Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by approximating attention) to sparse spectrum Gaussian processes (by approximating the covariance function). Efficiency can be further improved by speeding up the convergence of these estimates: a variance reduction problem. We tackle this through the unifying framework of optimal transport, using theoretical insights and numerical algorithms to develop novel, high-performing RF couplings for kernels defined on Euclidean and discrete input spaces. They enjoy concrete theoretical performance guarantees and sometimes provide strong empirical downstream gains, including for scalable approximate inference on graphs. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm.

Node classification is a fundamental task, but obtaining node classification labels can be challenging and expensive in many real-world scenarios. Transfer learning has emerged as a promising solution to address this challenge by leveraging knowledge from source domains to enhance learning in a target domain. Existing transfer learning methods for node classification primarily focus on integrating Graph Convolutional Networks (GCNs) with various transfer learning techniques. While these approaches have shown promising results, they often suffer from a lack of theoretical guarantees, restrictive conditions, and high sensitivity to hyperparameter choices. To overcome these limitations, we propose a Graph Convolutional Multinomial Logistic Regression (GCR) model and a transfer learning method based on the GCR model, called Trans-GCR. We provide theoretical guarantees of the estimate obtained under GCR model in high-dimensional settings. Moreover, Trans-GCR demonstrates superior empirical performance, has a low computational cost, and requires fewer hyperparameters than existing methods.

Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than Langevin-based algorithms in the deterministic setting Lee et al. (2021), has yet to be explored in its stochastic variants. In this paper, we study the Stochastic Proximal Samplers (SPS) for sampling from non-log-concave distributions. We first establish a general framework for implementing stochastic proximal samplers and establish the convergence theory accordingly. We show that the convergence to the target distribution can be guaranteed as long as the second moment of the algorithm trajectory is bounded and restricted Gaussian oracles can be well approximated. We then provide two implementable variants based on Stochastic gradient Langevin dynamics (SGLD) and Metropolis-adjusted Langevin algorithm (MALA), giving rise to SPS-SGLD and SPS-MALA. We further show that SPS-SGLD and SPS-MALA can achieve $\epsilon$-sampling error in total variation (TV) distance within $\tilde{\mathcal{O}}(d\epsilon^{-2})$ and $\tilde{\mathcal{O}}(d^{1/2}\epsilon^{-2})$ gradient complexities, which outperform the best-known result by at least an $\tilde{\mathcal{O}}(d^{1/3})$ factor. This enhancement in performance is corroborated by our empirical studies on synthetic data with various dimensions, demonstrating the efficiency of our proposed algorithm.

Uncertainty quantification for multi-view learning is motivated by the increasing use of multi-view data in scientific problems. A common variant of multi-view learning is late fusion: train separate predictors on individual views and combine them after single-view predictions are available. Existing methods for uncertainty quantification for late fusion often rely on undesirable distributional assumptions for validity. Conformal prediction is one approach that avoids such distributional assumptions. However, naively applying conformal prediction to late-stage fusion pipelines often produces overly conservative and uninformative prediction regions, limiting its downstream utility. We propose a novel methodology, Multi-View Conformal Prediction (MVCP), where conformal prediction is instead performed separately on the single-view predictors and only fused subsequently. Our framework extends the standard scalar formulation of a score function to a multivariate score that produces more efficient downstream prediction regions in both classification and regression settings. We then demonstrate that such improvements can be realized in methods built atop conformalized regressors, specifically in robust predict-then-optimize pipelines.

Machine learning (ML) provides algorithms to create computer programs based on data without explicitly programming them. In business process management (BPM), ML applications are used to analyse and improve processes efficiently. Three frequent examples of using ML are providing decision support through predictions, discovering accurate process models, and improving resource allocation. This paper organises the body of knowledge on ML in BPM. We extract BPM tasks from different literature streams, summarise them under the phases of a process`s lifecycle, explain how ML helps perform these tasks and identify technical commonalities in ML implementations across tasks. This study is the first exhaustive review of how ML has been used in BPM. We hope that it can open the door for a new era of cumulative research by helping researchers to identify relevant preliminary work and then combine and further develop existing approaches in a focused fashion. Our paper helps managers and consultants to find ML applications that are relevant in the current project phase of a BPM initiative, like redesigning a business process. We also offer - as a synthesis of our review - a research agenda that spreads ten avenues for future research, including applying novel ML concepts like federated learning, addressing less regarded BPM lifecycle phases like process identification, and delivering ML applications with a focus on end-users.

