Precision beekeeping allows to monitor bees' living conditions by equipping beehives with sensors. The data recorded by these hives can be analyzed by machine learning models to learn behavioral patterns of or search for unusual events in bee colonies. One typical target is the early detection of bee swarming as apiarists want to avoid this due to economical reasons. Advanced methods should be able to detect any other unusual or abnormal behavior arising from illness of bees or from technical reasons, e.g. sensor failure.
In this position paper we present an autoencoder, a deep learning model, which detects any type of anomaly in data independent of its origin. Our model is able to reveal the same swarms as a simple rule-based swarm detection algorithm but is also triggered by any other anomaly. We evaluated our model on real world data sets that were collected on different hives and with different sensor setups.
University of Würzburg(维尔茨堡大学);Institute of Computer Science, Chair of Computer Science X, University of Würzburg(维尔茨堡大学计算机科学研究所计算机科学X教授)
Sensor-equipped beehives allow monitoring the living conditions of bees. Machine learning models can use the data of such hives to learn behavioral patterns and find anomalous events. One type of event that is of particular interest to apiarists for economical reasons is bee swarming. Other events of interest are behavioral anomalies from illness and technical anomalies, e.g. sensor failure. Beekeepers can be supported by suitable machine learning models which can detect these events. In this paper we compare multiple machine learning models for anomaly detection and evaluate them for their ap…
The increasing complexity of mobility plus the growing population in cities, together with the importance of privacy when sharing data from vehicles or any device, makes traffic forecasting that uses data from infrastructure and citizens an open and challenging task. In this paper, we introduce a novel approach to deal with predictions of speed, volume, and main traffic direction, in a new aggregated way of traffic data presented as videos. The approach leverages the continuity in a sequence of frames and its dynamics, learning to predict changing areas in a low dimensional space and then, rec…
Hong Kong University of Science and Technology(香港科技大学)
Hybrid methods that utilize both content and rating information are commonly used in many recommender systems. However, most of them use either handcrafted features or the bag-of-words representation as a surrogate for the content information but they are neither effective nor natural enough. To address this problem, we develop a collaborative recurrent autoencoder (CRAE) which is a denoising recurrent autoencoder (DRAE) that models the generation of content sequences in the collaborative filtering (CF) setting. The model generalizes recent advances in recurrent deep learning from i.i.d. input…
We present an application of anomaly detection techniques based on deep recurrent autoencoders to the problem of detecting gravitational wave signals in laser interferometers. Trained on noise data, this class of algorithms could detect signals using an unsupervised strategy, i.e., without targeting a specific kind of source. We develop a custom architecture to analyze the data from two interferometers. We compare the obtained performance to that obtained with other autoencoder architectures and with a convolutional classifier. The unsupervised nature of the proposed strategy comes with a cost…
Technical University of Denmark(丹麦技术大学);Niras(尼拉斯公司)
In the digitization of energy systems, sensors and smart meters are increasingly being used to monitor production, operation and demand. Detection of anomalies based on smart meter data is crucial to identify potential risks and unusual events at an early stage, which can serve as a reference for timely initiation of appropriate actions and improving management. However, smart meter data from energy systems often lack labels and contain noise and various patterns without distinctively cyclical. Meanwhile, the vague definition of anomalies in different energy scenarios and highly complex tempor…
With substantial recent developments in aviation technologies, Unmanned Aerial Vehicles (UAVs) are becoming increasingly integrated in commercial and military operations internationally. Research into the applications of aircraft data is essential in improving safety, reducing operational costs, and developing the next frontier of aerial technology. Having an outlier detection system that can accurately identify anomalous behaviour in aircraft is crucial for these reasons. This paper proposes a system incorporating a Long Short-Term Memory (LSTM) Deep Learning Autoencoder based method with a n…
