We introduce a new small area predictor when the Fay-Herriot normal error model is fitted to a logarithmically transformed response variable, and the covariate is measured with error. This framework has been previously studied by Mosaferi et al. (2023). The empirical predictor given in their manuscript cannot perform uniformly better than the direct estimator. Our proposed predictor in this manuscript is unbiased and can perform uniformly better than the one proposed in Mosaferi et al. (2023). We derive an approximation of the mean squared error (MSE) for the predictor. The prediction intervals based on the MSE suffer from coverage problems. Thus, we propose a non-parametric bootstrap prediction interval which is more accurate. This problem is of great interest in small area applications since statistical agencies and agricultural surveys are often asked to produce estimates of right skewed variables with covariates measured with errors. With Monte Carlo simulation studies and two Census Bureau's data sets, we demonstrate the superiority of our proposed methodology.
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Out-of-distribution (OOD) generalization is a complicated problem due to the idiosyncrasies of possible distribution shifts between training and test domains. Most benchmarks employ diverse datasets to address this issue; however, the degree of the distribution shift between the training domains and the test domains of each dataset remains largely fixed. This may lead to biased conclusions that either underestimate or overestimate the actual OOD performance of a model. Our study delves into a more nuanced evaluation setting that covers a broad range of shift degrees. We show that the robustness of models can be quite brittle and inconsistent under different degrees of distribution shifts, and therefore one should be more cautious when drawing conclusions from evaluations under a limited range of degrees. In addition, we observe that large-scale pre-trained models, such as CLIP, are sensitive to even minute distribution shifts of novel downstream tasks. This indicates that while pre-trained representations may help improve downstream in-distribution performance, they could have minimal or even adverse effects on generalization in certain OOD scenarios of the downstream task if not used properly. In light of these findings, we encourage future research to conduct evaluations across a broader range of shift degrees whenever possible.
Graph diffusion equations are intimately related to graph neural networks (GNNs) and have recently attracted attention as a principled framework for analyzing GNN dynamics, formalizing their expressive power, and justifying architectural choices. One key open questions in graph learning is the generalization capabilities of GNNs. A major limitation of current approaches hinges on the assumption that the graph topologies in the training and test sets come from the same distribution. In this paper, we make steps towards understanding the generalization of GNNs by exploring how graph diffusion equations extrapolate and generalize in the presence of varying graph topologies. We first show deficiencies in the generalization capability of existing models built upon local diffusion on graphs, stemming from the exponential sensitivity to topology variation. Our subsequent analysis reveals the promise of non-local diffusion, which advocates for feature propagation over fully-connected latent graphs, under the assumption of a specific data-generating condition. In addition to these findings, we propose a novel graph encoder backbone, Advective Diffusion Transformer (ADiT), inspired by advective graph diffusion equations that have a closed-form solution backed up with theoretical guarantees of desired generalization under topological distribution shifts. The new model, functioning as a versatile graph Transformer, demonstrates superior performance across a wide range of graph learning tasks.
Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.
The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that characterizes the Green's function within a local solution representation. This paper studies various approximations of the SPM, under the condition that an appropriate reference is used for perturbation. In particular, we justify the convergence of the SPM approximations with respect to the size of scattering region and scattering length of reference, which are the central numerical parameters to achieve a linear scaling method with MST. We also present some numerical experiments on several typical systems to support the theory.
This paper develops an updatable inverse probability weighting (UIPW) estimation for the generalized linear models with response missing at random in streaming data sets. A two-step online updating algorithm is provided for the proposed method. In the first step we construct an updatable estimator for the parameter in propensity function and hence obtain an updatable estimator of the propensity function; in the second step we propose an UIPW estimator with the inverse of the updating propensity function value at each observation as the weight for estimating the parameter of interest. The UIPW estimation is universally applicable due to its relaxation on the constraint on the number of data batches. It is shown that the proposed estimator is consistent and asymptotically normal with the same asymptotic variance as that of the oracle estimator, and hence the oracle property is obtained. The finite sample performance of the proposed estimator is illustrated by the simulation and real data analysis. All numerical studies confirm that the UIPW estimator performs as well as the batch learner.
Mapping two modalities, speech and text, into a shared representation space, is a research topic of using text-only data to improve end-to-end automatic speech recognition (ASR) performance in new domains. However, the length of speech representation and text representation is inconsistent. Although the previous method up-samples the text representation to align with acoustic modality, it may not match the expected actual duration. In this paper, we proposed novel representations match strategy through down-sampling acoustic representation to align with text modality. By introducing a continuous integrate-and-fire (CIF) module generating acoustic representations consistent with token length, our ASR model can learn unified representations from both modalities better, allowing for domain adaptation using text-only data of the target domain. Experiment results of new domain data demonstrate the effectiveness of the proposed method.
We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.
Neural radiance field (NeRF) is an emerging view synthesis method that samples points in a three-dimensional (3D) space and estimates their existence and color probabilities. The disadvantage of NeRF is that it requires a long training time since it samples many 3D points. In addition, if one samples points from occluded regions or in the space where an object is unlikely to exist, the rendering quality of NeRF can be degraded. These issues can be solved by estimating the geometry of 3D scene. This paper proposes a near-surface sampling framework to improve the rendering quality of NeRF. To this end, the proposed method estimates the surface of a 3D object using depth images of the training set and sampling is performed around there only. To obtain depth information on a novel view, the paper proposes a 3D point cloud generation method and a simple refining method for projected depth from a point cloud. Experimental results show that the proposed near-surface sampling NeRF framework can significantly improve the rendering quality, compared to the original NeRF and a state-of-the-art depth-based NeRF method. In addition, one can significantly accelerate the training time of a NeRF model with the proposed near-surface sampling framework.
We consider the problem of forming prediction sets in an online setting where the distribution generating the data is allowed to vary over time. Previous approaches to this problem suffer from over-weighting historical data and thus may fail to quickly react to the underlying dynamics. Here we correct this issue and develop a novel procedure with provably small regret over all local time intervals of a given width. We achieve this by modifying the adaptive conformal inference (ACI) algorithm of Gibbs and Cand\`{e}s (2021) to contain an additional step in which the step-size parameter of ACI's gradient descent update is tuned over time. Crucially, this means that unlike ACI, which requires knowledge of the rate of change of the data-generating mechanism, our new procedure is adaptive to both the size and type of the distribution shift. Our methods are highly flexible and can be used in combination with any baseline predictive algorithm that produces point estimates or estimated quantiles of the target without the need for distributional assumptions. We test our techniques on two real-world datasets aimed at predicting stock market volatility and COVID-19 case counts and find that they are robust and adaptive to real-world distribution shifts.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
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