Active Learning

Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose ALMAB-DC, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at $K=4$ the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4% CIFAR-10 accuracy (outperforming BOHB by 1.7,pp and Optuna by 1.1,pp), reduces airfoil drag to $C_D = 0.059$ (36.9% below Grid Search), and improves RL return by 50% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney $U$ tests. Distributed execution achieves $7.5\times$ speedup at $K = 16$ agents, consistent with Amdahl's Law.

Pairwise comparison labeling is emerging as it yields higher inter-rater reliability than conventional classification labeling, but exhaustive comparisons require quadratic cost. We propose Dodgersort, which leverages CLIP-based hierarchical pre-ordering, a neural ranking head and probabilistic ensemble (Elo, BTL, GP), epistemic--aleatoric uncertainty decomposition, and information-theoretic pair selection. It reduces human comparisons while improving the reliability of the rankings. In visual ranking tasks in medical imaging, historical dating, and aesthetics, Dodgersort achieves a 11--16% annotation reduction while improving inter-rater reliability. Cross-domain ablations across four datasets show that neural adaptation and ensemble uncertainty are key to this gain. In FG-NET with ground-truth ages, the framework extracts 5--20$\times$ more ranking information per comparison than baselines, yielding Pareto-optimal accuracy--efficiency trade-offs.

Personalizing Automatic Speech Recognition (ASR) for non-normative speech remains challenging because data collection is labor-intensive and model training is technically complex. To address these limitations, we propose Adapt4Me, a web-based decentralized environment that operationalizes Bayesian active learning to enable end-to-end personalization without expert supervision. The app exposes data selection, adaptation, and validation to lay users through a three-stage human-in-the-loop workflow: (1) rapid profiling via greedy phoneme sampling to capture speaker-specific acoustics; (2) backend personalization using Variational Inference Low-Rank Adaptation (VI-LoRA) to enable fast, incremental updates; and (3) continuous improvement, where users guide model refinement by resolving visualized model uncertainty via low-friction top-k corrections. By making epistemic uncertainty explicit, Adapt4Me reframes data efficiency as an interactive design feature rather than a purely algorithmic concern. We show how this enables users to personalize robust ASR models, transforming them from passive data sources into active authors of their own assistive technology.

Medical image quality assessment (Med-IQA) is a prerequisite for clinical AI deployment, yet multimodal large language models (MLLMs) still fall substantially short of human experts, particularly when required to provide descriptive assessments with clinical reasoning beyond simple quality scores. However, improving them is hindered by the high cost of acquiring descriptive annotations and by the inability of one-time data collection to adapt to the model's evolving weaknesses. To address these challenges, we propose MedQ-Engine, a closed-loop data engine that iteratively evaluates the model to discover failure prototypes via data-driven clustering, explores a million-scale image pool using these prototypes as retrieval anchors with progressive human-in-the-loop annotation, and evolves through quality-assured fine-tuning, forming a self-improving cycle. Models are evaluated on complementary perception and description tasks. An entropy-guided routing mechanism triages annotations to minimize labeling cost. Experiments across five medical imaging modalities show that MedQ-Engine elevates an 8B-parameter model to surpass GPT-4o by over 13% and narrow the gap with human experts to only 4.34%, using only 10K annotations with more than 4x sample efficiency over random sampling.

Fine-tuning large language models (LLMs) with high-quality knowledge has been shown to enhance their performance effectively. However, there is a paucity of research on the depth of domain-specific knowledge comprehension by LLMs and the application of targeted active learning to improve their expertise. To address this gap, we introduce the Knowledge-Aware Active Learning (KA2L) framework. This framework assesses LLMs' mastery of specific knowledge points to aid in constructing unanswerable or unknowable questions through latent space analysis. This active learning strategy enhances training efficiency by focusing on knowledge the model has yet to master, thereby minimizing redundancy in learning already acquired information. This study innovatively employs a knowledge distribution probing technique to examine the hidden states of specific Transformer layers and identify the distribution of known and unknown knowledge within the LLM. Additionally, a hidden-state decoding method is proposed to generate numerous unknown questions in natural language from the latent knowledge space. In our experiments, we selected nine open-source LLMs to validate the effectiveness of the proposed framework. Results indicate that KA2L not only significantly reduces 50% annotation and computation costs across two open-domain and one vertical-domain dataset but also achieves better performance, offering valuable insights into active learning strategies for LLMs. The code is available at https://github.com/greenjerry/KA2L.

Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-consistent aerodynamic metrics. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at $Re=6\times10^6$ with cruise at $α=2^\circ$ (maximize $E=L/D$) and take-off at $α=10^\circ$ (maximize $C_L$) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, RANS evaluations were required for only 14.78% and 9.5% of the condition-specific candidate evaluations at cruise and take-off, respectively. These percentages quantify the reduction in high-fidelity usage relative to the fixed automated RANS workflow adopted as the high-fidelity reference in this study.

Active seriation aims at recovering an unknown ordering of $n$ items by adaptively querying pairwise similarities. The observations are noisy measurements of entries of an underlying $n$ x $n$ permuted Robinson matrix, whose permutation encodes the latent ordering. The framework allows the algorithm to start with partial information on the latent ordering, including seriation from scratch as a special case. We propose an active seriation algorithm that provably recovers the latent ordering with high probability. Under a uniform separation condition on the similarity matrix, optimal performance guarantees are established, both in terms of the probability of error and the number of observations required for successful recovery.

Rashomon sets are model sets within one model class that perform nearly as well as a reference model from the same model class. They reveal the existence of alternative well-performing models, which may support different interpretations. This enables selecting models that match domain knowledge, hidden constraints, or user preferences. However, efficient construction methods currently exist for only a few model classes. Applied machine learning usually searches many model classes, and the best class is unknown beforehand. We therefore study Rashomon sets in the combined algorithm selection and hyperparameter optimization (CASH) setting and call them CASHomon sets. We propose TruVaRImp, a model-based active learning algorithm for level set estimation with an implicit threshold, and provide convergence guarantees. On synthetic and real-world datasets, TruVaRImp reliably identifies CASHomon sets members and matches or outperforms naive sampling, Bayesian optimization, classical and implicit level set estimation methods, and other baselines. Our analyses of predictive multiplicity and feature-importance variability across model classes question the common practice of interpreting data through a single model class.

Addressing the domain adaptation problem becomes more challenging when distribution shifts across domains stem from latent confounders that affect both covariates and outcomes. Existing proxy-based approaches that address latent shift rely on a strong completeness assumption to uniquely determine (point-identify) a robust predictor. Completeness requires that proxies have sufficient information about variations in latent confounders. For imperfect proxies the mapping from confounders to the space of proxy distributions is non-injective, and multiple latent confounder values can generate the same proxy distribution. This breaks the completeness assumption and observed data are consistent with multiple potential predictors (set-identified). To address this, we introduce latent equivalent classes (LECs). LECs are defined as groups of latent confounders that induce the same conditional proxy distribution. We show that point-identification for the robust predictor remains achievable as long as multiple domains differ sufficiently in how they mix proxy-induced LECs to form the robust predictor. This domain diversity condition is formalized as a cross-domain rank condition on the mixture weights, which is substantially weaker assumption than completeness. We introduce the Proximal Quasi-Bayesian Active learning (PQAL) framework, which actively queries a small, targeted set of diverse domains that satisfy this rank condition. PQAL can recover the point-identified predictor, demonstrates robustness to varying degrees of shift and outperforms previous methods on synthetic data and semi-synthetic dSprites, IHDP, ACS Folktables datasets.

