Refining Coarse-Grained Spatial Data Using Auxiliary Spatial Data Sets with Various Granularities

Tanaka, Yusuke; Iwata, Tomoharu; Tanaka, Toshiyuki; Kurashima, Toshio; Okawa, Maya; Toda, Hiroyuki

doi:10.1609/aaai.v33i01.33015091

Cited by 5 publications

(5 citation statements)

References 15 publications

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“…A Gaussian process-based model was recently proposed for refining coarse-grained areal data by utilizing auxiliary data sets with various granularities [26]. In this model, a Gaussian process regression is first applied to each auxiliary data set for deriving a predictive distribution defined on the continuous space; this conceptually corresponds to spatial interpolation.…”

Section: Related Workmentioning

confidence: 99%

“…In addition, these regression-based models (e.g., [15,21,26]) do not consider the spatial aggregation constraints for the auxiliary data sets; meanwhile it is a critical factor in estimating the multivariate function from multiple areal data sets, which is the problem focused in this paper. Different from the regression-based models, we design a joint distribution that incorporates the spatial aggregation process for all areal data sets (i.e., for both target and auxiliary data sets).…”

Section: Related Workmentioning

confidence: 99%

“…Baselines. We compared the proposed model, SAGP, with naive Gaussian process regression (GPR) [22], two-stage GP-based model (2-stage GP) [26], and semiparametric latent factor model (SLFM) [28]. GPR predicts the fine-grained target data simply by using only the coarse-grained target data.…”

mentioning

confidence: 99%

“…We thus associate each areal observation with the centroid of the region. This simplification is also used for modeling the auxiliary data sets in [26].…”

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confidence: 99%

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Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

Tanaka,

Iwata

et al. 2019

Preprint

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We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models require the fine-grained auxiliary data sets on the same domain. With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design its observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine the coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.One promising approach to address this problem is to utilize a wide variety of data sets from the same city. Existing regression-based models learn relationships between target data and auxiliary Preprint. Under review.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

mentioning

confidence: 99%

“…We thus associate each areal observation with the centroid of the region. This simplification is also used for modeling the auxiliary data sets in [26].…”

mentioning

confidence: 99%

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Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

Tanaka,

Iwata

et al. 2019

Preprint

Self Cite

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“…Developing machine learning algorithms that learn coarse labels to make finegrained predictions is difficult, because the information the algorithm aims to learn is not explicitly provided by the labels in the training set. In previous literature, the research most relevant to ours is using Gaussian Process based approaches to learning fine-grained estimation from aggregate outputs 17,18 . They assume that the aggregate output or group statistics (e.g., the average fine-grained label) of a bag of inputs is known.…”

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confidence: 99%

Learning fine-grained estimation of physiological states from coarse-grained labels by distribution restoration

Qin

Chen

Jiang

et al. 2020

Sci Rep

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Due to its importance in clinical science, the estimation of physiological states (e.g., the severity of pathological tremor) has aroused growing interest in machine learning community. While the physiological state is a continuous variable, its continuity is lost when the physiological state is quantized into a few discrete classes during recording and labeling. The discreteness introduces misalignment between the true value and its label, meaning that these labels are unfortunately imprecise and coarse-grained. Most previous work did not consider the inaccuracy and directly utilized the coarse labels to train the machine learning algorithms, whose predictions are also coarse-grained. In this work, we propose to learn a precise, fine-grained estimation of physiological states using these coarse-grained ground truths. Established on mathematical rigorous proof, we utilize imprecise labels to restore the probabilistic distribution of precise labels in an approximate order-preserving fashion, then the deep neural network learns from this distribution and offers fine-grained estimation. We demonstrate the effectiveness of our approach in assessing the pathological tremor in Parkinson’s Disease and estimating the systolic blood pressure from bioelectrical signals.

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Entropic herding

2023

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Herding is a deterministic algorithm used to generate data points regarded as random samples satisfying input moment conditions. This algorithm is based on a high-dimensional dynamical system and rooted in the maximum entropy principle of statistical inference. We propose an extension, entropic herding, which generates a sequence of distributions instead of points. We derived entropic herding from an optimization problem obtained using the maximum entropy principle. Using the proposed entropic herding algorithm as a framework, we discussed a closer connection between the herding and maximum entropy principle. Specifically, we interpreted the original herding algorithm as a tractable version of the entropic herding, the ideal output distribution of which is mathematically represented. We further discussed how the complex behavior of the herding algorithm contributes to optimization. We argued that the proposed entropic herding algorithm extends the herding to probabilistic modeling. In contrast to the original herding, the entropic herding can generate a smooth distribution such that both efficient probability density calculation and sample generation become possible. To demonstrate the viability of these arguments in this study, numerical experiments were conducted, including a comparison with other conventional methods, on both synthetic and real data.

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Refining Coarse-Grained Spatial Data Using Auxiliary Spatial Data Sets with Various Granularities

Cited by 5 publications

References 15 publications

Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs

Learning fine-grained estimation of physiological states from coarse-grained labels by distribution restoration

Entropic herding

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