The class of recurrent mixture density networks is an important class of probabilistic models used extensively in sequence modeling and sequence-to-sequence mapping applications. In this class of models, the density of a target sequence in each time-step is modeled by a Gaussian mixture model with the parameters given by a recurrent neural network. In this paper, we generalize recurrent mixture density networks by defining a Gaussian mixture model on a non-linearly transformed target sequence in each time-step. The non-linearly transformed space is created by normalizing flow. We observed that this model significantly improves the fit to image sequences measured by the log-likelihood. We also applied the proposed model on some speech and image data, and observed that the model has significant modeling power outperforming other state-of-the-art methods in terms of the log-likelihood.
Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel mixture layer and constructing an adaptive RNN. The mixture layer augmented RNN (termed as M-RNN) partitions patterns in training sequences into several clusters and stores the principle patterns as prototype vectors of components in a mixture model. By leveraging the mixture layer, the proposed method can adaptively update states according to the similaritie…
Stanford University（斯坦福大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process modeling with normalizing flows. The proposed method defines a conditional distribution for each variable in a sequential process by conditioning the parameters of a normalizing flow with recurrent neural connections. Complex conditional relationships are learned through the recurrent network parameters. In this work, we present an initial design for a recurr…
Université Bourgogne Franche-Comté（弗朗什-孔泰大学）；UTBM（贝尔福-蒙贝利亚技术大学）；Université de Lorraine（洛林大学）；LORIA（洛林计算机科学与应用实验室）；CNRS（法国国家科学研究中心）
Predicting smartphone users location with WiFi fingerprints has been a popular research topic recently. In this work, we propose two novel deep learning-based models, the convolutional mixture density recurrent neural network and the VAE-based semi-supervised learning model. The convolutional mixture density recurrent neural network is designed for path prediction, in which the advantages of convolutional neural networks, recurrent neural networks and mixture density networks are combined. Further, since most of real-world datasets are not labeled, we devise the VAE-based model for the semi-su…
Mobility-on-demand (MoD) systems represent a rapidly developing mode of transportation wherein travel requests are dynamically handled by a coordinated fleet of vehicles. Crucially, the efficiency of an MoD system highly depends on how well supply and demand distributions are aligned in spatio-temporal space (i.e., to satisfy user demand, cars have to be available in the correct place and at the desired time). To do so, we argue that predictive models should aim to explicitly disentangle between temporal} and spatial variability in the evolution of urban mobility demand. However, current appro…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；University of Helsinki（赫尔辛基大学）
Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Handling discrete latent variables is then challenging because the sampling process is not differentiable. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one, causing problems especially with models havi…
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）
In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data distributions. In spite of the outstanding sample quality achieved by those early methods, they model the target distributions \emph{implicitly}, in the sense that the probability density functions induced by them are not explicitly accessible. This fact renders those methods unfit for tasks that require, for example, scoring new instances of data with the learned d…
National Research University Higher School of Economics（国立研究型大学高等经济学院）；Samsung AI Center（三星人工智能中心）
Bayesian methods have been successfully applied to sparsify weights of neural networks and to remove structure units from the networks, e. g. neurons. We apply and further develop this approach for gated recurrent architectures. Specifically, in addition to sparsification of individual weights and neurons, we propose to sparsify preactivations of gates and information flow in LSTM. It makes some gates and information flow components constant, speeds up forward pass and improves compression. Moreover, the resulting structure of gate sparsity is interpretable and depends on the task. Code is ava…
In this paper we propose a deep recurrent architecture for the probabilistic modelling of high-frequency market prices, important for the risk management of automated trading systems. Our proposed architecture incorporates probabilistic mixture models into deep recurrent neural networks. The resulting deep mixture models simultaneously address several practical challenges important in the development of automated high-frequency trading strategies that were previously neglected in the literature: 1) probabilistic forecasting of the price movements; 2) single objective prediction of both the dir…
We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM) and the neural network based probability distributions for the hidden states of the HMM, can provide a robust classification performance. The combined model is called normalizing-flow mixture model based HMM (NMM-HMM). It can be trained using a combination of expectation-maximization (EM) and backpropagation. We verify the improved robustness of NMM-HMM class…
Brown's 1971 paper "Admissible estimators, recurrent diffusions and insoluble boundary value problems" is a landmark in the admissibility literature. It nearly completely settles the issue of admissibility/inadmissibility for estimating the mean of a multivariate normal distribution with identity covariance under sum of squared error loss. We revisit this wonderful tour de force on its 50th anniversary and present an alternative and more direct proof of the result for generalized Bayes estimators corresponding to priors which are a subclass of scale mixtures of spherical normals.