Image segmentation is fundamental to microstructural analysis for defect identification and structure-property correlation, yet remains challenging due to pronounced heterogeneity in materials images arising from varied processing and testing conditions. Conventional image processing techniques often fail to capture such complex features rendering them ineffective for large-scale analysis. Even deep learning approaches struggle to generalize across heterogeneous datasets due to scarcity of high-quality labeled data. Consequently, segmentation workflows often rely on manual expert-driven annotations which are labor intensive and difficult to scale. Using an additive manufacturing (AM) dataset as a case study, we present a semi-automated active learning based segmentation pipeline that integrates a U-Net based convolutional neural network with an interactive user annotation and correction interface and a representative core-set image selection strategy. The active learning workflow iteratively updates the model by incorporating user corrected segmentations into the training pool while the core-set strategy identifies representative images for annotation. Three subset selection strategies, manual selection, uncertainty driven sampling and proposed maximin Latin hypercube sampling from embeddings (SMILE) method were evaluated over six refinement rounds. The SMILE strategy consistently outperformed other approaches, improving the macro F1 score from 0.74 to 0.93 while reducing manual annotation time by about 65 percent. The segmented defect regions were further analyzed using a coupled classification model to categorize defects based on microstructural characteristics and map them to corresponding AM process parameters. The proposed framework reduces labeling effort while maintaining scalability and robustness and is broadly applicable to image based analysis across diverse materials systems.

Near-term quantum devices provide only finite-shot measurements and prepare imperfect, contaminated states. This motivates algorithms that convert samples into reliable low-energy estimates without full tomography or exhaustive measurements. We propose Active Sampling Sample-based Quantum Diagonalization (AS-SQD), framing SQD as an active learning problem: given measured bitstrings, which additional basis states should be included to efficiently recover the ground-state energy? SQD restricts the Hamiltonian to a selected set of basis states and classically diagonalizes the restricted matrix. However, naive SQD using only sampled states suffers from bias under finite-shot sampling and excited-state contamination, while blind random expansion is inefficient as system size grows. We introduce a perturbation-theoretic acquisition function based on Epstein--Nesbet second-order energy corrections to rank candidate basis states connected to the current subspace. At each iteration, AS-SQD diagonalizes the restricted Hamiltonian, generates connected candidates, and adds the most valuable ones according to this score. We evaluate AS-SQD on disordered Heisenberg and Transverse-Field Ising (TFIM) spin chains up to 16 qubits under a preparation model mixing 80% ground state and 20% first excited state. Furthermore, we validate its robustness against real-world state preparation and measurement (SPAM) errors using physical samples from an IBM Quantum processor. Across simulated and hardware evaluations, AS-SQD consistently achieves substantially lower absolute energy errors than standard SQD and random expansion. Detailed ablation studies demonstrate that physics-guided basis acquisition effectively concentrates computation on energetically relevant directions, bypassing exponential combinatorial bottlenecks.

Active learning (AL) aims to reduce annotation costs while maximizing model performance by iteratively selecting valuable instances. While foundation models have made it easier to identify these instances, existing selection strategies still lack robustness across different models, annotation budgets, and datasets. To highlight the potential weaknesses of existing AL strategies and provide a reference point for research, we explore oracle strategies, i.e., strategies that approximate the optimal selection by accessing ground-truth information unavailable in practical AL scenarios. Current oracle strategies, however, fail to scale effectively to large datasets and complex deep neural networks. To tackle these limitations, we introduce the Best-of-Strategy Selector (BoSS), a scalable oracle strategy designed for large-scale AL scenarios. BoSS constructs a set of candidate batches through an ensemble of selection strategies and then selects the batch yielding the highest performance gain. As an ensemble of selection strategies, BoSS can be easily extended with new state-of-the-art strategies as they emerge, ensuring it remains a reliable oracle strategy in the future. Our evaluation demonstrates that i) BoSS outperforms existing oracle strategies, ii) state-of-the-art AL strategies still fall noticeably short of oracle performance, especially in large-scale datasets with many classes, and iii) one possible solution to counteract the inconsistent performance of AL strategies might be to employ an ensemble-based approach for the selection.

