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Register a new userCOVID-19 Time-series Prediction by Joint Dictionary Learning and Online NMF
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Hanbaek Lyu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Predicting the spread and containment of COVID-19 is a challenge of utmost importance that the broader scientific community is currently facing. One of the main sources of difficulty is that a very limited amount of daily COVID-19 case data is available, and with few exceptions, the majority of countries are currently in the exponential spread stage, and thus there is scarce information available which would enable one to predict the phase transition between spread and containment. In this paper, we propose a novel approach to predicting the spread of COVID-19 based on dictionary learning and online nonnegative matrix factorization (online NMF). The key idea is to learn dictionary patterns of short evolution instances of the new daily cases in multiple countries at the same time, so that their latent correlation structures are captured in the dictionary patterns. We first learn such patterns by minibatch learning from the entire time-series and then further adapt them to the time-series by online NMF. As we progressively adapt and improve the learned dictionary patterns to the more recent observations, we also use them to make one-step predictions by the partial fitting. Lastly, by recursively applying the one-step predictions, we can extrapolate our predictions into the near future. Our prediction results can be directly attributed to the learned dictionary patterns due to their interpretability.
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Extreme events are occurrences whose magnitude and potential cause extensive damage on people, infrastructure, and the environment. Motivated by the extreme nature of the current global health landscape, which is plagued by the coronavirus pandemic, we seek to better understand and model extreme events. Modeling extreme events is common in practice and plays an important role in time-series prediction applications. Our goal is to (i) compare and investigate the effect of some common extreme events modeling methods to explore which method can be practical in reality and (ii) accelerate the deep learning training process, which commonly uses deep recurrent neural network (RNN), by implementing the asynchronous local Stochastic Gradient Descent (SGD) framework among multiple compute nodes. In order to verify our distributed extreme events modeling, we evaluate our proposed framework on a stock data set S&P500, with a standard recurrent neural network. Our intuition is to explore the (best) extreme events modeling method which could work well under the distributed deep learning setting. Moreover, by using asynchronous distributed learning, we aim to significantly reduce the communication cost among the compute nodes and central server, which is the main bottleneck of almost all distributed learning frameworks. We implement our proposed work and evaluate its performance on representative data sets, such as S&P500 stock in $5$-year period. The experimental results validate the correctness of the design principle and show a significant training duration reduction upto $8$x, compared to the baseline single compute node. Our results also show that our proposed work can achieve the same level of test accuracy, compared to the baseline setting.
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are unknown, the corresponding optimization is inherently non-convex. This was a major challenge until recently, when provable algorithms for dictionary learning were proposed. Yet, these provide guarantees only on the recovery of the dictionary, without explicit recovery guarantees on the coefficients. Moreover, any estimation error in the dictionary adversely impacts the ability to successfully localize and estimate the coefficients. This potentially limits the utility of existing provable dictionary learning methods in applications where coefficient recovery is of interest. To this end, we develop NOODL: a simple Neurally plausible alternating Optimization-based Online Dictionary Learning algorithm, which recovers both the dictionary and coefficients exactly at a geometric rate, when initialized appropriately. Our algorithm, NOODL, is also scalable and amenable for large scale distributed implementations in neural architectures, by which we mean that it only involves simple linear and non-linear operations. Finally, we corroborate these theoretical results via experimental evaluation of the proposed algorithm with the current state-of-the-art techniques. Keywords: dictionary learning, provable dictionary learning, online dictionary learning, non-convex, sparse coding, support recovery, iterative hard thresholding, matrix factorization, neural architectures, neural networks, noodl, sparse representations, sparse signal processing.
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function changes continuously across rounds with respect to the learners decisions. We show that COL covers and more appropriately describes many interesting applications, from general equilibrium problems (EPs) to optimization in episodic MDPs. Using this new setup, we revisit the difficulty of achieving sublinear dynamic regret. We prove that there is a fundamental equivalence between achieving sublinear dynamic regret in COL and solving certain EPs, and we present a reduction from dynamic regret to both static regret and convergence rate of the associated EP. At the end, we specialize these new insights into online imitation learning and show improved understanding of its learning stability.
We consider an online revenue maximization problem over a finite time horizon subject to lower and upper bounds on cost. At each period, an agent receives a context vector sampled i.i.d. from an unknown distribution and needs to make a decision adaptively. The revenue and cost functions depend on the context vector as well as some fixed but possibly unknown parameter vector to be learned. We propose a novel offline benchmark and a new algorithm that mixes an online dual mirror descent scheme with a generic parameter learning process. When the parameter vector is known, we demonstrate an $O(sqrt{T})$ regret result as well an $O(sqrt{T})$ bound on the possible constraint violations. When the parameter is not known and must be learned, we demonstrate that the regret and constraint violations are the sums of the previous $O(sqrt{T})$ terms plus terms that directly depend on the convergence of the learning process.
Machine Learning (ML) models typically require large-scale, balanced training data to be robust, generalizable, and effective in the context of healthcare. This has been a major issue for developing ML models for the coronavirus-disease 2019 (COVID-19) pandemic where data is highly imbalanced, particularly within electronic health records (EHR) research. Conventional approaches in ML use cross-entropy loss (CEL) that often suffers from poor margin classification. For the first time, we show that contrastive loss (CL) improves the performance of CEL especially for imbalanced EHR data and the related COVID-19 analyses. This study has been approved by the Institutional Review Board at the Icahn School of Medicine at Mount Sinai. We use EHR data from five hospitals within the Mount Sinai Health System (MSHS) to predict mortality, intubation, and intensive care unit (ICU) transfer in hospitalized COVID-19 patients over 24 and 48 hour time windows. We train two sequential architectures (RNN and RETAIN) using two loss functions (CEL and CL). Models are tested on full sample data set which contain all available data and restricted data set to emulate higher class imbalance.CL models consistently outperform CEL models with the restricted data set on these tasks with differences ranging from 0.04 to 0.15 for AUPRC and 0.05 to 0.1 for AUROC. For the restricted sample, only the CL model maintains proper clustering and is able to identify important features, such as pulse oximetry. CL outperforms CEL in instances of severe class imbalance, on three EHR outcomes with respect to three performance metrics: predictive power, clustering, and feature importance. We believe that the developed CL framework can be expanded and used for EHR ML work in general.
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