Predicting smartphone users activity using WiFi fingerprints has been a popular approach for indoor positioning in recent years. However, such a high dimensional time-series prediction problem can be very tricky to solve. To address this issue, we propose a novel deep learning model, the convolutional mixture density recurrent neural network (CMDRNN), which combines the strengths of convolutional neural networks, recurrent neural networks and mixture density networks. In our model, the CNN sub-model is employed to detect the feature of the high dimensional input, the RNN sub-model is utilized …
Learning Discriminators for Resampling in the Ensemble Gaussian Mixture Filter through a Normalizing Flow Approach
Department of Mathematics, The University of Hawaii at Manoa（夏威夷大学马诺阿分校数学系）；Department of Information and Computer Sciences, The University of Hawaii at Manoa（夏威夷大学马诺阿分校信息与计算机科学系）
We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the random effects parameters influencing the response at different times. The order of the autoregression may be assumed unknown and object of inference and we consider two alternative approaches to …
In this paper, we develop a statistical methodology applied to the characterization of flowering curves using Gaussian mixture models. Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming properties of each one. In this regard, we also suggest our own selection criterion to take into account the lack of symmetry of most of the flowering curves. Three classes are created on the basis of a principal component analysis conducted on a set of reblooming indicators, and a subclassification is made using a longitudinal $k$--mea…
We present a method for pretraining a recurrent mixture density network (RMDN). We also propose a slight modification to the architecture of the RMDN-GARCH proposed by Nikolaev et al. [2012]. The pretraining method helps the RMDN avoid bad local minima during training and improves its robustness to the persistent NaN problem, as defined by Guillaumes [2017], which is often encountered with mixture density networks. Such problem consists in frequently obtaining "Not a number" (NaN) values during training. The pretraining method proposed resolves these issues by training the linear nodes in the …
The goal of personalized history-based recommendation is to automatically output a distribution over all the items given a sequence of previous purchases of a user. In this work, we present a novel approach that uses a recurrent network for summarizing the history of purchases, continuous vectors representing items for scalability, and a novel attention-based recurrent mixture density network, which outputs each component in a mixture sequentially, for modelling a multi-modal conditional distribution. We evaluate the proposed approach on two publicly available datasets, MovieLens-20M and RecSy…
Target tracking represents a state estimation problem recurrent in many practical scenarios like air traffic control, autonomous vehicles, marine radar surveillance and so on. In a Bayesian perspective, when phenomena like clutter are present, the vast majority of the existing tracking algorithms have to deal with association hypotheses which can grow in the number over time; in that case, the posterior state distribution can become computationally intractable and approximations have to be introduced. In this work, the impact of the number of hypotheses and corresponding reductions is investig…
Recurrent event data are common in clinical studies when participants are followed longitudinally, and are often subject to a terminal event. With the increasing popularity of large pragmatic trials with a heterogeneous source population, participants are often nested in clinics and can be either susceptible or structurally unsusceptible to the recurrent process. These complications require new modeling strategies to accommodate potential zero-event inflation as well as hierarchical data structures in both the terminal and non-terminal event processes. In this paper, we develop a Bayesian semi…
Accurate demand forecasts can help on-line retail organizations better plan their supply-chain processes. The challenge, however, is the large number of associative factors that result in large, non-stationary shifts in demand, which traditional time series and regression approaches fail to model. In this paper, we propose a Neural Network architecture called AR-MDN, that simultaneously models associative factors, time-series trends and the variance in the demand. We first identify several causal features and use a combination of feature embeddings, MLP and LSTM to represent them. We then mode…
Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient tree-based matching algorithm to construct image-like feature maps from high-fidelity meteorological datasets - wind, temperature and convective weather. We then model the track points on trajectories as conditional Gaussian mixtures with parameters to be learned from our proposed deep generative model, which is an end-to-end convolutional recurrent neural network …
The interest in developing smart cities has increased dramatically in recent years. In this context an intelligent transportation system depicts a major topic. The forecast of traffic flow is indispensable for an efficient intelligent transportation system. The traffic flow forecast is a difficult task, due to its stochastic and non linear nature. Besides classical statistical methods, neural networks are a promising possibility to predict future traffic flow. In our work, this prediction is performed with various recurrent neural networks. These are trained on measurements of induction loops,…
Depth-Recurrent Attention Mixtures: Giving Latent Reasoning the Attention it Deserves
Aleph Alpha Research, Heidelberg, Germany（Aleph Alpha研究机构）；Technical University of Munich, Germany（慕尼黑技术大学）；Research Group Social Computing, Technical University of Munich, Germany（社会计算研究组，慕尼黑技术大学）；Lab1141, Germany（Lab1141研究机构）；Computer Science Department, TU Darmstadt, Germany（图林根达姆施塔特技术大学计算机科学系）
Amirkabir University of Technology (Tehran Polytechnic)（德黑兰理工大学）；Department of Mathematics and Computer Science（数学与计算机科学系）；Department of Computer Engineering（计算机工程系）
With great advances in vision and natural language processing, the generation of image captions becomes a need. In a recent paper, Mathews, Xie and He [1], extended a new model to generate styled captions by separating semantics and style. In continuation of this work, here a new captioning model is developed including an image encoder to extract the features, a mixture of recurrent networks to embed the set of extracted features to a set of words, and a sentence generator that combines the obtained words as a stylized sentence. The resulted system that entitled as Mixture of Recurrent Experts…
XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting with High Volatility
Concordia University（康考迪亚大学）；Concordia Institute for Information Systems Engineering (CIISE)（康考迪亚信息系统工程研究所）；Concordia John Molson School of Business (JMSB)（康考迪亚约翰莫尔森商学院）
针对 MoD 需求受内外因素影响且高波动、传统点预测难以刻画不确定性的问题，提出 XRMDN 深度概率预测框架，并在真实数据集上验证其优于基准模型。
Tsinghua University（清华大学）；The University of Hong Kong（香港大学）；Shanghai Qizhi Institute（上海期智研究院）
Partially Observable Markov Decision Process (POMDP) provides a principled and generic framework to model real world sequential decision making processes but yet remains unsolved, especially for high dimensional continuous space and unknown models. The main challenge lies in how to accurately obtain the belief state, which is the probability distribution over the unobservable environment states given historical information. Accurately calculating this belief state is a precondition for obtaining an optimal policy of POMDPs. Recent advances in deep learning techniques show great potential to le…
In this paper we propose a deep recurrent model based on the order flow for the stationary modelling of the high-frequency directional prices movements. The order flow is the microsecond stream of orders arriving at the exchange, driving the formation of prices seen on the price chart of a stock or currency. To test the stationarity of our proposed model we train our model on data before the 2017 Bitcoin bubble period and test our model during and after the bubble. We show that without any retraining, the proposed model is temporally stable even as Bitcoin trading shifts into an extremely vola…
Personal robots assisting humans must perform complex manipulation tasks that are typically difficult to specify in traditional motion planning pipelines, where multiple objectives must be met and the high-level context be taken into consideration. Learning from demonstration (LfD) provides a promising way to learn these kind of complex manipulation skills even from non-technical users. However, it is challenging for existing LfD methods to efficiently learn skills that can generalize to task specifications that are not covered by demonstrations. In this paper, we introduce a state transition …
