arXiv subjects

Vahid Tarokh

Publications and source records attributed to Vahid Tarokh.

At least 37 records · Page 2Linked to original sources

arXiv2025

Reinforcement Learning-Based Optimization of CT Acquisition and Reconstruction Parameters Through Virtual Imaging Trials

Protocol optimization is critical in Computed Tomography (CT) to achieve high diagnostic image quality while minimizing radiation dose. However, due to the complex interdependencies among CT acquisition and reconstruction parameters, traditional optimization methods rely on exhaustive testing of combinations of these parameters, which is often impractical. This study introduces a novel methodology that combines virtual imaging tools with reinforcement learning to optimize CT protocols more efficiently. Human models with liver lesions were imaged using a validated CT simulator and reconstructed with a novel CT reconstruction toolkit. The optimization parameter space included tube voltage, tube current, reconstruction kernel, slice thickness, and pixel size. The optimization process was performed using a Proximal Policy Optimization (PPO) agent, which was trained to maximize an image quality objective, specifically the detectability index (d') of liver lesions in the reconstructed images. Optimization performance was compared against an exhaustive search performed on a supercomputer. The proposed reinforcement learning approach achieved the global maximum d' across test cases while requiring 79.7% fewer steps than the exhaustive search, demonstrating both accuracy and computational efficiency. The proposed framework is flexible and can accommodate various image quality objectives. The findings highlight the potential of integrating virtual imaging tools with reinforcement learning for CT protocol management.

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arXiv2025

PASTA: A Unified Framework for Offline Assortment Learning

We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical customer choice data. The combinatorial nature of assortment optimization often results in insufficient data coverage, posing a significant challenge in designing provably effective solutions. To address this, we introduce a novel Pessimistic Assortment Optimization (PASTA) framework that leverages the principle of pessimism to achieve optimal expected revenue under general choice models. Notably, PASTA requires only that the offline data distribution contains an optimal assortment, rather than providing the full coverage of all feasible assortments. Theoretically, we establish the first finite-sample regret bounds for offline assortment optimization across several widely used choice models, including the multinomial logit and nested logit models. Additionally, we derive a minimax regret lower bound, proving that PASTA is minimax optimal in terms of sample and model complexity. Numerical experiments further demonstrate that our method outperforms existing baseline approaches.

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arXiv2025

Dual-Function Radar-Communication Beamforming with Outage Probability Metric

The integrated design of communication and sensing may offer a potential solution to address spectrum congestion. In this work, we develop a beamforming method for a dual-function radar-communication system, where the transmit signal is used for both radar surveillance and communication with multiple downlink users, despite imperfect channel state information (CSI). We focus on two scenarios of interest: radar-centric and communication-centric. In the radar-centric scenario, the primary goal is to optimize radar performance while attaining acceptable communication performance. To this end, we minimize a weighted sum of the mean-squared error in achieving a desired beampattern and a mean-squared cross correlation of the radar returns from directions of interest (DOI). We also seek to ensure that the probability of outage for the communication users remains below a desired threshold. In the communication-centric scenario, our main objective is to minimize the maximum probability of outage among the communication users while keeping the aforementioned radar metrics below a desired threshold. Both optimization problems are stochastic and untractable. We first take advantage of central limit theorem to obtain deterministic non-convex problems and then consider relaxations of these problems in the form of semidefinite programs with rank-1 constraints. We provide numerical experiments demonstrating the effectiveness of the proposed designs.

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arXiv2025

Robust Score-Based Quickest Change Detection

Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre- and post-change distributions are known. Recent work has extended these results to the case where the pre- and post-change distributions are known only by their score functions. This work considers the case where the pre- and post-change score functions are known only to correspond to distributions in two disjoint sets. This work selects a pair of least-favorable distributions from these sets to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the least-favorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm.

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arXiv2025

Diffusion-Based Hypothesis Testing and Change-Point Detection

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.

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arXiv2025

CATE Estimation With Potential Outcome Imputation From Local Regression

One of the most significant challenges in Conditional Average Treatment Effect (CATE) estimation is the statistical discrepancy between distinct treatment groups. To address this issue, we propose a model-agnostic data augmentation method for CATE estimation. First, we derive regret bounds for general data augmentation methods suggesting that a small imputation error may be necessary for accurate CATE estimation. Inspired by this idea, we propose a contrastive learning approach that reliably imputes missing potential outcomes for a selected subset of individuals formed using a similarity measure. We augment the original dataset with these reliable imputations to reduce the discrepancy between different treatment groups while inducing minimal imputation error. The augmented dataset can subsequently be employed to train standard CATE estimation models. We provide both theoretical guarantees and extensive numerical studies demonstrating the effectiveness of our approach in improving the accuracy and robustness of numerous CATE estimation models.

