You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Author(s): Qin, C; Rusu, F | Abstract: Model calibration is a major challenge faced by the plethora of statistical analytics packages that are increasingly used in Big Data applications. Identifying the optimal model parameters is a time-consuming process that has to be executed from scratch for every dataset model combination even by experienced data scientists. We argue that the incapacity to evaluate multiple parameter configurations simultaneously and the lack of support to quickly identify sub-optimal configurations are the principal causes. In this paper, we develop two database-inspired techniques for efficient model calibration. Speculative parameter testing applies advanced parallel multi-query processing methods to evaluate several configurations concurrently. The number of configurations is determined adaptively at runtime, while the configurations themselves are extracted from a distribution that is continuously learned following a Bayesian process. Online aggregation is applied to identify sub-optimal configurations early in the processing by incrementally sampling the training dataset and estimating the objective function corresponding to each configuration. We design concurrent online aggregation estimators and define halting conditions to accurately and timely stop the execution. We apply the proposed techniques to distributed gradient descent optimization -- batch and incremental -- for support vector machines and logistic regression models. We implement the resulting solutions in GLADE PF-OLA -- a state-of-the-art Big Data analytics system -- and evaluate their performance over terascale-size synthetic and real datasets. The results confirm that as many as 32 configurations can be evaluated concurrently almost as fast as one, while sub-optimal configurations are detected accurately in as little as a @math fraction of the time.

Cited Abstract(s):
[1]: Incremental gradient descent is a general technique to solve a large class of convex optimization problems arising in many machine learning tasks. GLADE is a parallel infrastructure for big data analytics providing a generic task specification interface. In this paper, we present a scalable and efficient parallel solution for incremental gradient descent in GLADE. We provide empirical evidence that our solution is limited only by the physical hardware characteristics, uses effectively the available resources, and achieves maximum scalability. When deployed in the cloud, our solution has the potential to dramatically reduce the cost of complex analytics over massive datasets.

[2]: Online aggregation provides continuous estimates to the final result of a computation during the actual processing. The user can stop the computation as soon as the estimate is accurate enough, typically early in the execution, or can let the processing terminate and obtain the exact result. In this demonstration, we introduce a general framework for parallel online aggregation in which estimation does not incur overhead on top of the actual processing. We define a generic interface to express any estimation model that abstracts completely the execution details. We design multiple sampling-based estimators suited for parallel online aggregation and implement them inside the framework. Demonstration participants are shown how estimates to general SQL aggregation queries over terabytes of TPC-H data are generated during the entire processing. Due to parallel execution, the estimate converges to the correct result in a matter of seconds even for the most difficult queries. The behavior of the estimators is evaluated under different operating regimes of the distributed cluster used in the demonstration.

[3]: Online aggregation provides estimates to the final result of a computation during the actual processing. The user can stop the computation as soon as the estimate is accurate enough, typically early in the execution. This allows for the interactive data exploration of the largest datasets. In this paper we introduce the first framework for parallel online aggregation in which the estimation virtually does not incur any overhead on top of the actual execution. We define a generic interface to express any estimation model that abstracts completely the execution details. We design a novel estimator specifically targeted at parallel online aggregation. When executed by the framework over a massive 8 TB TPC-H instance, the estimator provides accurate confidence bounds early in the execution even when the cardinality of the final result is seven orders of magnitude smaller than the dataset size and without incurring overhead.

[4]: Distributed solution for solving low-rank matrix factorization (LMF), an important problem in recommendation system, has recently been studied a lot in order to better deal with the exploding data under the context of Big Data. Stochastic gradient descent is a general technique to solve a large class of convex optimization problems and it is often been chosen to solve problems that deals with large data sets in particular. In this work, we summarize the existing distributed solutions of LMF problem using stochastic gradient descent. We then proposed a novel distributed solution for LMF problem and our solution is able to achieve the best convergence rate as well as fastest execution time when compared with existing solutions. When deployed in the cloud, our solution has the potential to dramatically reduce the cost of complex analytics over massive datasets.
* GLADE PF-OLA. The novelty of our work compared to the PF-OLA framework [3] [2] comes from applying online aggregation estimators to complex analytics, rather than focusing on standard SQL aggregates---the case in previous literature. We are the first to model gradient descent optimization as an aggregation problem. This allows us to design multiple concurrent estimators and to define halting mechanisms that stop the execution when model update and loss computation are overlapped. Moreover, the integration of online aggregation with speculative step evaluation allows for early identification of sub-optimal step sizes and directs the system resources toward the promising configurations. None of the existing systems, including GLADE PF-OLA, support concurrent hyper-parameter evaluation or concurrent estimators. Our previous work on gradient descent optimization in GLADE [1] [4] is limited to IGD. In this paper, we also consider BGD and propose general methods applicable to distributed gradient descent optimization.