Active learning (AL) has emerged as a powerful paradigm for accelerating materials discovery by iteratively steering experiments toward promising candidates, reducing the number of costly synthesis-and-characterization cycles needed to identify optimal materials. However, current AL relies predominantly on Gaussian Process (GP) and Random Forest (RF) surrogates, which suffer from complementary limitations: GP underfits complex composition-property landscapes due to rigid kernel assumptions, while RF produces unreliable heuristic uncertainty estimates in small-data regimes. This small-data challenge is pervasive in materials science, making reliable surrogate modeling extremely difficult with models trained from scratch on each new dataset. Here we propose In-Context Active Learning (ICAL), which addresses this bottleneck by replacing conventional surrogates with TabPFN, a transformer-based foundation model (FM) pre-trained on millions of synthetic regression tasks to meta-learn a universal prior over tabular data, upon which TabPFN performs principled Bayesian inference in a single forward pass without dataset-specific retraining, delivering strong small-data regression performance and well-calibrated predictive uncertainty (required for effective AL). We benchmark ICAL against GP and RF across 10 materials datasets and TabPFN wins on 8 out of 10 datasets, achieving a mean saving of 52% in extra evaluations relative to GP and 29.77% relative to RF. Cross-validation analysis confirms that TabPFN's advantage stems from superior uncertainty calibration, achieving the lowest Negative Log-Likelihood and Area Under the Sparsification Error curve among all surrogates. These results demonstrate that pre-trained FMs can serve as effective surrogates for active learning, enabling data-efficient discovery across diverse materials systems and small-data experimental sciences.

Interactive segmentation is commonly used in medical image analysis to obtain precise, pixel-level labeling, typically involving iterative user input to correct mislabeled regions. However, existing approaches often fail to fully utilize user knowledge from interactive inputs and achieve comprehensive feature extraction. Specifically, these methods tend to treat all mislabeled regions equally, selecting them randomly for refinement without evaluating each region's potential impact on segmentation quality. Additionally, most models rely solely on spatial domain features, overlooking frequency domain information that could enhance feature extraction and improve performance. To address these limitations, we propose ActiveFreq, a novel interactive segmentation framework that integrates active learning and frequency domain analysis to minimize human intervention while achieving high-quality labeling. ActiveFreq introduces AcSelect, an autonomous module that prioritizes the most informative mislabeled regions, ensuring maximum performance gain from each click. Moreover, we develop FreqFormer, a segmentation backbone incorporating a Fourier transform module to map features from the spatial to the frequency domain, enabling richer feature extraction. Evaluations on the ISIC-2017 and OAI-ZIB datasets demonstrate that ActiveFreq achieves high performance with reduced user interaction, achieving 3.74 NoC@90 on ISIC-2017 and 9.27 NoC@90 on OAI-ZIB, with 23.5% and 12.8% improvements over previous best results, respectively. Under minimal input conditions, such as two clicks, ActiveFreq reaches mIoU scores of 85.29% and 75.76% on ISIC-2017 and OAI-ZIB, highlighting its efficiency and accuracy in interactive medical segmentation.

The Segment Anything Model (SAM) has revolutionized interactive segmentation through spatial prompting. While existing work primarily focuses on automating prompts in various settings, real-world annotation workflows involve iterative refinement where annotators observe model outputs and strategically place prompts to resolve ambiguities. Current pipelines typically rely on the annotator's visual assessment of the predicted mask quality. We postulate that a principled approach for automated interactive prompting is to use a model-derived criterion to identify the most informative region for the next prompt. In this work, we establish active prompting: a spatial active learning approach where locations within images constitute an unlabeled pool and prompts serve as queries to prioritize information-rich regions, increasing the utility of each interaction. We further present BALD-SAM: a principled framework adapting Bayesian Active Learning by Disagreement (BALD) to spatial prompt selection by quantifying epistemic uncertainty. To do so, we freeze the entire model and apply Bayesian uncertainty modeling only to a small learned prediction head, making intractable uncertainty estimation practical for large multi-million parameter foundation models. Across 16 datasets spanning natural, medical, underwater, and seismic domains, BALD-SAM demonstrates strong cross-domain performance, ranking first or second on 14 of 16 benchmarks. We validate these gains through a comprehensive ablation suite covering 3 SAM backbones and 35 Laplace posterior configurations, amounting to 38 distinct ablation settings. Beyond strong average performance, BALD-SAM surpasses human prompting and, in several categories, even oracle prompting, while consistently outperforming one-shot baselines in final segmentation quality, particularly on thin and structurally complex objects.