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arXiv2025

Conditional Average Treatment Effect Estimation Under Hidden Confounders

One of the major challenges in estimating conditional potential outcomes and conditional average treatment effects (CATE) is the presence of hidden confounders. Since testing for hidden confounders cannot be accomplished only with observational data, conditional unconfoundedness is commonly assumed in the literature of CATE estimation. Nevertheless, under this assumption, CATE estimation can be significantly biased due to the effects of unobserved confounders. In this work, we consider the case where in addition to a potentially large observational dataset, a small dataset from a randomized controlled trial (RCT) is available. Notably, we make no assumptions on the existence of any covariate information for the RCT dataset, we only require the outcomes to be observed. We propose a CATE estimation method based on a pseudo-confounder generator and a CATE model that aligns the learned potential outcomes from the observational data with those observed from the RCT. Our method is applicable to many practical scenarios of interest, particularly those where privacy is a concern (e.g., medical applications). Extensive numerical experiments are provided demonstrating the effectiveness of our approach for both synthetic and real-world datasets.

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arXiv2025

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.

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arXiv2025

Elliptic Loss Regularization

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping between the data input space and the loss value. We specify the level of regularity by requiring that the loss of the network satisfies an elliptic operator over the data domain. To do this, we modify the usual empirical risk minimization objective such that we instead minimize a new objective that satisfies an elliptic operator over points within the domain. This allows us to use existing theory on elliptic operators to anticipate the behavior of the error for points outside the training set. We propose a tractable computational method that approximates the behavior of the elliptic operator while being computationally efficient. Finally, we analyze the properties of the proposed regularization to understand the performance on common problems of distribution shift and group imbalance. Numerical experiments confirm the utility of the proposed regularization technique.

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arXiv2025

Parabolic Continual Learning

Regularizing continual learning techniques is important for anticipating algorithmic behavior under new realizations of data. We introduce a new approach to continual learning by imposing the properties of a parabolic partial differential equation (PDE) to regularize the expected behavior of the loss over time. This class of parabolic PDEs has a number of favorable properties that allow us to analyze the error incurred through forgetting and the error induced through generalization. Specifically, we do this through imposing boundary conditions where the boundary is given by a memory buffer. By using the memory buffer as a boundary, we can enforce long term dependencies by bounding the expected error by the boundary loss. Finally, we illustrate the empirical performance of the method on a series of continual learning tasks.

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arXiv2025

S2TX: Cross-Attention Multi-Scale State-Space Transformer for Time Series Forecasting

Time series forecasting has recently achieved significant progress with multi-scale models to address the heterogeneity between long and short range patterns. Despite their state-of-the-art performance, we identify two potential areas for improvement. First, the variates of the multivariate time series are processed independently. Moreover, the multi-scale (long and short range) representations are learned separately by two independent models without communication. In light of these concerns, we propose State Space Transformer with cross-attention (S2TX). S2TX employs a cross-attention mechanism to integrate a Mamba model for extracting long-range cross-variate context and a Transformer model with local window attention to capture short-range representations. By cross-attending to the global context, the Transformer model further facilitates variate-level interactions as well as local/global communications. Comprehensive experiments on seven classic long-short range time-series forecasting benchmark datasets demonstrate that S2TX can achieve highly robust SOTA results while maintaining a low memory footprint.

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arXiv2025

Teleportation With Null Space Gradient Projection for Optimization Acceleration

Optimization techniques have become increasingly critical due to the ever-growing model complexity and data scale. In particular, teleportation has emerged as a promising approach, which accelerates convergence of gradient descent-based methods by navigating within the loss invariant level set to identify parameters with advantageous geometric properties. Existing teleportation algorithms have primarily demonstrated their effectiveness in optimizing Multi-Layer Perceptrons (MLPs), but their extension to more advanced architectures, such as Convolutional Neural Networks (CNNs) and Transformers, remains challenging. Moreover, they often impose significant computational demands, limiting their applicability to complex architectures. To this end, we introduce an algorithm that projects the gradient of the teleportation objective function onto the input null space, effectively preserving the teleportation within the loss invariant level set and reducing computational cost. Our approach is readily generalizable from MLPs to CNNs, transformers, and potentially other advanced architectures. We validate the effectiveness of our algorithm across various benchmark datasets and optimizers, demonstrating its broad applicability.

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arXiv2025

Steinmetz Neural Networks for Complex-Valued Data

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, incorporates multi-view learning to construct more interpretable representations in the latent space. Moreover, we present the Analytic Neural Network, which incorporates a consistency penalty that encourages analytic signal representations in the latent space of the Steinmetz neural network. This penalty enforces a deterministic and orthogonal relationship between the real and imaginary components. Using an information-theoretic construction, we demonstrate that the generalization gap upper bound posited by the analytic neural network is lower than that of the general class of Steinmetz neural networks. Our numerical experiments depict the improved performance and robustness to additive noise, afforded by our proposed networks on benchmark datasets and synthetic examples.

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arXiv2025

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.

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arXiv2024

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.

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arXiv2024

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.

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arXiv2024

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.

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arXiv2024

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.

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