Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDivide-and-Conquer: A Distributed Hierarchical Factor Approach to Modeling Large-Scale Time Series Data
159
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using Principal Component Analysis (PCA) and shows great promises for modeling large-scale data that cannot be stored nor analyzed by a single machine. Each computer at the basic level performs a PCA to extract common factors among the time series assigned to it and transfers those factors to one and only one node of the second level. Each 2nd-level computer collects the common factors from its subordinates and performs another PCA to select the 2nd-level common factors. This process is repeated until the central server is reached, which collects common factors from its direct subordinates and performs a final PCA to select the global common factors. The noise terms of the 2nd-level approximate factor model are the unique common factors of the 1st-level clusters. We focus on the case of 2 levels in our theoretical derivations, but the idea can easily be generalized to any finite number of hierarchies. We discuss some clustering methods when the group memberships are unknown and introduce a new diffusion index approach to forecasting. We further extend the analysis to unit-root nonstationary time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. We use both simulated data and real examples to assess the performance of the proposed method in finite samples, and compare our method with the commonly used ones in the literature concerning the forecastability of extracted factors.
rate research
Read More
Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long time. In this paper, we propose a divide-and-conquer based large-scale spectral clustering method to strike a good balance between efficiency and effectiveness. In the proposed method, a divide-and-conquer based landmark selection algorithm and a novel approximate similarity matrix approach are designed to construct a sparse similarity matrix within extremely low cost. Then clustering results can be computed quickly through a bipartite graph partition process. The proposed method achieves the lower computational complexity than most existing large-scale spectral clustering. Experimental results on ten large-scale datasets have demonstrated the efficiency and effectiveness of the proposed methods. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li-Hongmin/MyPaperWithCode.
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within the Fourier measurement domain is distributed non-uniformly is often neglected during reconstruction. As a result, more densely sampled low-frequency information tends to dominate penalization schemes for reconstructing MRI at the expense of high-frequency details. In this paper, we propose a new framework for CS-MRI inversion in which we decompose the observed k-space data into subspaces via sets of filters in a lossless way, and reconstruct the images in these various spaces individually using off-the-shelf algorithms. We then fuse the results to obtain the final reconstruction. In this way we are able to focus reconstruction on frequency information within the entire k-space more equally, preserving both high and low frequency details. We demonstrate that the proposed framework is competitive with state-of-the-art methods in CS-MRI in terms of quantitative performance, and often improves an algorithms results qualitatively compared with its direct application to k-space.
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.
Virtual memory (VM) is critical to the usability and programmability of hardware accelerators. Unfortunately, implementing accelerator VM efficiently is challenging because the area and power constraints make it difficult to employ the large multi-level TLBs used in general-purpose CPUs. Recent research proposals advocate a number of restrictions on virtual-to-physical address mappings in order to reduce the TLB size or increase its reach. However, such restrictions are unattractive because they forgo many of the original benefits of traditional VM, such as demand paging and copy-on-write. We propose SPARTA, a divide and conquer approach to address translation. SPARTA splits the address translation into accelerator-side and memory-side parts. The accelerator-side translation hardware consists of a tiny TLB covering only the accelerators cache hierarchy (if any), while the translation for main memory accesses is performed by shared memory-side TLBs. Performing the translation for memory accesses on the memory side allows SPARTA to overlap data fetch with translation, and avoids the replication of TLB entries for data shared among accelerators. To further improve the performance and efficiency of the memory-side translation, SPARTA logically partitions the memory space, delegating translation to small and efficient per-partition translation hardware. Our evaluation on index-traversal accelerators shows that SPARTA virtually eliminates translation overhead, reducing it by over 30x on average (up to 47x) and improving performance by 57%. At the same time, SPARTA requires minimal accelerator-side translation hardware, reduces the total number of TLB entries in the system, gracefully scales with memory size, and preserves all key VM functionalities.
We develop a novel decouple-recouple dynamic predictive strategy and contribute to the literature on forecasting and economic decision making in a data-rich environment. Under this framework, clusters of predictors generate different latent states in the form of predictive densities that are later synthesized within an implied time-varying latent factor model. As a result, the latent inter-dependencies across predictive densities and biases are sequentially learned and corrected. Unlike sparse modeling and variable selection procedures, we do not assume a priori that there is a given subset of active predictors, which characterize the predictive density of a quantity of interest. We test our procedure by investigating the predictive content of a large set of financial ratios and macroeconomic variables on both the equity premium across different industries and the inflation rate in the U.S., two contexts of topical interest in finance and macroeconomics. We find that our predictive synthesis framework generates both statistically and economically significant out-of-sample benefits while maintaining interpretability of the forecasting variables. In addition, the main empirical results highlight that our proposed framework outperforms both LASSO-type shrinkage regressions, factor based dimension reduction, sequential variable selection, and equal-weighted linear pooling methodologies.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