Hochschule Bonn-Rhein-Sieg(波恩-莱茵-锡格应用技术大学);Fraunhofer Center for Machine Learning and SCAI(弗劳恩霍夫机器学习中心与SCAI)
Ice accumulation in the blades of wind turbines can cause them to describe anomalous rotations or no rotations at all, thus affecting the generation of electricity and power output. In this work, we investigate the problem of ice accumulation in wind turbines by framing it as anomaly detection of multi-variate time series. Our approach focuses on two main parts: first, learning low-dimensional representations of time series using a Variational Recurrent Autoencoder (VRAE), and second, using unsupervised clustering algorithms to classify the learned representations as normal (no ice accumulated…
University of Malaya(马来亚大学);International University of Business Agriculture and Technology(国际商业农业与技术大学);Stamford University Bangladesh(孟加拉国斯坦福大学)
Flowers play an essential role in removing the duller from the environment. The life cycle of the flowering plants involves pollination, fertilization, flowering, seed-formation, dispersion, and germination. Honeybees pollinate approximately 75% of all flowering plants. Environmental pollution, climate change, natural landscape demolition, and so on, threaten the natural habitats, thus continuously reducing the number of honeybees. As a result, several researchers are attempting to resolve this issue. Applying acoustic classification to recordings of beehive sounds may be a way of detecting ch…
Wildcard Pharmaceutical Consulting(万卡医药咨询公司);Science Data Software LLC(科学数据软件有限责任公司)
Chemical autoencoders are attractive models as they combine chemical space navigation with possibilities for de-novo molecule generation in areas of interest. This enables them to produce focused chemical libraries around a single lead compound for employment early in a drug discovery project. Here it is shown that the choice of chemical representation, such as SMILES strings, has a large influence on the properties of the latent space. It is further explored to what extent translating between different chemical representations influences the latent space similarity to the SMILES strings or ci…
UC Los Angeles(加州大学洛杉矶分校);ICSI(国际计算机科学研究所);UC Berkeley(加州大学伯克利分校)
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our net…
EPFL(洛桑联邦理工学院);Cyber-Defence Campus, armasuisse Science and Technology(瑞士联邦国防采购局科技网络防御园区);University of Geneva(日内瓦大学);University of Applied Sciences of Western Switzerland(瑞士西部应用科学大学)
Because of the considerable heterogeneity and complexity of the technological landscape, building accurate models to forecast is a challenging endeavor. Due to their high prevalence in many complex systems, S-curves are a popular forecasting approach in previous work. However, their forecasting performance has not been directly compared to other technology forecasting approaches. Additionally, recent developments in time series forecasting that claim to improve forecasting accuracy are yet to be applied to technological development data. This work addresses both research gaps by comparing the …
Recurrent Neural Networks (RNN) received a vast amount of attention last decade. Recently, the architectures of Recurrent AutoEncoders (RAE) found many applications in practice. RAE can extract the semantically valuable information, called context that represents a latent space useful for further processing. Nevertheless, recurrent autoencoders are hard to train, and the training process takes much time. In this paper, we propose an autoencoder architecture with sequence-aware encoding, which employs 1D convolutional layer to improve its performance in terms of model training time. We prove th…
ADVA Optical Networking SE(ADVA光网络公司);Christian-Albrechts-Universität zu Kiel(基尔大学)
Secure and reliable data communication in optical networks is critical for high-speed Internet. However, optical fibers, serving as the data transmission medium providing connectivity to billons of users worldwide, are prone to a variety of anomalies resulting from hard failures (e.g., fiber cuts) and malicious physical attacks (e.g., optical eavesdropping (fiber tapping)) etc. Such anomalies may cause network disruption and thereby inducing huge financial and data losses, or compromise the confidentiality of optical networks by gaining unauthorized access to the carried data, or gradually deg…
ADVA Optical Networking SE(ADVA光网络公司);Christian-Albrechts-Universität zu Kiel(基尔大学)
We propose a deep learning approach based on an autoencoder for identifying and localizing fiber faults in passive optical networks. The experimental results show that the proposed method detects faults with 97% accuracy, pinpoints them with an RMSE of 0.18 m and outperforms conventional techniques.
