Score-Based Metropolis-Hastings Algorithms

In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack an energy function, making the Metropolis-Hastings adjustment step inaccessible. Consequently, the unadjusted Langevin algorithm is often used for sampling using estimated score functions. The lack of an energy function then prevents the application of the Metropolis-adjusted Langevin algorithm and other Metropolis-Hastings methods, limiting the wealth of other algorithms developed that use acceptance functions. We address this limitation by introducing a new loss function based on the \emph{detailed balance condition}, allowing the estimation of the Metropolis-Hastings acceptance probabilities given a learned score function. We demonstrate the effectiveness of the proposed method for various scenarios, including sampling from heavy-tail distributions.

Learn2Mix: Training Neural Networks Using Adaptive Data Integration

Accelerating model convergence in resource-constrained environments is essential for fast and efficient neural network training. This work presents learn2mix, a new training strategy that adaptively adjusts class proportions within batches, focusing on classes with higher error rates. Unlike classical training methods that use static class proportions, learn2mix continually adapts class proportions during training, leading to faster convergence. Empirical evaluations on benchmark datasets show that neural networks trained with learn2mix converge faster than those trained with classical approaches, achieving improved results for classification, regression, and reconstruction tasks under limited training resources and with imbalanced classes. Our empirical findings are supported by theoretical analysis.

Offline Stochastic Optimization of Black-Box Objective Functions

Many challenges in science and engineering, such as drug discovery and communication network design, involve optimizing complex and expensive black-box functions across vast search spaces. Thus, it is essential to leverage existing data to avoid costly active queries of these black-box functions. To this end, while Offline Black-Box Optimization (BBO) is effective for deterministic problems, it may fall short in capturing the stochasticity of real-world scenarios. To address this, we introduce Stochastic Offline BBO (SOBBO), which tackles both black-box objectives and uncontrolled uncertainties. We propose two solutions: for large-data regimes, a differentiable surrogate allows for gradient-based optimization, while for scarce-data regimes, we directly estimate gradients under conservative field constraints, improving robustness, convergence, and data efficiency. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world tasks.

Indiscriminate Disruption of Conditional Inference on Multivariate Gaussians

The multivariate Gaussian distribution underpins myriad operations-research, decision-analytic, and machine-learning models (e.g., Bayesian optimization, Gaussian influence diagrams, and variational autoencoders). However, despite recent advances in adversarial machine learning (AML), inference for Gaussian models in the presence of an adversary is notably understudied. Therefore, we consider a self-interested attacker who wishes to disrupt a decisionmaker's conditional inference and subsequent actions by corrupting a set of evidentiary variables. To avoid detection, the attacker also desires the attack to appear plausible wherein plausibility is determined by the density of the corrupted evidence. We consider white- and grey-box settings such that the attacker has complete and incomplete knowledge about the decisionmaker's underlying multivariate Gaussian distribution, respectively. Select instances are shown to reduce to quadratic and stochastic quadratic programs, and structural properties are derived to inform solution methods. We assess the impact and efficacy of these attacks in three examples, including, real estate evaluation, interest rate estimation and signals processing. Each example leverages an alternative underlying model, thereby highlighting the attacks' broad applicability. Through these applications, we also juxtapose the behavior of the white- and grey-box attacks to understand how uncertainty and structure affect attacker behavior.

Asymptotically Optimal Change Detection for Unnormalized Pre- and Post-Change Distributions

This paper addresses the problem of detecting changes when only unnormalized pre- and post-change distributions are accessible. This situation happens in many scenarios in physics such as in ferromagnetism, crystallography, magneto-hydrodynamics, and thermodynamics, where the energy models are difficult to normalize. Our approach is based on the estimation of the Cumulative Sum (CUSUM) statistics, which is known to produce optimal performance. We first present an intuitively appealing approximation method. Unfortunately, this produces a biased estimator of the CUSUM statistics and may cause performance degradation. We then propose the Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration (TI) in order to estimate the log-ratio of normalizing constants of pre- and post-change distributions. It is proved that this approach gives an unbiased estimate of the log-partition function and the CUSUM statistics, and leads to an asymptotically optimal performance. Moreover, we derive a relationship between the required sample size for thermodynamic integration and the desired detection delay performance, offering guidelines for practical parameter selection. Numerical studies are provided demonstrating the efficacy of our approach.

Steinmetz Neural Networks for Complex-Valued Data

In this work, we introduce a new approach to processing complex-valued data using DNNs consisting of parallel real-valued subnetworks with coupled outputs. Our proposed class of architectures, referred to as Steinmetz Neural Networks, leverages multi-view learning to construct more interpretable representations within the latent space. Subsequently, we present the Analytic Neural Network, which implements a consistency penalty that encourages analytic signal representations in the Steinmetz neural network's latent space. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Utilizing an information-theoretic construction, we demonstrate that the upper bound on the generalization error posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments demonstrate the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.

DynamicFL: Federated Learning with Dynamic Communication Resource Allocation

Federated Learning (FL) is a collaborative machine learning framework that allows multiple users to train models utilizing their local data in a distributed manner. However, considerable statistical heterogeneity in local data across devices often leads to suboptimal model performance compared with independently and identically distributed (IID) data scenarios. In this paper, we introduce DynamicFL, a new FL framework that investigates the trade-offs between global model performance and communication costs for two widely adopted FL methods: Federated Stochastic Gradient Descent (FedSGD) and Federated Averaging (FedAvg). Our approach allocates diverse communication resources to clients based on their data statistical heterogeneity, considering communication resource constraints, and attains substantial performance enhancements compared to uniform communication resource allocation. Notably, our method bridges the gap between FedSGD and FedAvg, providing a flexible framework leveraging communication heterogeneity to address statistical heterogeneity in FL. Through extensive experiments, we demonstrate that DynamicFL surpasses current state-of-the-art methods with up to a 10% increase in model accuracy, demonstrating its adaptability and effectiveness in tackling data statistical heterogeneity challenges.

Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions

The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.

Generative Learning for Simulation of Vehicle Faults

We develop a novel generative model to simulate vehicle health and forecast faults, conditioned on practical operational considerations. The model, trained on data from the US Army's Predictive Logistics program, aims to support predictive maintenance. It forecasts faults far enough in advance to execute a maintenance intervention before a breakdown occurs. The model incorporates real-world factors that affect vehicle health. It also allows us to understand the vehicle's condition by analyzing operating data, and characterizing each vehicle into discrete states. Importantly, the model predicts the time to first fault with high accuracy. We compare its performance to other models and demonstrate its successful training.

Generative Learning for Simulation of US Army Vehicle Faults

We develop a novel generative model to simulate vehicle health and forecast faults, conditioned on practical operational considerations. The model, trained on data from the US Army's Predictive Logistics program, aims to support predictive maintenance. It forecasts faults far enough in advance to execute a maintenance intervention before a breakdown occurs. The model incorporates real-world factors that affect vehicle health. It also allows us to understand the vehicle's condition by analyzing operating data, and characterizing each vehicle into discrete states. Importantly, the model predicts the time to first fault with high accuracy. We compare its performance to other models and demonstrate its successful training.