arXiv subjects

Raed Al Kontar

Publications and source records attributed to Raed Al Kontar.

At least 19 recordsLinked to original sources

arXiv2026

Language-Induced Priors for Domain Adaptation

Domain adaptation faces a fundamental paradox in the cold-start regime. When target data is scarce, statistical methods fail to distinguish relevant source domains from irrelevant ones, which often leads to negative transfer. In this paper, we address this challenge by leveraging expert textual descriptions of the target domain, a resource that is often available but overlooked. We propose a probabilistic framework that translates these semantic descriptions into a choice model, namely a Language-Induced Prior (LIP), that learns the preferences from a pretrained Large Language Model (LLM). The LIP is then integrated into an Expectation-Maximization algorithm to identify source relevance. Methodologically, this framework is compatible with any parametric model where a likelihood is available. It allows the LIP to guide the selection of sources when target signals are weak, while gradually refining these choices as samples accumulate. Theoretically, we prove that the estimator roughly matches an oracle cold-start MSE under a correct prior, while remaining asymptotically consistent regardless of the quality of the LIP. Empirically, we validated the framework on a descriptive (Gaussian estimation), a predictive (C-MAPSS dataset), and a prescriptive task (MuJoCo hopper).

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arXiv2026

Collaborative Contextual Bayesian Optimization

Discovering optimal designs through sequential data collection is essential in many real-world applications. While Bayesian Optimization (BO) has achieved remarkable success in this setting, growing attention has recently turned to context-specific optimal design, formalized as Contextual Bayesian Optimization (CBO). Unlike BO, CBO is inherently more challenging as it must approximate an entire mapping from the context space to its corresponding optimal design, requiring simultaneous exploration across contexts and exploitation within each. In many modern applications, such tasks arise across multiple potentially heterogeneous but related clients, where collaboration can significantly improve learning efficiency. We propose CCBO, Collaborative Contextual Bayesian Optimization, a unified framework enabling multiple clients to jointly perform CBO with controllable contexts, supporting both online collaboration and offline initialization from peers' historical beliefs, with an optional privacy-preserving communication mechanism. We establish sublinear regret guarantees and demonstrate, through extensive simulations and a real-world hot rolling application, that CCBO achieves substantial improvements over existing approaches even under client heterogeneity. The code to reproduce the results can be found at https://github.com/cchihyu/Collaborative-Contextual-Bayesian-Optimization

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arXiv2025

Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

cs.CL↗

arXiv2025

LLINBO: Trustworthy LLM-in-the-Loop Bayesian Optimization

Bayesian optimization (BO) is a sequential decision-making tool widely used for optimizing expensive black-box functions. Recently, Large Language Models (LLMs) have shown remarkable adaptability in low-data regimes, making them promising tools for black-box optimization by leveraging contextual knowledge to propose high-quality query points. However, relying solely on LLMs as optimization agents introduces risks due to their lack of explicit surrogate modeling and calibrated uncertainty, as well as their inherently opaque internal mechanisms. This structural opacity makes it difficult to characterize or control the exploration-exploitation trade-off, ultimately undermining theoretical tractability and reliability. To address this, we propose LLINBO: LLM-in-the-Loop BO, a hybrid framework for BO that combines LLMs with statistical surrogate experts (e.g., Gaussian Processes (GP)). The core philosophy is to leverage contextual reasoning strengths of LLMs for early exploration, while relying on principled statistical models to guide efficient exploitation. Specifically, we introduce three mechanisms that enable this collaboration and establish their theoretical guarantees. We end the paper with a real-life proof-of-concept in the context of 3D printing. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/LLM-in-the-Loop-BO.

