We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to incorporate certain structured information of the data. We develop a simple-to-implement training procedure that smoothly accommodates the use of mixed Gaussian as prior. Theory is provided to quantify the benefits of our proposed models, compared to the classical diffusion models. Numerical experiments with synthetic, image and operational data are conducted to show comparative advantages of our model. Our method is shown to be robust to mis-specifications and in particular suits situations where training resources are limited or faster training in real time is desired.

This paper introduces Target Strangeness, a novel difficulty estimator for conformal prediction (CP) that offers an alternative approach for normalizing prediction intervals (PIs). By assessing how atypical a prediction is within the context of its nearest neighbours' target distribution, Target Strangeness can surpass the current state-of-the-art performance. This novel difficulty estimator is evaluated against others in the context of several conformal regression experiments.

Although recent advancements in end-to-end learning-based link prediction (LP) methods have shown remarkable capabilities, the significance of traditional similarity-based LP methods persists in unsupervised scenarios where there are no known link labels. However, the selection of node features for similarity computation in similarity-based LP can be challenging. Less informative node features can result in suboptimal LP performance. To address these challenges, we integrate self-supervised graph learning techniques into similarity-based LP and propose a novel method: Self-Supervised Similarity-based LP (3SLP). 3SLP is suitable for the unsupervised condition of similarity-based LP without the assistance of known link labels. Specifically, 3SLP introduces a dual-view contrastive node representation learning (DCNRL) with crafted data augmentation and node representation learning. DCNRL is dedicated to developing more informative node representations, replacing the node attributes as inputs in the similarity-based LP backbone. Extensive experiments over benchmark datasets demonstrate the salient improvement of 3SLP, outperforming the baseline of traditional similarity-based LP by up to 21.2% (AUC).

Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying iterative process and provide convergence (rate) guarantees for the resulting derivative iterates. We adapt these convergence results and apply them to proximal gradient descent with variable step size and FISTA when solving partly smooth problems. We confirm our findings numerically by solving $\ell_1$ and $\ell_2$-regularized linear and logisitc regression respectively. Our theoretical and numerical results show that the convergence rate of the algorithm is reflected in its derivative iterates.

Beam tracking is an essential functionality of millimeter wave (mmWave, 30-100 GHz) and sub-terahertz (sub-THz, 100-300 GHz) 5G/6G systems. It operates by performing antenna sweeping at both base station (BS) and user equipment (UE) sides using the Synchronization Signal Blocks (SSB). The optimal frequency of beam tracking events is not specified by 3GPP standards and heavily depends on the micromobility properties of the applications currently utilized by the user. In absence of explicit signalling for the type of application at the air interface, in this paper, we propose a way to remotely detect it at the BS side based on the received signal strength pattern. To this aim, we first perform a multi-stage measurement campaign at 156 GHz, belonging to the sub-THz band, to obtain the received signal strength traces of popular smartphone applications. Then, we proceed applying conventional statistical Mann-Whitney tests and various machine learning (ML) based classification techniques to discriminate applications remotely. Our results show that Mann-Whitney test can be used to differentiate between fast and slow application classes with a confidence of 0.95 inducing class detection delay on the order of 1 s after application initialization. With the same time budget, random forest classifiers can differentiate between applications with fast and slow micromobility with 80% accuracy using received signal strength metric only. The accuracy of detecting a specific application however is lower, reaching 60%. By utilizing the proposed technique one can estimate the optimal values of the beam tracking intervals without adding additional signalling to the air interface.

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

The growing adoption of data lakes for managing relational data necessitates efficient, open storage formats that provide high scan performance and competitive compression ratios. While existing formats achieve fast scans through lightweight encoding techniques, they have reached a plateau in terms of minimizing storage footprint. Recently, correlation-aware compression schemes have been shown to reduce file sizes further. Yet, current approaches either incur significant scan overheads or require manual specification of correlations, limiting their practicability. We present $\texttt{Virtual}$, a framework that integrates seamlessly with existing open formats to automatically leverage data correlations, achieving substantial compression gains while having minimal scan performance overhead. Experiments on data-gov datasets show that $\texttt{Virtual}$ reduces file sizes by up to 40% compared to Apache Parquet.

Federated learning has recently gained popularity as a framework for distributed clients to collaboratively train a machine learning model using local data. While traditional federated learning relies on a central server for model aggregation, recent advancements adopt a decentralized framework, enabling direct model exchange between clients and eliminating the single point of failure. However, existing decentralized frameworks often assume all clients train a shared model. Personalizing each client's model can enhance performance, especially with heterogeneous client data distributions. We propose FedSPD, an efficient personalized federated learning algorithm for the decentralized setting, and show that it learns accurate models even in low-connectivity networks. To provide theoretical guarantees on convergence, we introduce a clustering-based framework that enables consensus on models for distinct data clusters while personalizing to unique mixtures of these clusters at different clients. This flexibility, allowing selective model updates based on data distribution, substantially reduces communication costs compared to prior work on personalized federated learning in decentralized settings. Experimental results on real-world datasets show that FedSPD outperforms multiple decentralized variants of personalized federated learning algorithms, especially in scenarios with low-connectivity networks.

Abstract: This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.

In neuroscience, researchers typically conduct experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analysing high-dimensional spike data is a challenging statistical problem. To this end, Gaussian process factor analysis (GPFA), a popular class of latent variable models has been proposed. GPFA extracts smooth, low-dimensional latent trajectories underlying high-dimensional spike train datasets. However, such analyses are often done separately for each experimental condition, contrary to the nature of neural datasets, which contain recordings under multiple experimental conditions. Exploiting the parametric nature of these conditions, we propose a multi-condition GPFA model and inference procedure to learn the underlying latent structure in the corresponding datasets in sample-efficient manner. In particular, we propose a non-parametric Bayesian approach to learn a smooth tuning function over the experiment condition space. Our approach not only boosts model accuracy and is faster, but also improves model interpretability compared to approaches that separately fit models for each experimental condition.