No Arabic abstract
Quantitative analysis of large-scale data is often complicated by the presence of diverse subgroups, which reduce the accuracy of inferences they make on held-out data. To address the challenge of heterogeneous data analysis, we introduce DoGR, a method that discovers latent confounders by simultaneously partitioning the data into overlapping clusters (disaggregation) and modeling the behavior within them (regression). When applied to real-world data, our method discovers meaningful clusters and their characteristic behaviors, thus giving insight into group differences and their impact on the outcome of interest. By accounting for latent confounders, our framework facilitates exploratory analysis of noisy, heterogeneous data and can be used to learn predictive models that better generalize to new data. We provide the code to enable others to use DoGR within their data analytic workflows.
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that the covariance matrix is positive definite. To address the issue, we propose to use convolved Gaussian process (CGP) in this paper. The approach provides a semi-parametric model and offers a natural framework for modeling common mean structure and covariance structure simultaneously. The CGP enables the model to define different covariance structure for each component of the response variables. This flexibility ensures the model to cope with data coming from different resources or having different data structures, and thus to provide accurate estimation and prediction. In addition, the model is able to accommodate large-dimensional covariates. The definition of the model, the inference and the implementation, as well as its asymptotic properties, are discussed. Comprehensive numerical examples with both simulation studies and real data are presented.
Time series forecasting is a growing domain with diverse applications. However, changes of the system behavior over time due to internal or external influences are challenging. Therefore, predictions of a previously learned fore-casting model might not be useful anymore. In this paper, we present EVent-triggered Augmented Refitting of Gaussian Process Regression for Seasonal Data (EVARS-GPR), a novel online algorithm that is able to handle sudden shifts in the target variable scale of seasonal data. For this purpose, EVARS-GPR com-bines online change point detection with a refitting of the prediction model using data augmentation for samples prior to a change point. Our experiments on sim-ulated data show that EVARS-GPR is applicable for a wide range of output scale changes. EVARS-GPR has on average a 20.8 % lower RMSE on different real-world datasets compared to methods with a similar computational resource con-sumption. Furthermore, we show that our algorithm leads to a six-fold reduction of the averaged runtime in relation to all comparison partners with a periodical refitting strategy. In summary, we present a computationally efficient online fore-casting algorithm for seasonal time series with changes of the target variable scale and demonstrate its functionality on simulated as well as real-world data. All code is publicly available on GitHub: https://github.com/grimmlab/evars-gpr.
Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood procedure. A limitation of CNPs is their inability to model dependencies in the outputs. This significantly hurts predictive performance and renders it impossible to draw coherent function samples, which limits the applicability of CNPs in down-stream applications and decision making. Neural Processes (NPs; Garnelo et al., 2018) attempt to alleviate this issue by using latent variables, relying on these to model output dependencies, but introduces difficulties stemming from approximate inference. One recent alternative (Bruinsma et al.,2021), which we refer to as the FullConvGNP, models dependencies in the predictions while still being trainable via exact maximum-likelihood. Unfortunately, the FullConvGNP relies on expensive 2D-dimensional convolutions, which limit its applicability to only one-dimensional data. In this work, we present an alternative way to model output dependencies which also lends itself maximum likelihood training but, unlike the FullConvGNP, can be scaled to two- and three-dimensional data. The proposed models exhibit good performance in synthetic experiments.
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.
Both classification and regression tasks are susceptible to the biased distribution of training data. However, existing approaches are focused on the class-imbalanced learning and cannot be applied to the problems of numerical regression where the learning targets are continuous values rather than discrete labels. In this paper, we aim to improve the accuracy of the regression analysis by addressing the data skewness/bias during model training. We first introduce two metrics, uniqueness and abnormality, to reflect the localized data distribution from the perspectives of their feature (i.e., input) space and target (i.e., output) space. Combining these two metrics we propose a Variation-Incentive Loss re-weighting method (VILoss) to optimize the gradient descent-based model training for regression analysis. We have conducted comprehensive experiments on both synthetic and real-world data sets. The results show significant improvement in the model quality (reduction in error by up to 11.9%) when using VILoss as the loss criterion in training.