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arXiv2025

ALBATROSS: Cheap Filtration Based Geometry via Stochastic Sub-Sampling

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory requirements and gives access to scientists with modest computing resources. We validate this protocol against two empirical datasets, showing that it replicates previous findings with much lower memory requirements. Finally, we demonstrate the power of the protocol by mapping the topology of functional correlations for the human cortex at high spatial resolution, something that was previously infeasible without this novel approach.

q-bio.QM↗

arXiv2025

Online Learning of Optimal Sequential Testing Policies

This paper studies an online learning problem that seeks optimal testing policies for a stream of subjects, each of whom can be evaluated through a sequence of candidate tests drawn from a common pool. We refer to this problem as the Online Testing Problem (OTP). Although conducting every candidate test for a subject provides more information, it is often preferable to select only a subset when tests are correlated and costly, and make decisions with partial information. If the joint distribution of test outcomes were known, the problem could be cast as a Markov Decision Process (MDP) and solved exactly. In practice, this distribution is unknown and must be learned online as subjects are tested. When a subject is not fully tested, the resulting missing data can bias estimates, making the problem fundamentally harder than standard episodic MDPs. We prove that the minimax regret must scale at least as $Ω(T^{\frac{2}{3}})$, in contrast to the $Θ(\sqrt{T})$ rate in episodic MDPs, revealing the difficulty introduced by missingness. This elevated lower bound is then matched by an Explore-Then-Commit algorithm whose cumulative regret is $\tilde{O}(T^{\frac{2}{3}})$ for both discrete and Gaussian distributions. To highlight the consequence of missingness-dependent rewards in OTP, we study a variant called the Online Cost-sensitive Maximum Entropy Sampling Problem, where rewards are independent of missing data. This structure enables an iterative-elimination algorithm that achieves $\tilde{O}(\sqrt{T})$ regret, breaking the $Ω(T^{\frac{2}{3}})$ lower bound for OTP. Numerical results confirm our theory in both settings. Overall, this work deepens the understanding of the exploration--exploitation trade-off under missing data and guides the design of efficient sequential testing policies.

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arXiv2025

Diffusion-Based Surrogate Modeling and Multi-Fidelity Calibration

Physics simulations have become fundamental tools to study myriad engineering systems. As physics simulations often involve simplifications, their outputs should be calibrated using real-world data. In this paper, we present a diffusion-based surrogate (DBS) that calibrates multi-fidelity physics simulations with diffusion generative processes. DBS categorizes multi-fidelity physics simulations into inexpensive and expensive simulations, depending on the computational costs. The inexpensive simulations, which can be obtained with low latency, directly inject contextual information into diffusion models. Furthermore, when results from expensive simulations are available, \name refines the quality of generated samples via a guided diffusion process. This design circumvents the need for large amounts of expensive physics simulations to train denoising diffusion models, thus lending flexibility to practitioners. DBS builds on Bayesian probabilistic models and is equipped with a theoretical guarantee that provides upper bounds on the Wasserstein distance between the sample and underlying true distribution. The probabilistic nature of DBS also provides a convenient approach for uncertainty quantification in prediction. Our models excel in cases where physics simulations are imperfect and sometimes inaccessible. We use a numerical simulation in fluid dynamics and a case study in laser-based metal powder deposition additive manufacturing to demonstrate how DBS calibrates multi-fidelity physics simulations with observations to obtain surrogates with superior predictive performance.

stat.CO↗

arXiv2025

A Collaborative Process Parameter Recommender System for Fleets of Networked Manufacturing Machines -- with Application to 3D Printing

Fleets of networked manufacturing machines of the same type, that are collocated or geographically distributed, are growing in popularity. An excellent example is the rise of 3D printing farms, which consist of multiple networked 3D printers operating in parallel, enabling faster production and efficient mass customization. However, optimizing process parameters across a fleet of manufacturing machines, even of the same type, remains a challenge due to machine-to-machine variability. Traditional trial-and-error approaches are inefficient, requiring extensive testing to determine optimal process parameters for an entire fleet. In this work, we introduce a machine learning-based collaborative recommender system that optimizes process parameters for each machine in a fleet by modeling the problem as a sequential matrix completion task. Our approach leverages spectral clustering and alternating least squares to iteratively refine parameter predictions, enabling real-time collaboration among the machines in a fleet while minimizing the number of experimental trials. We validate our method using a mini 3D printing farm consisting of ten 3D printers for which we optimize acceleration and speed settings to maximize print quality and productivity. Our approach achieves significantly faster convergence to optimal process parameters compared to non-collaborative matrix completion.