We propose ThalNet, a deep learning model inspired by neocortical communication via the thalamus. Our model consists of recurrent neural modules that send features through a routing center, endowing the modules with the flexibility to share features over multiple time steps. We show that our model learns to route information hierarchically, processing input data by a chain of modules. We observe common architectures, such as feed forward neural networks and skip connections, emerging as special cases of our architecture, while novel connectivity patterns are learned for the text8 compression t…
Delft University of Technology（代尔夫特理工大学）；City University of Hong Kong（香港城市大学）；Virginia Polytechnic Institute and State University（弗吉尼亚理工学院暨州立大学）
Short-term forecasting of passenger flow is critical for transit management and crowd regulation. Spatial dependencies, temporal dependencies, inter-station correlations driven by other latent factors, and exogenous factors bring challenges to the short-term forecasts of passenger flow of urban rail transit networks. An innovative deep learning approach, Multi-Graph Convolutional-Recurrent Neural Network (MGC-RNN) is proposed to forecast passenger flow in urban rail transit systems to incorporate these complex factors. We propose to use multiple graphs to encode the spatial and other heterogen…
Recurrent Neural Networks (RNNs) play a major role in the field of sequential learning, and have outperformed traditional algorithms on many benchmarks. Training deep RNNs still remains a challenge, and most of the state-of-the-art models are structured with a transition depth of 2-4 layers. Recurrent Highway Networks (RHNs) were introduced in order to tackle this issue. These have achieved state-of-the-art performance on a few benchmarks using a depth of 10 layers. However, the performance of this architecture suffers from a bottleneck, and ceases to improve when an attempt is made to add mor…
Recurrent neural networks have shown remarkable success in modeling sequences. However low resource situations still adversely affect the generalizability of these models. We introduce a new family of models, called Lattice Recurrent Units (LRU), to address the challenge of learning deep multi-layer recurrent models with limited resources. LRU models achieve this goal by creating distinct (but coupled) flow of information inside the units: a first flow along time dimension and a second flow along depth dimension. It also offers a symmetry in how information can flow horizontally and vertically…
A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the `recurrent R-U-Net' surrogate model is shown to be capable of …
In recent years, there has been increasing demand for automatic architecture search in deep learning. Numerous approaches have been proposed and led to state-of-the-art results in various applications, including image classification and language modeling. In this paper, we propose a novel way of architecture search by means of weighted networks (WeNet), which consist of a number of networks, with each assigned a weight. These weights are updated with back-propagation to reflect the importance of different networks. Such weighted networks bear similarity to mixture of experts. We conduct experi…
In this paper, we investigate a deep learning approach for speech denoising through an efficient ensemble of specialist neural networks. By splitting up the speech denoising task into non-overlapping subproblems and introducing a classifier, we are able to improve denoising performance while also reducing computational complexity. More specifically, the proposed model incorporates a gating network which assigns noisy speech signals to an appropriate specialist network based on either speech degradation level or speaker gender. In our experiments, a baseline recurrent network is compared agains…
Learning scene flow from a monocular camera still remains a challenging task due to its ill-posedness as well as lack of annotated data. Self-supervised methods demonstrate learning scene flow estimation from unlabeled data, yet their accuracy lags behind (semi-)supervised methods. In this paper, we introduce a self-supervised monocular scene flow method that substantially improves the accuracy over the previous approaches. Based on RAFT, a state-of-the-art optical flow model, we design a new decoder to iteratively update 3D motion fields and disparity maps simultaneously. Furthermore, we prop…
Swedish e-Science Research Centre (SeRC)（瑞典电子科学研究中心）
In this paper, the prediction capabilities of recurrent neural networks are assessed in the low-order model of near-wall turbulence by Moehlis {\it et al.} (New J. Phys. {\bf 6}, 56, 2004). Our results show that it is possible to obtain excellent predictions of the turbulence statistics and the dynamic behavior of the flow with properly trained long short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. We also observe that using a loss function based only on the instantaneous predictions of the flow may not lead to the best predictions in t…
