隐马尔可夫结构对模拟复杂的现实过程如语音信号具有吸引力。在高斯核的情况下，我们给出了模型参数的保证上升的EM更新方程，以及在实践中大大加快训练的放松更新公式。实验表明，与自回归模型、HMMs及其组合等传统技术相比，KDE-HMMs在几个具有挑战性的自然和合成数据序列上具有更高的保持集概率。
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英文标题：
《Kernel Density Estimation-Based Markov Models with Hidden State》
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作者：
Gustav Eje Henter, Arne Leijon and W. Bastiaan Kleijn
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最新提交年份：
2018
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
  We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov models (KDE-MMs) we discuss are nonlinear, nonparametric, fully probabilistic representations of stationary processes, based on techniques with strong asymptotic consistency properties. The models generate new data by concatenating points from the training data sequences in a context-sensitive manner, together with some additive driving noise. We present novel EM-type maximum-likelihood algorithms for data-driven bandwidth selection in KDE-MMs. Additionally, we augment the KDE-MMs with a hidden state, yielding a new model class, KDE-HMMs. The added state variable captures non-Markovian long memory and signal structure (e.g., slow oscillations), complementing the short-range dependences described by the Markov process. The resulting joint Markov and hidden-Markov structure is appealing for modelling complex real-world processes such as speech signals. We present guaranteed-ascent EM-update equations for model parameters in the case of Gaussian kernels, as well as relaxed update formulas that greatly accelerate training in practice. Experiments demonstrate increased held-out set probability for KDE-HMMs on several challenging natural and synthetic data series, compared to traditional techniques such as autoregressive models, HMMs, and their combinations.
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PDF链接：
https://arxiv.org/pdf/1807.1132