When sensors collect spatio-temporal data in a large geographical area, the existence of missing data cannot be escaped. Missing data negatively impacts the performance of data analysis and machine learning algorithms. In this paper, we study deep autoencoders for missing data imputation in spatio-temporal problems. We propose a convolution bidirectional-LSTM for capturing spatial and temporal patterns. Moreover, we analyze an autoencoder's latent feature representation in spatio-temporal data and illustrate its performance for missing data imputation. Traffic flow data are used for evaluation…
Cloud platforms, under the hood, consist of a complex inter-connected stack of hardware and software components. Each of these components can fail which may lead to an outage. Our goal is to improve the quality of Cloud services through early detection of such failures by analyzing resource utilization metrics. We tested Gated-Recurrent-Unit-based autoencoder with a likelihood function to detect anomalies in various multi-dimensional time series and achieved high performance.
The de novo design of molecular structures using deep learning generative models introduces an encouraging solution to drug discovery in the face of the continuously increased cost of new drug development. From the generation of original texts, images, and videos, to the scratching of novel molecular structures, the incredible creativity of deep learning generative models surprised us about the height machine intelligence can achieve. The purpose of this paper is to review the latest advances in generative chemistry which relies on generative modeling to expedite the drug discovery process. Th…
Secure and reliable data communication in optical networks is critical for high-speed internet. We propose a data driven approach for the anomaly detection and faults identification in optical networks to diagnose physical attacks such as fiber breaks and optical tapping. The proposed methods include an autoencoder-based anomaly detection and an attention-based bidirectional gated recurrent unit algorithm for the fiber fault identification and localization. We verify the efficiency of our methods by experiments under various attack scenarios using real operational data.
Qualcomm AI Research, Qualcomm Technologies, Inc.(高通技术公司高通人工智能研究院);Qualcomm AI Research, Qualcomm Technologies Netherlands B.V.(高通技术荷兰私人有限公司高通人工智能研究院);University of California San Diego(加州大学圣地亚哥分校)
In this work, we propose a new recurrent autoencoder architecture, termed Feedback Recurrent AutoEncoder (FRAE), for online compression of sequential data with temporal dependency. The recurrent structure of FRAE is designed to efficiently extract the redundancy along the time dimension and allows a compact discrete representation of the data to be learned. We demonstrate its effectiveness in speech spectrogram compression. Specifically, we show that the FRAE, paired with a powerful neural vocoder, can produce high-quality speech waveforms at a low, fixed bitrate. We further show that by addin…
EEG-based emotion recognition often requires sufficient labeled training samples to build an effective computational model. Labeling EEG data, on the other hand, is often expensive and time-consuming. To tackle this problem and reduce the need for output labels in the context of EEG-based emotion recognition, we propose a semi-supervised pipeline to jointly exploit both unlabeled and labeled data for learning EEG representations. Our semi-supervised framework consists of both unsupervised and supervised components. The unsupervised part maximizes the consistency between original and reconstruc…
University of Pisa(比萨大学);University of Padova(帕多瓦大学)
Training RNNs to learn long-term dependencies is difficult due to vanishing gradients. We explore an alternative solution based on explicit memorization using linear autoencoders for sequences, which allows to maximize the short-term memory and that can be solved with a closed-form solution without backpropagation. We introduce an initialization schema that pretrains the weights of a recurrent neural network to approximate the linear autoencoder of the input sequences and we show how such pretraining can better support solving hard classification tasks with long sequences. We test our approach…
University of Florida(佛罗里达大学);UiT - The Arctic University of Norway(挪威北极圈大学)
We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the $p$-th head is responsible for generating the $p$-th dimension of $\mathbf{x}$ (i.e., $\mathbf{x}^p$). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adj…
Mechanical and Aerospace Engineering, Princeton University(普林斯顿大学机械与航空航天工程系(注:此处按要求提取到大学级别,故保留系名与大学名));Princeton University(普林斯顿大学)
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encode…
Qualcomm AI Research, Qualcomm Technologies Netherlands B.V.(高通人工智能研究院,高通技术荷兰有限公司);Qualcomm AI Research, Qualcomm Technologies, Inc.(高通人工智能研究院,高通技术公司);University of Oxford(牛津大学)