Active learning for regression reduces labeling costs by selecting the most informative samples. Improved Greedy Sampling is a prominent method that balances feature-space diversity and output-space uncertainty using a static, multiplicative rule. We propose Weighted improved Greedy Sampling (WiGS), which replaces this framework with a dynamic, additive criterion. We formulate weight selection as a reinforcement learning problem, enabling an agent to adapt the exploration-investigation balance throughout learning. Experiments on 18 benchmark datasets and a synthetic environment show WiGS outperforms iGS and other baseline methods in both accuracy and labeling efficiency, particularly in domains with irregular data density where the baseline's multiplicative rule ignores high-error samples in dense regions.

Federated active learning (FAL) seeks to reduce annotation cost under privacy constraints, yet its effectiveness degrades in realistic settings with severe global class imbalance and highly heterogeneous clients. We conduct a systematic study of query-model selection in FAL and uncover a central insight: the model that achieves more class-balanced sampling, especially for minority classes, consistently leads to better final performance. Moreover, global-model querying is beneficial only when the global distribution is highly imbalanced and client data are relatively homogeneous; otherwise, the local model is preferable. Based on these findings, we propose FairFAL, an adaptive class-fair FAL framework. FairFAL (1) infers global imbalance and local-global divergence via lightweight prediction discrepancy, enabling adaptive selection between global and local query models; (2) performs prototype-guided pseudo-labeling using global features to promote class-aware querying; and (3) applies a two-stage uncertainty-diversity balanced sampling strategy with k-center refinement. Experiments on five benchmarks show that FairFAL consistently outperforms state-of-the-art approaches under challenging long-tailed and non-IID settings. The code is available at https://github.com/chenchenzong/FairFAL.

Reinforcement Learning from Human Feedback (RLHF) has become the standard for aligning Large Language Models (LLMs), yet its efficacy is bottlenecked by the high cost of acquiring preference data, especially in low-resource and expert domains. To address this, we introduce ACTIVEULTRAFEEDBACK, a modular active learning pipeline that leverages uncertainty estimates to dynamically identify the most informative responses for annotation. Our pipeline facilitates the systematic evaluation of standard response selection methods alongside DOUBLE REVERSE THOMPSON SAMPLING (DRTS) and DELTAUCB, two novel methods prioritizing response pairs with large predicted quality gaps, leveraging recent results showing that such pairs provide good signals for fine-tuning. Our experiments demonstrate that ACTIVEULTRAFEEDBACK yields high-quality datasets that lead to significant improvements in downstream performance, notably achieving comparable or superior results with as little as one-sixth of the annotated data relative to static baselines. Our pipeline is available at https://github.com/lasgroup/ActiveUltraFeedback and our preference datasets at https://huggingface.co/ActiveUltraFeedback.

Accurate on-orbit reliability prediction for satellite electronics is often hindered by limited data availability, varying operational conditions, and considerable unit-to-unit variability. To overcome these obstacles, this paper proposes a novel integrated online reliability prediction framework. The main contributions are twofold. First, a Wiener process-based degradation model is developed, incorporating a generalized Arrhenius link function, individual random effects, and spatial correlations among adjacent units. A customized maximum likelihood estimation method is further devised to facilitate efficient and accurate parameter inference. Second, a two-stage active learning sampling scheme is designed to adaptively enhance prediction accuracy. This strategy initially selects representative units based on spatial configuration, and subsequently determines optimal sampling times using a comprehensive criterion that balances unit-specific information, model uncertainty, and degradation dynamics. Numerical experiments and a practical case study from the Tiangong space station demonstrate that the proposed method markedly improves reliability prediction accuracy while significantly reducing data requirements, offering an efficient solution for the prognostic and health management of complex satellite electronic systems.