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arXiv2024

Collaborative and Federated Black-box Optimization: A Bayesian Optimization Perspective

We focus on collaborative and federated black-box optimization (BBOpt), where agents optimize their heterogeneous black-box functions through collaborative sequential experimentation. From a Bayesian optimization perspective, we address the fundamental challenges of distributed experimentation, heterogeneity, and privacy within BBOpt, and propose three unifying frameworks to tackle these issues: (i) a global framework where experiments are centrally coordinated, (ii) a local framework that allows agents to make decisions based on minimal shared information, and (iii) a predictive framework that enhances local surrogates through collaboration to improve decision-making. We categorize existing methods within these frameworks and highlight key open questions to unlock the full potential of federated BBOpt. Our overarching goal is to shift federated learning from its predominantly descriptive/predictive paradigm to a prescriptive one, particularly in the context of BBOpt - an inherently sequential decision-making problem.

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arXiv2024

Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the common and unique components from these noisy observations? This is a challenging task as the number of parameters to estimate is approximately thrice the number of observations. Despite the difficulty, we propose an intuitive alternating minimization algorithm called triple component matrix factorization (TCMF) to recover the three components exactly. TCMF is distinguished from existing works in literature thanks to two salient features. First, TCMF is a principled method to separate the three components given noisy observations provably. Second, the bulk of the computation in TCMF can be distributed. On the technical side, we formulate the problem as a constrained nonconvex nonsmooth optimization problem. Despite the intricate nature of the problem, we provide a Taylor series characterization of its solution by solving the corresponding Karush-Kuhn-Tucker conditions. Using this characterization, we can show that the alternating minimization algorithm makes significant progress at each iteration and converges into the ground truth at a linear rate. Numerical experiments in video segmentation and anomaly detection highlight the superior feature extraction abilities of TCMF.

cs.LG↗

arXiv2024

The Traveling Bandit: A Framework for Bayesian Optimization with Movement Costs

This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.

stat.ME↗

arXiv2024

FCOM: A Federated Collaborative Online Monitoring Framework via Representation Learning

Online learning has demonstrated notable potential to dynamically allocate limited resources to monitor a large population of processes, effectively balancing the exploitation of processes yielding high rewards, and the exploration of uncertain processes. However, most online learning algorithms were designed under 1) a centralized setting that requires data sharing across processes to obtain an accurate prediction or 2) a homogeneity assumption that estimates a single global model from the decentralized data. To facilitate the online learning of heterogeneous processes from the decentralized data, we propose a federated collaborative online monitoring method, which captures the latent representative models inherent in the population through representation learning and designs a novel federated collaborative UCB algorithm to estimate the representative models from sequentially observed decentralized data. The efficiency of our method is illustrated through theoretical analysis, simulation studies, and decentralized cognitive degradation monitoring in Alzheimer's disease.

cs.LG↗

arXiv2024

Heterogeneous Matrix Factorization: When Features Differ by Datasets

In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios is to recover the shared and source-specific factors. Despite the existence of a few heuristic approaches, a generic algorithm with theoretical guarantees has yet to be established. In this paper, we tackle the problem by proposing a method called Heterogeneous Matrix Factorization to separate the shared and unique factors for a class of problems. HMF maintains the orthogonality between the shared and unique factors by leveraging an invariance property in the objective. The algorithm is easy to implement and intrinsically distributed. On the theoretic side, we show that for the square error loss, HMF will converge into the optimal solutions, which are close to the ground truth. HMF can be integrated auto-encoders to learn nonlinear feature mappings. Through a variety of case studies, we showcase HMF's benefits and applicability in video segmentation, time-series feature extraction, and recommender systems.