Recent advances in deep generative modeling have enabled efficient modeling of high dimensional data distributions and opened up a new horizon for solving data compression problems. Specifically, autoencoder based learned image or video compression solutions are emerging as strong competitors to traditional approaches. In this work, We propose a new network architecture, based on common and well studied components, for learned video compression operating in low latency mode. Our method yields state of the art MS-SSIM/rate performance on the high-resolution UVG dataset, among both learned video…
Variational autoencoders were proven successful in domains such as computer vision and speech processing. Their adoption for modeling user preferences is still unexplored, although recently it is starting to gain attention in the current literature. In this work, we propose a model which extends variational autoencoders by exploiting the rich information present in the past preference history. We introduce a recurrent version of the VAE, where instead of passing a subset of the whole history regardless of temporal dependencies, we rather pass the consumption sequence subset through a recurrent…
This paper presents a generative approach to speech enhancement based on a recurrent variational autoencoder (RVAE). The deep generative speech model is trained using clean speech signals only, and it is combined with a nonnegative matrix factorization noise model for speech enhancement. We propose a variational expectation-maximization algorithm where the encoder of the RVAE is fine-tuned at test time, to approximate the distribution of the latent variables given the noisy speech observations. Compared with previous approaches based on feed-forward fully-connected architectures, the proposed …
Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from model-based techniques in that they provide only posterior predictions for quantities (time series) of interest, not posterior models with calibrated parameters. DSI methods require a large number of flow simulations to first be performed on prior geological realizations. Given observed data, posterior predictions can then be generated directly. DSI operates in a Bayesian setting and provides posterior samples of the data vector…
University of Glasgow(格拉斯哥大学);The University of British Columbia(不列颠哥伦比亚大学)
It is challenging to construct generalized physical models of wave propagation in nature owing to their complex physics as well as widely varying environmental parameters and dynamical scales. In this article, we present the convolutional autoencoder recurrent network (CRAN) as a data-driven model for learning wave propagation phenomena. The CRAN consists of a convolutional autoencoder for learning low-dimensional system representation and a long short-term memory recurrent neural network for the system evolution in low dimension. We show that the convolutional autoencoder significantly outper…
It has been previously observed that training Variational Recurrent Autoencoders (VRAE) for text generation suffers from serious uninformative latent variables problem. The model would collapse into a plain language model that totally ignore the latent variables and can only generate repeating and dull samples. In this paper, we explore the reason behind this issue and propose an effective regularizer based approach to address it. The proposed method directly injects extra constraints on the posteriors of latent variables into the learning process of VRAE, which can flexibly and stably control…
Lawrence Berkeley National Laboratory(劳伦斯伯克利国家实验室);Texas A&M University(得克萨斯农工大学)
Botnets are increasingly used by malicious actors, creating increasing threat to a large number of internet users. To address this growing danger, we propose to study methods to detect botnets, especially those that are hard to capture with the commonly used methods, such as the signature based ones and the existing anomaly-based ones. More specifically, we propose a novel machine learning based method, named Recurrent Variational Autoencoder (RVAE), for detecting botnets through sequential characteristics of network traffic flow data including attacks by botnets. We validate robustness of our…
This project develops and trains a Recurrent Neural Network (RNN) that monitors sleeping infants from an auxiliary microphone for cases of Sudden Infant Death Syndrome (SIDS), manifested in sudden or gradual respiratory arrest. To minimize invasiveness and maximize economic viability, an electret microphone, and parabolic concentrator, paired with a specially designed and tuned amplifier circuit, was used as a very sensitive audio monitoring device, which fed data to the RNN model. This RNN was trained and operated in the frequency domain, where the respiratory activity is most unique from noi…