Open-set active learning (OSAL) aims to identify informative samples for annotation when unlabeled data may contain previously unseen classes-a common challenge in safety-critical and open-world scenarios. Existing approaches typically rely on separately trained open-set detectors, introducing substantial training overhead and overlooking the supervisory value of labeled unknowns for improving known-class learning. In this paper, we propose E$^2$OAL (Effective and Efficient Open-set Active Learning), a unified and detector-free framework that fully exploits labeled unknowns for both stronger supervision and more reliable querying. E$^2$OAL first uncovers the latent class structure of unknowns through label-guided clustering in a frozen contrastively pre-trained feature space, optimized by a structure-aware F1-product objective. To leverage labeled unknowns, it employs a Dirichlet-calibrated auxiliary head that jointly models known and unknown categories, improving both confidence calibration and known-class discrimination. Building on this, a logit-margin purity score estimates the likelihood of known classes to construct a high-purity candidate pool, while an OSAL-specific informativeness metric prioritizes partially ambiguous yet reliable samples. These components together form a flexible two-stage query strategy with adaptive precision control and minimal hyperparameter sensitivity. Extensive experiments across multiple OSAL benchmarks demonstrate that E$^2$OAL consistently surpasses state-of-the-art methods in accuracy, efficiency, and query precision, highlighting its effectiveness and practicality for real-world applications. The code is available at github.com/chenchenzong/E2OAL.

Deploying medical AI across resource-constrained institutions demands data-efficient learning pipelines that respect patient privacy. Federated Learning (FL) enables collaborative medical AI without centralising data, yet real-world clinical pools are inherently open-set, containing out-of-distribution (OOD) noise such as imaging artifacts and wrong modalities. Standard Active Learning (AL) query strategies mistake this noise for informative samples, wasting scarce annotation budgets. We propose PromptGate, a dynamic VLM-gated framework for Open-Set Federated AL that purifies unlabeled pools before querying. PromptGate introduces a federated Class-Specific Context Optimization: lightweight, learnable prompt vectors that adapt a frozen BiomedCLIP backbone to local clinical domains and aggregate globally via FedAvg -- without sharing patient data. As new annotations arrive, prompts progressively sharpen the ID/OOD boundary, turning the VLM into a dynamic gatekeeper that is strategy-agnostic: a plug-and-play pre-selection module enhancing any downstream AL strategy. Experiments on distributed dermatology and breast imaging benchmarks show that while static VLM prompting degrades to 50% ID purity, PromptGate maintains $>$95% purity with 98% OOD recall.

In this article, bipartite ranking, a statistical learning problem involved in many applications and widely studied in the passive context, is approached in a much more general active setting than the discrete one previously considered in the literature. While the latter assumes that the conditional distribution is piece wise constant, the framework we develop permits in contrast to deal with continuous conditional distributions, provided that they fulfill a Hölder smoothness constraint. We first show that a naive approach based on discretisation at a uniform level, fixed a priori and consisting in applying next the active strategy designed for the discrete setting generally fails. Instead, we propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the $\sup$ norm. We show that, for a fixed confidence level $ε>0$ and probability $δ\in (0,1)$, smooth-rank is PAC$(ε,δ)$. In addition, we provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC$(ε,δ)$ algorithm. Beyond the theoretical analysis carried out, numerical results are presented, providing solid empirical evidence of the performance of the algorithm proposed, which compares favorably with alternative approaches.

The increasing size and heterogeneity of exoplanet catalogs have made systematic habitability assessment challenging, particularly given the extreme scarcity of potentially habitable planets and the evolving nature of their labels. In this study, we explore the use of pool-based active learning to improve the efficiency of habitability classification under realistic observational constraints. We construct a unified dataset from the Habitable World Catalog and the NASA Exoplanet Archive and formulate habitability assessment as a binary classification problem. A supervised baseline based on gradient-boosted decision trees is established and optimized for recall in order to prioritize the identification of rare potentially habitable planets. This model is then embedded within an active learning framework, where uncertainty-based margin sampling is compared against random querying across multiple runs and labeling budgets. We find that active learning substantially reduces the number of labeled instances required to approach supervised performance, demonstrating clear gains in label efficiency. To connect these results to a practical astronomical use case, we aggregate predictions from independently trained active-learning models into an ensemble and use the resulting mean probabilities and uncertainties to rank planets originally labeled as non-habitable. This procedure identifies a single robust candidate for further study, illustrating how active learning can support conservative, uncertainty-aware prioritization of follow-up targets rather than speculative reclassification. Our results indicate that active learning provides a principled framework for guiding habitability studies in data regimes characterized by label imbalance, incomplete information, and limited observational resources.

Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying a set function requires assigning values to an exponentially large number of subsets in general, a task that is often resource-intensive in practice, particularly when the values derive from external sources such as retraining of machine learning models. A~simple omission of certain values introduces ambiguity that becomes even more significant when the incomplete set function has to be further optimized over. Motivated by the well-known result about inapproximability of subadditive functions using deterministic value queries with respect to a multiplicative error, we study a problem of approximating an unknown subadditive (or a subclass of thereof) set function with respect to an additive error -- i. e., we aim to efficiently close the distance between minimal and maximal completions. Our contributions are threefold: (i) a thorough exploration of minimal and maximal completions of different classes of set functions with missing values and an analysis of their resulting distance; (ii) the development of methods to minimize this distance over classes of set functions with a known prior, achieved by disclosing values of additional subsets in both offline and online manner; and (iii) empirical demonstrations of the algorithms' performance in practical scenarios.

Active automata learning (AAL) algorithms can learn a behavioral model of a system from interacting with it. The primary challenge remains scaling to larger models, in particular in the presence of many possible inputs to the system. Modern AAL algorithms fail to scale even if, in every state, most inputs lead to errors. In various challenging problems from the literature, these errors are observable, i.e., they emit a known error output. Motivated by these problems, we study learning these systems more efficiently. Further, we consider various degrees of knowledge about which inputs are non-error producing at which state. For each level of knowledge, we provide a matching adaptation of the state-of-the-art AAL algorithm L# to make the most of this domain knowledge. Our empirical evaluation demonstrates that the methods accelerate learning by orders of magnitude with strong but realistic domain knowledge to a single order of magnitude with limited domain knowledge.

Active data acquisition is central to many learning and optimization tasks in deep neural networks, yet remains challenging because most approaches rely on predictive uncertainty estimates that are difficult to obtain reliably. To this end, we propose Goal-Oriented Influence- Maximizing Data Acquisition (GOIMDA), an active acquisition algorithm that avoids explicit posterior inference while remaining uncertainty-aware through inverse curvature. GOIMDA selects inputs by maximizing their expected influence on a user-specified goal functional, such as test loss, predictive entropy, or the value of an optimizer-recommended design. Leveraging first-order influence functions, we derive a tractable acquisition rule that combines the goal gradient, training-loss curvature, and candidate sensitivity to model parameters. We show theoretically that, for generalized linear models, GOIMDA approximates predictive-entropy minimization up to a correction term accounting for goal alignment and prediction bias, thereby, yielding uncertainty-aware behavior without maintaining a Bayesian posterior. Empirically, across learning tasks (including image and text classification) and optimization tasks (including noisy global optimization benchmarks and neural-network hyperparameter tuning), GOIMDA consistently reaches target performance with substantially fewer labeled samples or function evaluations than uncertainty-based active learning and Gaussian-process Bayesian optimization baselines.