stat.ME↗

arXiv2024

Real-time Adaptation for Condition Monitoring Signal Prediction using Label-aware Neural Processes

Building a predictive model that rapidly adapts to real-time condition monitoring (CM) signals is critical for engineering systems/units. Unfortunately, many current methods suffer from a trade-off between representation power and agility in online settings. For instance, parametric methods that assume an underlying functional form for CM signals facilitate efficient online prediction updates. However, this simplification leads to vulnerability to model specifications and an inability to capture complex signals. On the other hand, approaches based on over-parameterized or non-parametric models can excel at explaining complex nonlinear signals, but real-time updates for such models pose a challenging task. In this paper, we propose a neural process-based approach that addresses this trade-off. It encodes available observations within a CM signal into a representation space and then reconstructs the signal's history and evolution for prediction. Once trained, the model can encode an arbitrary number of observations without requiring retraining, enabling on-the-spot real-time predictions along with quantified uncertainty and can be readily updated as more online data is gathered. Furthermore, our model is designed to incorporate qualitative information (i.e., labels) from individual units. This integration not only enhances individualized predictions for each unit but also enables joint inference for both signals and their associated labels. Numerical studies on both synthetic and real-world data in reliability engineering highlight the advantageous features of our model in real-time adaptation, enhanced signal prediction with uncertainty quantification, and joint prediction for labels and signals.

cs.LG↗

arXiv2024

Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative sensor design experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.

cs.LG↗

arXiv2024

Personalized PCA: Decoupling Shared and Unique Features

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining the unique features of each source. To this end, we propose personalized PCA (PerPCA), which uses mutually orthogonal global and local principal components to encode both unique and shared features. We show that, under mild conditions, both unique and shared features can be identified and recovered by a constrained optimization problem, even if the covariance matrices are immensely different. Also, we design a fully federated algorithm inspired by distributed Stiefel gradient descent to solve the problem. The algorithm introduces a new group of operations called generalized retractions to handle orthogonality constraints, and only requires global PCs to be shared across sources. We prove the linear convergence of the algorithm under suitable assumptions. Comprehensive numerical experiments highlight PerPCA's superior performance in feature extraction and prediction from heterogeneous datasets. As a systematic approach to decouple shared and unique features from heterogeneous datasets, PerPCA finds applications in several tasks, including video segmentation, topic extraction, and feature clustering.

cs.LG↗

arXiv2023

SEE-OoD: Supervised Exploration For Enhanced Out-of-Distribution Detection

Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However, methods that utilize real OoD samples lack exploration and are prone to overfit the OoD samples at hand. Whereas synthetic samples are often generated based on features extracted from training data, rendering them less effective when the training and OoD data are highly overlapped in the feature space. In this work, we propose a Wasserstein-score-based generative adversarial training scheme to enhance OoD detection accuracy, which, for the first time, performs data augmentation and exploration simultaneously under the supervision of limited OoD samples. Specifically, the generator explores OoD spaces and generates synthetic OoD samples using feedback from the discriminator, while the discriminator exploits both the observed and synthesized samples for OoD detection using a predefined Wasserstein score. We provide theoretical guarantees that the optimal solutions of our generative scheme are statistically achievable through adversarial training in empirical settings. We then demonstrate that the proposed method outperforms state-of-the-art techniques on various computer vision datasets and exhibits superior generalizability to unseen OoD data.

cs.LG↗

arXiv2023

Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce a mode orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm that is guaranteed to converge to a stationary point. By learning unique and common representations across datasets, we demonstrate perTucker's effectiveness in anomaly detection, client classification, and clustering through a simulation study and two case studies on solar flare detection and tonnage signal classification.

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