The Work Disability Functional Assessment Battery (WD-FAB) is a multidimensional item response theory (IRT) instrument designed for assessing work-related mental and physical function based on responses to an item bank. In prior iterations it was developed using traditional means -- linear factorization, followed by statistical testing for item selection, and finally, calibration of disjoint unidimensional IRT models. As a result, the WD-FAB, like many other IRT instruments, is a posthoc model. In this manuscript, we derive an interpretable probabilistic autoencoder architecture that embeds as the decoder a Bayesian hierarchical model for self-consistently performing the following simultaneous tasks: scale factorization, item selection, parameter identification, and response scoring. This method obviates the linear factorization and null hypothesis statistical tests that are usually required for developing multidimensional IRT models, so that partitioning is consistent with the ultimate nonlinear factor model. We use the method on WD-FAB item responses and compare the resulting item discriminations to those obtained using the traditional method.
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The ever-growing size of modern space-time data sets, such as those collected by remote sensing, requires new techniques for their efficient and automated processing, including gap-filling of missing values. CUDA-based parallelization on GPU has become a popular way to dramatically increase computational efficiency of various approaches. Recently, we have proposed a computationally efficient and competitive, yet simple spatial prediction approach inspired from statistical physics models, called modified planar rotator (MPR) method. Its GPU implementation allowed additional impressive computational acceleration exceeding two orders of magnitude in comparison with CPU calculations. In the current study we propose a rather general approach to modelling spatial heterogeneity in GPU-implemented spatial prediction methods for two-dimensional gridded data by introducing spatial variability to model parameters. Predictions of unknown values are obtained from non-equilibrium conditional simulations, assuming ``local'' equilibrium conditions. We demonstrate that the proposed method leads to significant improvements in both prediction performance and computational efficiency.
Current deep learning classifiers, carry out supervised learning and store class discriminatory information in a set of shared network weights. These weights cannot be easily altered to incrementally learn additional classes, since the classification weights all require retraining to prevent old class information from being lost and also require the previous training data to be present. We present a novel two stage architecture which couples visual feature learning with probabilistic models to represent each class in the form of a Gaussian Mixture Model. By using these independent class representations within our classifier, we outperform a benchmark of an equivalent network with a Softmax head, obtaining increased accuracy for sample sizes smaller than 12 and increased weighted F1 score for 3 imbalanced class profiles in that sample range. When learning new classes our classifier exhibits no catastrophic forgetting issues and only requires the new classes' training images to be present. This enables a database of growing classes over time which can be visually indexed and reasoned over.
Deep transfer learning (DTL) has formed a long-term quest toward enabling deep neural networks (DNNs) to reuse historical experiences as efficiently as humans. This ability is named knowledge transferability. A commonly used paradigm for DTL is firstly learning general knowledge (pre-training) and then reusing (fine-tuning) them for a specific target task. There are two consensuses of transferability of pre-trained DNNs: (1) a larger domain gap between pre-training and downstream data brings lower transferability; (2) the transferability gradually decreases from lower layers (near input) to higher layers (near output). However, these consensuses were basically drawn from the experiments based on natural images, which limits their scope of application. This work aims to study and complement them from a broader perspective by proposing a method to measure the transferability of pre-trained DNN parameters. Our experiments on twelve diverse image classification datasets get similar conclusions to the previous consensuses. More importantly, two new findings are presented, i.e., (1) in addition to the domain gap, a larger data amount and huge dataset diversity of downstream target task also prohibit the transferability; (2) although the lower layers learn basic image features, they are usually not the most transferable layers due to their domain sensitivity.
Let $G=(V,E)$ be a multigraph with a set $T\subseteq V$ of terminals. A path in $G$ is called a $T$-path if its ends are distinct vertices in $T$ and no internal vertices belong to $T$. In 1978, Mader showed a characterization of the maximum number of edge-disjoint $T$-paths. In this paper, we provide a combinatorial, deterministic algorithm for finding the maximum number of edge-disjoint $T$-paths. The algorithm adopts an augmenting path approach. More specifically, we utilize a new concept of short augmenting walks in auxiliary labeled graphs to capture a possible augmentation of the number of edge-disjoint $T$-paths. To design a search procedure for a short augmenting walk, we introduce blossoms analogously to the matching algorithm of Edmonds (1965). When the search procedure terminates without finding a short augmenting walk, the algorithm provides a certificate for the optimality of the current edge-disjoint $T$-paths. From this certificate, one can obtain the Edmonds--Gallai type decomposition introduced by Seb\H{o} and Szeg\H{o} (2004). The algorithm runs in $O(|E|^2)$ time, which is much faster than the best known deterministic algorithm based on a reduction to linear matroid parity. We also present a strongly polynomial algorithm for the maximum integer free multiflow problem, which asks for a nonnegative integer combination of $T$-paths maximizing the sum of the coefficients subject to capacity constraints on the edges.