Active Learning (AL) reduces annotation costs in medical imaging by selecting only the most informative samples for labeling, but suffers from cold-start when labeled data are scarce. Vision-Language Models (VLMs) address the cold-start problem via zero-shot predictions, yet their temperature-scaled softmax outputs treat text-image similarities as deterministic scores while ignoring inherent uncertainty, leading to overconfidence. This overconfidence misleads sample selection, wasting annotation budgets on uninformative cases. To overcome these limitations, the Similarity-as-Evidence (SaE) framework calibrates text-image similarities by introducing a Similarity Evidence Head (SEH), which reinterprets the similarity vector as evidence and parameterizes a Dirichlet distribution over labels. In contrast to a standard softmax that enforces confident predictions even under weak signals, the Dirichlet formulation explicitly quantifies lack of evidence (vacuity) and conflicting evidence (dissonance), thereby mitigating overconfidence caused by rigid softmax normalization. Building on this, SaE employs a dual-factor acquisition strategy: high-vacuity samples (e.g., rare diseases) are prioritized in early rounds to ensure coverage, while high-dissonance samples (e.g., ambiguous diagnoses) are prioritized later to refine boundaries, providing clinically interpretable selection rationales. Experiments on ten public medical imaging datasets with a 20% label budget show that SaE attains state-of-the-art macro-averaged accuracy of 82.57%. On the representative BTMRI dataset, SaE also achieves superior calibration, with a negative log-likelihood (NLL) of 0.425.

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before. This dissertation focuses on three different projects rooted in mathematical theory for machine learning applications. The first project deals with supervised learning and manifold learning. In theory, one of the main problems in supervised learning is that of function approximation: that is, given some data set $\mathcal{D}=\{(x_j,f(x_j))\}_{j=1}^M$, can one build a model $F\approx f$? We introduce a method which aims to remedy several of the theoretical shortcomings of the current paradigm for supervised learning. The second project deals with transfer learning, which is the study of how an approximation process or model learned on one domain can be leveraged to improve the approximation on another domain. We study such liftings of functions when the data is assumed to be known only on a part of the whole domain. We are interested in determining subsets of the target data space on which the lifting can be defined, and how the local smoothness of the function and its lifting are related. The third project is concerned with the classification task in machine learning, particularly in the active learning paradigm. Classification has often been treated as an approximation problem as well, but we propose an alternative approach leveraging techniques originally introduced for signal separation problems. We introduce theory to unify signal separation with classification and a new algorithm which yields competitive accuracy to other recent active learning algorithms while providing results much faster.

In active sequential testing, also termed pure exploration, a learner is tasked with the goal to adaptively acquire information so as to identify an unknown ground-truth hypothesis with as few queries as possible. This problem has several motivating applications, including Best-Arm Identification (BAI) in bandits, where actions index hypotheses, and generalized search problems, where strategically chosen queries reveal partial information about a hidden label. In many modern settings, however, the hypothesis, or recommendation space, is continuous: for example, identifying a near optimal action in a continuous-armed bandit, localizing an $ε$-ball contained in a target region, or estimating the minimizer of a function from noisy observations. Existing methods are predominantly frequentist and model-specific, while learned approaches have been limited to finite recommendation spaces. We introduce C-ICPE, a theory-guided learned model for Bayesian fixed-confidence pure exploration with continuous recommendations. C-ICPE meta-trains sequential architectures over a task prior to jointly learn exploration, stopping and recommendations strategies. At inference time, it actively gathers evidence on tasks and identifies an $ε$-optimal recommendation without parameter updates.

In environmental monitoring, data collection is often costly, sparse, and shaped by urgent public-health needs. This is particularly true for cancer-causing PFAS (Per- and polyfluoroalkyl substances) contamination, where discussions with domain experts and environmental organizations highlight the need to strategically identify high-risk, under-observed regions under tight sampling budgets. More broadly, similar challenges arise in disaster response and public health settings, where dynamic environments make it essential to efficiently uncover hidden targets from limited ground truth. Yet sparse and biased geospatial labels limit the applicability of existing learning-based methods, such as reinforcement learning. To address this, we propose a unified geospatial discovery framework that integrates active learning, online meta-learning, and concept-guided reasoning. Our approach introduces two key innovations built on a shared notion of concept relevance, capturing how domain-specific factors influence target presence: a concept-weighted uncertainty sampling strategy, where uncertainty is modulated by learned relevance from readily available concepts such as land cover and source proximity; and a relevance-aware meta-batch formation strategy that promotes semantic diversity during online-meta updates, improving generalization in dynamic environments. We evaluate our framework on PFAS contamination discovery as a real-world inspired environmental monitoring task, demonstrating robust target discovery under limited data and changing conditions.