Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For the $x=a+b$ example, $a$ can be fluorescence background and $b$ the signal of interest whose statistics are to be learned from the measured $x$. Similarly, when writing $x=ab$, $a$ can be thought of as the illumination intensity and $b$ the density of fluorescent molecules of interest. Yet dividing or subtracting stochastic signals amplifies noise, and we ask instead whether, using the statistics of $a$ and the measurement of $x$ as input, we can recover the statistics of $b$. Here, we show how normalizing flows can generate an approximation of the probability distribution over $b$, thereby avoiding subtraction or division altogether. This method is implemented in our software package, NFdeconvolve, available on GitHub with a tutorial linked in the main text.

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound (ELBO), only convergence to a local optimum can be guaranteed. In this work, we instead establish the global convergence of a particular VI method. This VI method, which may be considered an instance of neural posterior estimation (NPE), minimizes an expectation of the inclusive (forward) KL divergence to fit a variational distribution that is parameterized by a neural network. Our convergence result relies on the neural tangent kernel (NTK) to characterize the gradient dynamics that arise from considering the variational objective in function space. In the asymptotic regime of a fixed, positive-definite neural tangent kernel, we establish conditions under which the variational objective admits a unique solution in a reproducing kernel Hilbert space (RKHS). Then, we show that the gradient descent dynamics in function space converge to this unique function. In ablation studies and practical problems, we demonstrate that our results explain the behavior of NPE in non-asymptotic finite-neuron settings, and show that NPE outperforms ELBO-based optimization, which often converges to shallow local optima.

We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these costs, of $m$ reference measures given a set of coefficients belonging to the $m$-dimensional simplex. The analysis problem consists of finding the coefficients for the closest barycenter in the Wasserstein-2 distance to a given measure $\mu$. Under the weakest assumptions on the measures thus far in the literature, we compute the derivative of the entropy-regularized Wasserstein-2 cost. We leverage this to establish a characterization of regularized barycenters as solutions to a fixed-point equation for the average of the entropic maps from the barycenter to the reference measures. This characterization yields a finite-dimensional, convex, quadratic program for solving the analysis problem when $\mu$ is a barycenter. It is shown that these coordinates, as well as the value of the barycenter functional, can be estimated from samples with dimension-independent rates of convergence, a hallmark of entropy-regularized optimal transport, and we verify these rates experimentally. We also establish that barycentric coordinates are stable with respect to perturbations in the Wasserstein-2 metric, suggesting a robustness of these coefficients to corruptions. We employ the barycentric coefficients as features for classification of corrupted point cloud data, and show that compared to neural network baselines, our approach is more efficient in small training data regimes.

The softmax function is a cornerstone of multi-class classification, integral to a wide range of machine learning applications, from large-scale retrieval and ranking models to advanced large language models. However, its computational cost grows linearly with the number of classes, which becomes prohibitively expensive in scenarios with millions or even billions of classes. The sampled softmax, which relies on self-normalized importance sampling, has emerged as a powerful alternative, significantly reducing computational complexity. Yet, its estimator remains unbiased only when the sampling distribution matches the true softmax distribution. To improve both approximation accuracy and sampling efficiency, we propose the MIDX Sampler, a novel adaptive sampling strategy based on an inverted multi-index approach. Concretely, we decompose the softmax probability into several multinomial probabilities, each associated with a specific set of codewords and the last associated with the residual score of queries, thus reducing time complexity to the number of codewords instead of the number of classes. To further boost efficiency, we replace the query-specific residual probability with a simple uniform distribution, simplifying the computation while retaining high performance. Our method is backed by rigorous theoretical analysis, addressing key concerns such as sampling bias, gradient bias, convergence rates, and generalization error bounds. The results demonstrate that a smaller divergence from the ideal softmax distribution leads to faster convergence and improved generalization. Extensive experiments on large-scale language models, sequential recommenders, and extreme multi-class classification tasks confirm that the MIDX-Sampler delivers superior effectiveness and efficiency compared to existing approaches.

Feature extraction techniques are crucial in medical image classification; however, classical feature extractors in addition to traditional machine learning classifiers often exhibit significant limitations in providing sufficient discriminative information for complex image sets. While Convolutional Neural Networks (CNNs) and Vision Transformer (ViT) have shown promise in feature extraction, they are prone to overfitting due to the inherent characteristics of medical imaging data, including small sample sizes or high intra-class variance. In this work, the Medical Image Attention-based Feature Extractor (MIAFEx) is proposed, a novel method that employs a learnable refinement mechanism to enhance the classification token within the Transformer encoder architecture. This mechanism adjusts the token based on learned weights, improving the extraction of salient features and enhancing the model's adaptability to the challenges presented by medical imaging data. The MIAFEx output features quality is compared against classical feature extractors using traditional and hybrid classifiers. Also, the performance of these features is compared against modern CNN and ViT models in classification tasks, demonstrating its superiority in accuracy and robustness across multiple complex classification medical imaging datasets. This advantage is particularly pronounced in scenarios with limited training data, where traditional and modern models often struggle to generalize effectively. The source code of this proposal can be found at https://github.com/Oscar-RamosS/Medical-Image-Attention-based-Feature-Extractor-MIAFEx

