Federated Learning (FL) is a machine learning framework that enables multiple organizations to train a model without sharing their data with a central server. However, it experiences significant performance degradation if the data is non-identically independently distributed (non-IID). This is a problem in medical settings, where variations in the patient population contribute significantly to distribution differences across hospitals. Personalized FL addresses this issue by accounting for site-specific distribution differences. Clustered FL, a Personalized FL variant, was used to address this problem by clustering patients into groups across hospitals and training separate models on each group. However, privacy concerns remained as a challenge as the clustering process requires exchange of patient-level information. This was previously solved by forming clusters using aggregated data, which led to inaccurate groups and performance degradation. In this study, we propose Privacy-preserving Community-Based Federated machine Learning (PCBFL), a novel Clustered FL framework that can cluster patients using patient-level data while protecting privacy. PCBFL uses Secure Multiparty Computation, a cryptographic technique, to securely calculate patient-level similarity scores across hospitals. We then evaluate PCBFL by training a federated mortality prediction model using 20 sites from the eICU dataset. We compare the performance gain from PCBFL against traditional and existing Clustered FL frameworks. Our results show that PCBFL successfully forms clinically meaningful cohorts of low, medium, and high-risk patients. PCBFL outperforms traditional and existing Clustered FL frameworks with an average AUC improvement of 4.3% and AUPRC improvement of 7.8%.
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Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of their asymptotic frequentist convergence properties. In the present paper, we consider the theoretical recovery performance of the posterior distributions associated to Besov-Laplace priors in the density estimation model, under the assumption that the observations are generated by a possibly spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov-Laplace priors attain optimal posterior contraction rates. Furthermore, we show that hierarchical procedures involving a hyper-prior on the regularity parameter lead to adaptation to any smoothness level.
Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a re-evaluation of the top-performing candidate models post-retraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data (a few thousand samples) in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135-times speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).
Early warnings for dynamical transitions in complex systems or high-dimensional observation data are essential in many real world applications, such as gene mutation, brain diseases, natural disasters, financial crises, and engineering reliability. To effectively extract early warning signals, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in low-dimensional manifold. Applying the methodology to authentic electroencephalogram (EEG) data, we successfully find the appropriate effective coordinates, and derive early warning signals capable of detecting the tipping point during the state transition. Our method bridges the latent dynamics with the original dataset. The framework is validated to be accurate and effective through numerical experiments, in terms of density and transition probability. It is shown that the second coordinate holds meaningful information for critical transition in various evaluation metrics.
A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network without imposing any differentiability assumptions. Firstly, a tractable approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints and restricting the right-hand side of the constraints with a proper positive parameter, which will be iteratively solved by a random-fixed projection algorithm. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed feasibility. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and populating the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time convergence of the distributed optimization, a distributed termination algorithm is developed based on uniformly local consensus and zeroth-order optimality under uniformly strongly connected graphs. Fourthly, it is proved that the cutting-surface consensus approach converges within a finite number of iterations. Finally, the effectiveness of the approach is illustrated through a numerical example.
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of simple calculations. However, in some applications, the collected data are given with noise and most of schemes are not adequate to process them. In this paper, we present some new families of binary univariate linear subdivision schemes using weighted local polynomial regression. We study their properties, such as convergence, monotonicity, polynomial reproduction and approximation and denoising capabilities. For the convergence study, we develop some new theoretical results. Finally, some examples are presented to confirm the proven properties.
The objective of the multi-condition human motion synthesis task is to incorporate diverse conditional inputs, encompassing various forms like text, music, speech, and more. This endows the task with the capability to adapt across multiple scenarios, ranging from text-to-motion and music-to-dance, among others. While existing research has primarily focused on single conditions, the multi-condition human motion generation remains underexplored. In this paper, we address these challenges by introducing MCM, a novel paradigm for motion synthesis that spans multiple scenarios under diverse conditions. The MCM framework is able to integrate with any DDPM-like diffusion model to accommodate multi-conditional information input while preserving its generative capabilities. Specifically, MCM employs two-branch architecture consisting of a main branch and a control branch. The control branch shares the same structure as the main branch and is initialized with the parameters of the main branch, effectively maintaining the generation ability of the main branch and supporting multi-condition input. We also introduce a Transformer-based diffusion model MWNet (DDPM-like) as our main branch that can capture the spatial complexity and inter-joint correlations in motion sequences through a channel-dimension self-attention module. Quantitative comparisons demonstrate that our approach achieves SoTA results in both text-to-motion and competitive results in music-to-dance tasks, comparable to task-specific methods. Furthermore, the qualitative evaluation shows that MCM not only streamlines the adaptation of methodologies originally designed for text-to-motion tasks to domains like music-to-dance and speech-to-gesture, eliminating the need for extensive network re-configurations but also enables effective multi-condition modal control, realizing "once trained is motion need".
Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical $k$--$NN$ regression, termed $\alpha$--$k$--$NN$ regression, that yields a highly flexible non-parametric regression model for compositional data through the use of the $\alpha$-transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between the compositional response data and Euclidean predictor variables. Both suggest that $\alpha$--$k$--$NN$ regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the $\alpha$--$k$--$NN$ regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large scale, massive, or big data.
Estimating parameters from data is a fundamental problem in physics, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, researchers often employ their domain expertise to select a specific range of wavevectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through Fourier analysis at a selected range of wavevectors. We first show that DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model as the generative model. Then we derive the maximum marginal likelihood estimator, which optimally weighs information at all wavevectors, therefore eliminating the need to select the range of wavevectors. Furthermore, we substantially reduce the computational cost by utilizing the generalized Schur algorithm for Toeplitz covariances without approximation. Simulated studies validate that AIUQ significantly improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These outcomes collectively underscore AIUQ's versatility to capture system dynamics in an efficient and automated manner.
In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. Firstly, we analyze the symplectic conditions for two kinds of exponential integrators and obtain the symplectic method. In order to effectively solve highly oscillatory problems, we try to design the highly accurate implicit ERK integrators. By comparing the Taylor series expansion of numerical solution with exact solution, it can be verified that the order conditions of two new kinds of exponential methods are identical to classical Runge-Kutta (RK) methods, which implies that using the coefficients of RK methods, some highly accurate numerical methods are directly formulated. Furthermore, we also investigate the linear stability properties for these exponential methods. Finally, numerical results not only display the long time energy preservation of the symplectic method, but also present the accuracy and efficiency of these formulated methods in comparison with standard ERK methods.
Graph-centric artificial intelligence (graph AI) has achieved remarkable success in modeling interacting systems prevalent in nature, from dynamical systems in biology to particle physics. The increasing heterogeneity of data calls for graph neural architectures that can combine multiple inductive biases. However, combining data from various sources is challenging because appropriate inductive bias may vary by data modality. Multimodal learning methods fuse multiple data modalities while leveraging cross-modal dependencies to address this challenge. Here, we survey 140 studies in graph-centric AI and realize that diverse data types are increasingly brought together using graphs and fed into sophisticated multimodal models. These models stratify into image-, language-, and knowledge-grounded multimodal learning. We put forward an algorithmic blueprint for multimodal graph learning based on this categorization. The blueprint serves as a way to group state-of-the-art architectures that treat multimodal data by choosing appropriately four different components. This effort can pave the way for standardizing the design of sophisticated multimodal architectures for highly complex real-world problems.
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