Imitation learning aims to learn a policy from observing expert demonstrations without access to reward signals from environments. Generative adversarial imitation learning (GAIL) formulates imitation learning as adversarial learning, employing a generator policy learning to imitate expert behaviors and discriminator learning to distinguish the expert demonstrations from agent trajectories. Despite its encouraging results, GAIL training is often brittle and unstable. Inspired by the recent dominance of diffusion models in generative modeling, this work proposes Diffusion-Reward Adversarial Imitation Learning (DRAIL), which integrates a diffusion model into GAIL, aiming to yield more precise and smoother rewards for policy learning. Specifically, we propose a diffusion discriminative classifier to construct an enhanced discriminator; then, we design diffusion rewards based on the classifier's output for policy learning. We conduct extensive experiments in navigation, manipulation, and locomotion, verifying DRAIL's effectiveness compared to prior imitation learning methods. Moreover, additional experimental results demonstrate the generalizability and data efficiency of DRAIL. Visualized learned reward functions of GAIL and DRAIL suggest that DRAIL can produce more precise and smoother rewards.

First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their widespread, second-order optimization algorithms exhibit superior convergence properties compared to their first-order counterparts e.g. Adam and SGD. However, their practicality in training DNNs are still limited due to increased per-iteration computations and suboptimal accuracy compared to the first order methods. We present AdaFisher--an adaptive second-order optimizer that leverages a block-diagonal approximation to the Fisher information matrix for adaptive gradient preconditioning. AdaFisher aims to bridge the gap between enhanced convergence capabilities and computational efficiency in second-order optimization framework for training DNNs. Despite the slow pace of second-order optimizers, we showcase that AdaFisher can be reliably adopted for image classification, language modelling and stand out for its stability and robustness in hyperparameter tuning. We demonstrate that AdaFisher outperforms the SOTA optimizers in terms of both accuracy and convergence speed. Code available from \href{https://github.com/AtlasAnalyticsLab/AdaFisher}{https://github.com/AtlasAnalyticsLab/AdaFisher}

We address the problem of federated domain generalization in an unsupervised setting for the first time. We first theoretically establish a connection between domain shift and alignment of gradients in unsupervised federated learning and show that aligning the gradients at both client and server levels can facilitate the generalization of the model to new (target) domains. Building on this insight, we propose a novel method named FedGaLA, which performs gradient alignment at the client level to encourage clients to learn domain-invariant features, as well as global gradient alignment at the server to obtain a more generalized aggregated model. To empirically evaluate our method, we perform various experiments on four commonly used multi-domain datasets, PACS, OfficeHome, DomainNet, and TerraInc. The results demonstrate the effectiveness of our method which outperforms comparable baselines. Ablation and sensitivity studies demonstrate the impact of different components and parameters in our approach. The source code will be available online upon publication.

Autism Spectrum Disorder is a condition characterized by a typical brain development leading to impairments in social skills, communication abilities, repetitive behaviors, and sensory processing. There have been many studies combining brain MRI images with machine learning algorithms to achieve objective diagnosis of autism, but the correlation between white matter and autism has not been fully utilized. To address this gap, we develop a computer-aided diagnostic model focusing on white matter regions in brain MRI by employing radiomics and machine learning methods. This study introduced a MultiUNet model for segmenting white matter, leveraging the UNet architecture and utilizing manually segmented MRI images as the training data. Subsequently, we extracted white matter features using the Pyradiomics toolkit and applied different machine learning models such as Support Vector Machine, Random Forest, Logistic Regression, and K-Nearest Neighbors to predict autism. The prediction sets all exceeded 80% accuracy. Additionally, we employed Convolutional Neural Network to analyze segmented white matter images, achieving a prediction accuracy of 86.84%. Notably, Support Vector Machine demonstrated the highest prediction accuracy at 89.47%. These findings not only underscore the efficacy of the models but also establish a link between white matter abnormalities and autism. Our study contributes to a comprehensive evaluation of various diagnostic models for autism and introduces a computer-aided diagnostic algorithm for early and objective autism diagnosis based on MRI white matter regions.

The recently introduced Consistency models pose an efficient alternative to diffusion algorithms, enabling rapid and good quality image synthesis. These methods overcome the slowness of diffusion models by directly mapping noise to data, while maintaining a (relatively) simpler training. Consistency models enable a fast one- or few-step generation, but they typically fall somewhat short in sample quality when compared to their diffusion origins. In this work we propose a novel and highly effective technique for post-processing Consistency-based generated images, enhancing their perceptual quality. Our approach utilizes a joint classifier-discriminator model, in which both portions are trained adversarially. While the classifier aims to grade an image based on its assignment to a designated class, the discriminator portion of the very same network leverages the softmax values to assess the proximity of the input image to the targeted data manifold, thereby serving as an Energy-based Model. By employing example-specific projected gradient iterations under the guidance of this joint machine, we refine synthesized images and achieve an improved FID scores on the ImageNet 64x64 dataset for both Consistency-Training and Consistency-Distillation techniques.