Heterogeneous graph pre-training (HGP) has demonstrated remarkable performance across various domains. However, the issue of heterophily in real-world heterogeneous graphs (HGs) has been largely overlooked. To bridge this research gap, we proposed a novel heterogeneous graph contrastive learning framework, termed HGMS, which leverages connection strength and multi-view self-expression to learn homophilous node representations. Specifically, we design a heterogeneous edge dropping augmentation strategy that enhances the homophily of augmented views. Moreover, we introduce a multi-view self-expressive learning method to infer the homophily between nodes. In practice, we develop two approaches to solve the self-expressive matrix. The solved self-expressive matrix serves as an additional augmented view to provide homophilous information and is used to identify false negatives in contrastive loss. Extensive experimental results demonstrate the superiority of HGMS across different downstream tasks.

Federated Learning (FL) has emerged as a decentralized machine learning technique, allowing clients to train a global model collaboratively without sharing private data. However, most FL studies ignore the crucial challenge of heterogeneous domains where each client has a distinct feature distribution, which is common in real-world scenarios. Prototype learning, which leverages the mean feature vectors within the same classes, has become a prominent solution for federated learning under domain skew. However, existing federated prototype learning methods only consider inter-domain prototypes on the server and overlook intra-domain characteristics. In this work, we introduce a novel federated prototype learning method, namely I$^2$PFL, which incorporates $\textbf{I}$ntra-domain and $\textbf{I}$nter-domain $\textbf{P}$rototypes, to mitigate domain shifts and learn a generalized global model across multiple domains in federated learning. To construct intra-domain prototypes, we propose feature alignment with MixUp-based augmented prototypes to capture the diversity of local domains and enhance the generalization of local features. Additionally, we introduce a reweighting mechanism for inter-domain prototypes to generate generalized prototypes to provide inter-domain knowledge and reduce domain skew across multiple clients. Extensive experiments on the Digits, Office-10, and PACS datasets illustrate the superior performance of our method compared to other baselines.

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation.To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. Additionally, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates.Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

Many real-world systems can be modeled as dynamic graphs, where nodes and edges evolve over time, requiring specialized models to capture their evolving dynamics in risk-sensitive applications effectively. Temporal graph neural networks (GNNs) are one such category of specialized models. For the first time, our approach integrates a reject option strategy within the framework of GNNs for continuous-time dynamic graphs. This allows the model to strategically abstain from making predictions when the uncertainty is high and confidence is low, thus minimizing the risk of critical misclassification and enhancing the results and reliability. We propose a coverage-based abstention prediction model to implement the reject option that maximizes prediction within a specified coverage. It improves the prediction score for link prediction and node classification tasks. Temporal GNNs deal with extremely skewed datasets for the next state prediction or node classification task. In the case of class imbalance, our method can be further tuned to provide a higher weightage to the minority class. Exhaustive experiments are presented on four datasets for dynamic link prediction and two datasets for dynamic node classification tasks. This demonstrates the effectiveness of our approach in improving the reliability and area under the curve (AUC)/ average precision (AP) scores for predictions in dynamic graph scenarios. The results highlight our model's ability to efficiently handle the trade-offs between prediction confidence and coverage, making it a dependable solution for applications requiring high precision in dynamic and uncertain environments.

A fundamental challenge of shared autonomy is to use high-DoF robots to assist, rather than hinder, humans by first inferring user intent and then empowering the user to achieve their intent. Although successful, prior methods either rely heavily on a priori knowledge of all possible human intents or require many demonstrations and interactions with the human to learn these intents before being able to assist the user. We propose and study a zero-shot, vision-only shared autonomy (VOSA) framework designed to allow robots to use end-effector vision to estimate zero-shot human intents in conjunction with blended control to help humans accomplish manipulation tasks with unknown and dynamically changing object locations. To demonstrate the effectiveness of our VOSA framework, we instantiate a simple version of VOSA on a Kinova Gen3 manipulator and evaluate our system by conducting a user study on three tabletop manipulation tasks. The performance of VOSA matches that of an oracle baseline model that receives privileged knowledge of possible human intents while also requiring significantly less effort than unassisted teleoperation. In more realistic settings, where the set of possible human intents is fully or partially unknown, we demonstrate that VOSA requires less human effort and time than baseline approaches while being preferred by a majority of the participants. Our results demonstrate the efficacy and efficiency of using off-the-shelf vision algorithms to enable flexible and beneficial shared control of a robot manipulator. Code and videos available here: https://sites.google.com/view/zeroshot-sharedautonomy/home.