Graph Neural Networks (GNNs) have been predominant for graph learning tasks; however, recent studies showed that a well-known graph algorithm, Label Propagation (LP), combined with a shallow neural network can achieve comparable performance to GNNs in semi-supervised node classification on graphs with high homophily. In this paper, we show that this approach falls short on graphs with low homophily, where nodes often connect to the nodes of the opposite classes. To overcome this, we carefully design a combination of a base predictor with LP algorithm that enjoys a closed-form solution as well as convergence guarantees. Our algorithm first learns the class compatibility matrix and then aggregates label predictions using LP algorithm weighted by class compatibilities. On a wide variety of benchmarks, we show that our approach achieves the leading performance on graphs with various levels of homophily. Meanwhile, it has orders of magnitude fewer parameters and requires less execution time. Empirical evaluations demonstrate that simple adaptations of LP can be competitive in semi-supervised node classification in both homophily and heterophily regimes.
Node embedding methods map network nodes to low dimensional vectors that can be subsequently used in a variety of downstream prediction tasks. The popularity of these methods has grown significantly in recent years, yet, their robustness to perturbations of the input data is still poorly understood. In this paper, we assess the empirical robustness of node embedding models to random and adversarial poisoning attacks. Our systematic evaluation covers representative embedding methods based on Skip-Gram, matrix factorization, and deep neural networks. We compare edge addition, deletion and rewiring attacks computed using network properties as well as node labels. We also investigate the performance of popular node classification attack baselines that assume full knowledge of the node labels. We report qualitative results via embedding visualization and quantitative results in terms of downstream node classification and network reconstruction performances. We find that node classification results are impacted more than network reconstruction ones, that degree-based and label-based attacks are on average the most damaging and that label heterophily can strongly influence attack performance.
We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance from perfect calibration. Numerous calibration measures have been proposed in the literature, but it is unclear how they compare to each other, and many popular measures such as Expected Calibration Error (ECE) fail to satisfy basic properties like continuity. We present a rigorous framework for analyzing calibration measures, inspired by the literature on property testing. We propose a ground-truth notion of distance from calibration: the $\ell_1$ distance to the nearest perfectly calibrated predictor. We define a consistent calibration measure as one that is a polynomial factor approximation to the this distance. Applying our framework, we identify three calibration measures that are consistent and can be estimated efficiently: smooth calibration, interval calibration, and Laplace kernel calibration. The former two give quadratic approximations to the ground truth distance, which we show is information-theoretically optimal. Our work thus establishes fundamental lower and upper bounds on measuring distance to calibration, and also provides theoretical justification for preferring certain metrics (like Laplace kernel calibration) in practice.
Purpose: This study aims to explore training strategies to improve convolutional neural network-based image-to-image registration for abdominal imaging. Methods: Different training strategies, loss functions, and transfer learning schemes were considered. Furthermore, an augmentation layer which generates artificial training image pairs on-the-fly was proposed, in addition to a loss layer that enables dynamic loss weighting. Results: Guiding registration using segmentations in the training step proved beneficial for deep-learning-based image registration. Finetuning the pretrained model from the brain MRI dataset to the abdominal CT dataset further improved performance on the latter application, removing the need for a large dataset to yield satisfactory performance. Dynamic loss weighting also marginally improved performance, all without impacting inference runtime. Conclusion: Using simple concepts, we improved the performance of a commonly used deep image registration architecture, VoxelMorph. In future work, our framework, DDMR, should be validated on different datasets to further assess its value.
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based R\'enyi's entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank R\'enyi's entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 s)$ or even $\mathcal{O}(ns^2)$, where $n$ is the number of data samples and $s \ll n$. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based R\'enyi's entropy in terms of both performance and computational efficiency.
Transfer learning uses a data model, trained to make predictions or inferences on data from one population, to make reliable predictions or inferences on data from another population. Most existing transfer learning approaches are based on fine-tuning pre-trained neural network models, and fail to provide crucial uncertainty quantification. We develop a statistical framework for model predictions based on transfer learning, called RECaST. The primary mechanism is a Cauchy random effect that recalibrates a source model to a target population; we mathematically and empirically demonstrate the validity of our RECaST approach for transfer learning between linear models, in the sense that prediction sets will achieve their nominal stated coverage, and we numerically illustrate the method's robustness to asymptotic approximations for nonlinear models. Whereas many existing techniques are built on particular source models, RECaST is agnostic to the choice of source model. For example, our RECaST transfer learning approach can be applied to a continuous or discrete data model with linear or logistic regression, deep neural network architectures, etc. Furthermore, RECaST provides uncertainty quantification for predictions, which is mostly absent in the literature. We examine our method's performance in a simulation study and in an application to real hospital data.
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