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Spatiotemporally continuous long-term leaf area index (LAI) products are urgently needed to monitor environmental changes. The current filter- or curve-fitting-based time series reconstructive algorithms fail to reconstruct the LAI time series with many continuous missing values or missing values in key phenological periods, which are common issues in high-spatial-resolution LAI time series. In this article, a meteorological data-driven backpropagation neural network (MBPNN) was proposed to reconstruct discontinuous LAI profiles with a two-step process using vegetation phenological information. As the basis of the strong dependence of vegetation growth on meteorological conditions, a reasonable growth trajectory of reconstructed LAI can be guaranteed by the algorithm even though if many observed values are missing. Validations for reconstructed LAI were conducted both spatially and temporally based on reference maps and field-measured long-term observations. The results showed that the LAI predicted by the MBPNN had a similar accuracy (RMSE = 0.4076) as the Landsat LAI inversions (RMSE = 0.4083) and a similar reconstructed trajectory as the field-measured LAI series even though over 100 days of continuous data were missing (RMSE = 0.1620). A comparison with the Harmonic ANalysis of Time Series (HANTS) algorithm showed that the accuracy of MBPNN was more stable regardless of the size/position of the missing data, and the proposed method performed much better when the data were continuously missing for 50 days or more.

Communication overhead is one of the major performance bottlenecks in large-scale distributed computing systems, in particular for machine learning applications. Conventionally, compression techniques are used to reduce the load of communication by combining intermediate results of the same computation task as much as possible. Recently, via the development of coded distributed computing (CDC), it has been shown that it is possible to enable coding opportunities across intermediate results of different computation tasks to further reduce the communication load. We propose a new scheme, named compressed coded distributed computing (in short, compressed CDC ), which jointly exploits the above two techniques (i.e., combining the intermediate results of the same computation and coding across the intermediate results of different computations) to significantly reduce the communication load for computations with linear aggregation (reduction) of intermediate results in the final stage that are prevalent in machine learning (e.g., distributed training algorithms where partial gradients are computed distributedly and then averaged in the final stage). In particular, compressed CDC first compresses/combines several intermediate results for a single computation, and then utilizes multiple such combined packets to create a coded multicast packet that is simultaneously useful for multiple computations. We characterize the achievable communication load of compressed CDC and show that it substantially outperforms both combining methods and CDC scheme. Based on the compressed CDC technique, we then study a distributed training problem as one of its application. We characterize the communication load for this distributed training problem and show that it is asymptotically optimal.

How can we optimally trade extra computing power to reduce the communication load in distributed computing? We answer this question by characterizing a fundamental tradeoff between computation and communication in distributed computing, i.e., the two are inversely proportional to each other. More specifically, a general distributed computing framework, motivated by commonly used structures like MapReduce, is considered, where the overall computation is decomposed into computing a set of "Map" and "Reduce" functions distributedly across multiple computing nodes. A coded scheme, named "Coded Distributed Computing" (CDC), is proposed to demonstrate that increasing the computation load of the Map functions by a factor of $r$ (i.e., evaluating each function at $r$ carefully chosen nodes) can create novel coding opportunities that reduce the communication load by the same factor. An information-theoretic lower bound on the communication load is also provided, which matches the communication load achieved by the CDC scheme. As a result, the optimal computation-communication tradeoff in distributed computing is exactly characterized. Finally, the coding techniques of CDC is applied to the Hadoop TeraSort benchmark to develop a novel CodedTeraSort algorithm, which is empirically demonstrated to speed up the overall job execution by $1.97\times$ - $3.39\times$, for typical settings of interest., To appear in IEEE Transactions on Information Theory

We consider a wireless distributed computing system, in which multiple mobile users, connected wirelessly through an access point, collaborate to perform a computation task. In particular, users communicate with each other via the access point to exchange their locally computed intermediate computation results, which is known as data shuffling. We propose a scalable framework for this system, in which the required communication bandwidth for data shuffling does not increase with the number of users in the network. The key idea is to utilize a particular repetitive pattern of placing the dataset (thus a particular repetitive pattern of intermediate computations), in order to provide coding opportunities at both the users and the access point, which reduce the required uplink communication bandwidth from users to access point and the downlink communication bandwidth from access point to users by factors that grow linearly with the number of users. We also demonstrate that the proposed dataset placement and coded shuffling schemes are optimal (i.e., achieve the minimum required shuffling load) for both a centralized setting and a decentralized setting, by developing tight information-theoretic lower bounds., Comment: To appear in IEEE/ACM Transactions on Networking