Learning disentangled representations leads to interpretable models and facilitates data generation with style transfer, which has been extensively studied on static data such as images in an unsupervised learning framework. However, only a few works have explored unsupervised disentangled sequential representation learning due to challenges of generating sequential data. In this paper, we propose recurrent Wasserstein Autoencoder (R-WAE), a new framework for generative modeling of sequential data. R-WAE disentangles the representation of an input sequence into static and dynamic factors (i.e.…
In this paper we propose mmFall - a novel fall detection system, which comprises of (i) the emerging millimeter-wave (mmWave) radar sensor to collect the human body's point cloud along with the body centroid, and (ii) a variational recurrent autoencoder (VRAE) to compute the anomaly level of the body motion based on the acquired point cloud. A fall is claimed to have occurred when the spike in anomaly level and the drop in centroid height occur simultaneously. The mmWave radar sensor provides several advantages, such as privacycompliance and high-sensitivity to motion, over the traditional sen…
Pruning-aware Loss Functions for STOI-Optimized Pruned Recurrent Autoencoders for the Compression of the Stimulation Patterns of Cochlear Implants at Zero Delay
University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校)
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing equations onto a subspace spanned by basis functions obtained from the compression of a dataset of solution snapshots. However, this method is intrusive since the projection requires access to the system operators. Further, some systems may require special treatment of nonlinearities to ensure computational efficiency or additional modeling to preserve stabili…
University of Augsburg(奥格斯堡大学);Imperial College London(帝国理工学院);BMW AG(宝马股份公司)
Motivated by the attention mechanism of the human visual system and recent developments in the field of machine translation, we introduce our attention-based and recurrent sequence to sequence autoencoders for fully unsupervised representation learning from audio files. In particular, we test the efficacy of our novel approach on the task of speech-based sleepiness recognition. We evaluate the learnt representations from both autoencoders, and then conduct an early fusion to ascertain possible complementarity between them. In our frameworks, we first extract Mel-spectrograms from raw audio fil…
NCSA, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校国家超级计算应用中心);Department of Statistics, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校统计系);Department of Astronomy, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校天文系);Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校电气与计算机工程系)
Gravitational wave astronomy is a rapidly growing field of modern astrophysics, with observations being made frequently by the LIGO detectors. Gravitational wave signals are often extremely weak and the data from the detectors, such as LIGO, is contaminated with non-Gaussian and non-stationary noise, often containing transient disturbances which can obscure real signals. Traditional denoising methods, such as principal component analysis and dictionary learning, are not optimal for dealing with this non-Gaussian noise, especially for low signal-to-noise ratio gravitational wave signals. Furthe…
We introduce a neural-network architecture, termed the constrained recurrent sparse autoencoder (CRsAE), that solves convolutional dictionary learning problems, thus establishing a link between dictionary learning and neural networks. Specifically, we leverage the interpretation of the alternating-minimization algorithm for dictionary learning as an approximate Expectation-Maximization algorithm to develop autoencoders that enable the simultaneous training of the dictionary and regularization parameter (ReLU bias). The forward pass of the encoder approximates the sufficient statistics of the E…
Generative Adversarial Networks (GANs) have been used in many different applications to generate realistic synthetic data. We introduce a novel GAN with Autoencoder (GAN-AE) architecture to generate synthetic samples for variable length, multi-feature sequence datasets. In this model, we develop a GAN architecture with an additional autoencoder component, where recurrent neural networks (RNNs) are used for each component of the model in order to generate synthetic data to improve classification accuracy for a highly imbalanced medical device dataset. In addition to the medical device dataset, …
In sequence learning tasks such as language modelling, Recurrent Neural Networks must learn relationships between input features separated by time. State of the art models such as LSTM and Transformer are trained by backpropagation of losses into prior hidden states and inputs held in memory. This allows gradients to flow from present to past and effectively learn with perfect hindsight, but at a significant memory cost. In this paper we show that it is possible to train high performance recurrent networks using information that is local in time, and thereby achieve a significantly reduced mem…