The quantification of uncertainty on fluid flow in porous media is often hampered by multi-scale heterogeneity and insufficient site characterization. Monte-Carlo simulation (MCS), which runs numerical simulations for a large number of realization of input parameters , becomes infeasible when simulation cost is expensive or the degree of uncertainty is large. Many deep-neural-network-based methods are developed in order to replace the numerical flow simulation, but previous studies focused only on generating several snapshots of outputs at the fixed time steps, and lack to reflect the time dep…
Predicting traffic volume in real-time can improve both traffic flow and road safety. A precise traffic volume forecast helps alert drivers to the flow of traffic along their preferred routes, preventing potential deadlock situations. Existing parametric models cannot reliably forecast traffic volume in dynamic and complex traffic conditions. Therefore, in order to evaluate and forecast the traffic volume for every given time step in a real-time manner, we develop non-linear memory-based deep neural network models. Our extensive experiments run on the Metro Interstate Traffic Volume dataset de…
Pedestrian Volume Prediction Using a Diffusion Convolutional Gated Recurrent Unit Model
School of Statistics（统计学院）；Renmin University of China（中国人民大学）；School of Mathematics and Statistics（数学与统计学院）；The University of Melbourne（墨尔本大学）；School of Business, Law and Entrepreneurship（商学、法学与创业学院）；Swinburne University of Technology（斯威本科技大学）
Shanghai Jiao Tong University（上海交通大学）；Shanghai Transportation Information Center（上海交通信息中心）
Traffic prediction is a fundamental and vital task in Intelligence Transportation System (ITS), but it is very challenging to get high accuracy while containing low computational complexity due to the spatiotemporal characteristics of traffic flow, especially under the metropolitan circumstances. In this work, a new topological framework, called Linkage Network, is proposed to model the road networks and present the propagation patterns of traffic flow. Based on the Linkage Network model, a novel online predictor, named Graph Recurrent Neural Network (GRNN), is designed to learn the propagatio…
University of Pittsburgh（匹兹堡大学）；U.S. Geological Survey（美国地质调查局）；University of Minnesota（明尼苏达大学）
This paper proposes a physics-guided machine learning approach that combines advanced machine learning models and physics-based models to improve the prediction of water flow and temperature in river networks. We first build a recurrent graph network model to capture the interactions among multiple segments in the river network. Then we present a pre-training technique which transfers knowledge from physics-based models to initialize the machine learning model and learn the physics of streamflow and thermodynamics. We also propose a new loss function that balances the performance over differen…
In this paper we present an approach to polyphonic sound event detection in real life recordings based on bi-directional long short term memory (BLSTM) recurrent neural networks (RNNs). A single multilabel BLSTM RNN is trained to map acoustic features of a mixture signal consisting of sounds from multiple classes, to binary activity indicators of each event class. Our method is tested on a large database of real-life recordings, with 61 classes (e.g. music, car, speech) from 10 different everyday contexts. The proposed method outperforms previous approaches by a large margin, and the results a…
Donders Institute for Brain, Cognition and Behaviour（唐德斯大脑、认知与行为研究所）
Recurrent neural networks (RNNs) have been shown to perform better than feedforward architectures in visual object categorization tasks, especially in challenging conditions such as cluttered images. However, little is known about the exact computational role of recurrent information flow in these conditions. Here we test RNNs trained for object categorization on the hypothesis that recurrence iteratively aids object categorization via the communication of category-orthogonal auxiliary variables (the location, orientation, and scale of the object). Using diagnostic linear readouts, we find tha…
Multi-resolution Physics-Aware Recurrent Convolutional Neural Network for Complex Flows
School of Data Science, University of Virginia（数据科学学院，弗吉尼亚大学）；Department of Mechanical Engineering, University of Iowa（机械工程系，爱荷华大学）；Department of Mechanical and Aerospace Engineering, University of Virginia（机械与航空航天工程系，弗吉尼亚大学）