A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features/code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label/caption for a new image at test, averaging is performed across the distributi…
Center for the Neural Basis of Cognition, Machine Learning Department(认知神经基础中心,机器学习系);Carnegie Mellon University(卡内基梅隆大学)
The variational autoencoder (VAE) is a popular probabilistic generative model. However, one shortcoming of VAEs is that the latent variables cannot be discrete, which makes it difficult to generate data from different modes of a distribution. Here, we propose an extension of the VAE framework that incorporates a classifier to infer the discrete class of the modeled data. To model sequential data, we can combine our Classifying VAE with a recurrent neural network such as an LSTM. We apply this model to algorithmic music generation, where our model learns to generate musical sequences in differe…
In this paper, we explore the inclusion of latent random variables into the dynamic hidden state of a recurrent neural network (RNN) by combining elements of the variational autoencoder. We argue that through the use of high-level latent random variables, the variational RNN (VRNN)1 can model the kind of variability observed in highly structured sequential data such as natural speech. We empirically evaluate the proposed model against related sequential models on four speech datasets and one handwriting dataset. Our results show the important roles that latent random variables can play in the …
Denso Corporation(电装公司);Toyohashi University of Technology(丰桥技术科学大学)
Clustering algorithms have wide applications and play an important role in data analysis fields including time series data analysis. However, in time series analysis, most of the algorithms used signal shape features or the initial value of hidden variable of a neural network. Little has been discussed on the methods based on the generative model of the time series. In this paper, we propose a new clustering algorithm focusing on the generative process of the signal with a recurrent neural network and the variational Bayes method. Our experiments show that the proposed algorithm not only has a…
Variational autoencoders (VAEs) are powerful deep generative models widely used to represent high-dimensional complex data through a low-dimensional latent space learned in an unsupervised manner. In the original VAE model, the input data vectors are processed independently. Recently, a series of papers have presented different extensions of the VAE to process sequential data, which model not only the latent space but also the temporal dependencies within a sequence of data vectors and corresponding latent vectors, relying on recurrent neural networks or state-space models. In this paper, we p…
Time series sequence prediction and modelling has proven to be a challenging endeavor in real world datasets. Two key issues are the multi-dimensionality of data and the interaction of independent dimensions forming a latent output signal, as well as the representation of multi-dimensional temporal data inside of a predictive model. This paper proposes a multi-branch deep neural network approach to tackling the aforementioned problems by modelling a latent state vector representation of data windows through the use of a recurrent autoencoder branch and subsequently feeding the trained latent v…
In this paper, we present a deep learning technique for data-driven predictions of wave propagation in a fluid medium. The technique relies on an attention-based convolutional recurrent autoencoder network (AB-CRAN). To construct a low-dimensional representation of wave propagation data, we employ a denoising-based convolutional autoencoder. The AB-CRAN architecture with attention-based long short-term memory cells forms our deep neural network model for the time marching of the low-dimensional features. We assess the proposed AB-CRAN framework against the standard recurrent neural network for…
Missing data is a recurrent and challenging problem, especially when using machine learning algorithms for real-world applications. For this reason, missing data imputation has become an active research area, in which recent deep learning approaches have achieved state-of-the-art results. We propose DAEMA (Denoising Autoencoder with Mask Attention), an algorithm based on a denoising autoencoder architecture with an attention mechanism. While most imputation algorithms use incomplete inputs as they would use complete data - up to basic preprocessing (e.g. mean imputation) - DAEMA leverages a ma…
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still not solved for the non-linear Granger causality. The application works often deal with this problem in virtue of the proxy variables, who can be treated as a measure of the confounder with noise. But the proxy variables has been proved to be unreliable, because of the bias it may induce. In this paper, we try to "recover" the unobserved confounders for the …