Generative modeling has emerged as a powerful paradigm for representation learning, but its direct applicability to challenging fields like medical imaging remains limited: mere generation, without task alignment, fails to provide a robust foundation for clinical use. We propose MAGIC-Flow, a conditional multiscale normalizing flow architecture that performs generation and classification within a single modular framework. The model is built as a hierarchy of invertible and differentiable bijections, where the Jacobian determinant factorizes across sub-transformations. We show how this ensures exact likelihood computation and stable optimization, while invertibility enables explicit visualization of sample likelihoods, providing an interpretable lens into the model's reasoning. By conditioning on class labels, MAGIC-Flow supports controllable sample synthesis and principled class-probability estimation, effectively aiding both generative and discriminative objectives. We evaluate MAGIC-Flow against top baselines using metrics for similarity, fidelity, and diversity. Across multiple datasets, it addresses generation and classification under scanner noise, and modality-specific synthesis and identification. Results show MAGIC-Flow creates realistic, diverse samples and improves classification. MAGIC-Flow is an effective strategy for generation and classification in data-limited domains, with direct benefits for privacy-preserving augmentation, robust generalization, and trustworthy medical AI.

Learning mappings between functional spaces, also known as function-on-function regression, plays a crucial role in functional data analysis and has broad applications, e.g. spatiotemporal forecasting, curve prediction, and climate modeling. Existing approaches, such as functional linear models and neural operators, either fall short of capturing complex nonlinearities or lack reliable uncertainty quantification under noisy, sparse, and irregularly sampled data. To address these issues, we propose Deep Gaussian Processes for Functional Maps (DGPFM). Our method designs a sequence of GP-based linear and nonlinear transformations, leveraging integral transforms of kernels, GP interpolation, and nonlinear activations sampled from GPs. A key insight simplifies implementation: under fixed locations, discrete approximations of kernel integral transforms collapse into direct functional integral transforms, enabling flexible incorporation of various integral transform designs. To achieve scalable probabilistic inference, we use inducing points and whitening transformations to develop a variational learning algorithm. Empirical results on real-world and PDE benchmark datasets demonstrate that the advantage of DGPFM in both predictive performance and uncertainty calibration.

Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale non-private sparse regression - known as Best Subset Selection (BSS) - with millions of variables in minutes. However, extending these algorithmic advances to the setting of Differential Privacy (DP) has remained largely unexplored. In this paper, we introduce two new pure differentially private estimators for sparse variable selection, levering modern MIP techniques. Our framework is general and applies broadly to problems like sparse regression or classification, and we provide theoretical support recovery guarantees in the case of BSS. Inspired by the exponential mechanism, we develop structured sampling procedures that efficiently explore the non-convex objective landscape, avoiding the exhaustive combinatorial search in the exponential mechanism. We complement our theoretical findings with extensive numerical experiments, using both least squares and hinge loss for our objective function, and demonstrate that our methods achieve state-of-the-art empirical support recovery, outperforming competing algorithms in settings with up to $p=10^4$.

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable $d$-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset. Code and data of the proposed method are publicly available at https://github$.$com/PurdueMINDS/DAGPA.

Selecting an appropriate evaluation metric for classifiers is crucial for model comparison and parameter optimization, yet there is not consensus on a universally accepted metric that serves as a definitive standard. Moreover, there is often a misconception about the perceived need to mitigate imbalance in datasets used to train classification models. Since the final goal in classifier optimization is typically maximizing the return of investment or, equivalently, minimizing the Total Classification Cost (TCC), we define Weighted Accuracy (WA), an evaluation metric for binary classifiers with a straightforward interpretation as a weighted version of the well-known accuracy metric, coherent with the need of minimizing TCC. We clarify the conceptual framework for handling class imbalance in cost-sensitive scenarios, providing an alternative to rebalancing techniques. This framework can be applied to any metric that, like WA, can be expressed as a linear combination of example-dependent quantities and allows for comparing the results obtained in different datasets and for addressing discrepancies between the development dataset, used to train and validate the model, and the target dataset, where the model will be deployed. It also specifies in which scenarios using UCCs-unaware class rebalancing techniques or rebalancing metrics aligns with TCC minimization and when it is instead counterproductive. Finally, we propose a procedure to estimate the WA weight parameter in the absence of fully specified UCCs and demonstrate the robustness of WA by analyzing its correlation with TCC in example-dependent scenarios.

Text watermarking plays a crucial role in ensuring the traceability and accountability of large language model (LLM) outputs and mitigating misuse. While promising, most existing methods assume perfect pseudorandomness. In practice, repetition in generated text induces collisions that create structured dependence, compromising Type I error control and invalidating standard analyses. We introduce a statistical framework that captures this structure through a hierarchical two-layer partition. At its core is the concept of minimal units -- the smallest groups treatable as independent across units while permitting dependence within. Using minimal units, we define a non-asymptotic efficiency measure and cast watermark detection as a minimax hypothesis testing problem. Applied to Gumbel-max and inverse-transform watermarks, our framework produces closed-form optimal rules. It explains why discarding repeated statistics often improves performance and shows that within-unit dependence must be addressed unless degenerate. Both theory and experiments confirm improved detection power with rigorous Type I error control. These results provide the first principled foundation for watermark detection under imperfect pseudorandomness, offering both theoretical insight and practical guidance for reliable tracing of model outputs.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical ``what if?'' scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes -- blackbox and concept-based predictors -- and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

Reinforcement learning (RL) promises to solve long-horizon tasks even when training data contains only short fragments of the behaviors. This experience stitching capability is often viewed as the purview of temporal difference (TD) methods. However, outside of small tabular settings, trajectories never intersect, calling into question this conventional wisdom. Moreover, the common belief is that Monte Carlo (MC) methods should not be able to recombine experience, yet it remains unclear whether function approximation could result in a form of implicit stitching. The goal of this paper is to empirically study whether the conventional wisdom about stitching actually holds in settings where function approximation is used. We empirically demonstrate that Monte Carlo (MC) methods can also achieve experience stitching. While TD methods do achieve slightly stronger capabilities than MC methods (in line with conventional wisdom), that gap is significantly smaller than the gap between small and large neural networks (even on quite simple tasks). We find that increasing critic capacity effectively reduces the generalization gap for both the MC and TD methods. These results suggest that the traditional TD inductive bias for stitching may be less necessary in the era of large models for RL and, in some cases, may offer diminishing returns. Additionally, our results suggest that stitching, a form of generalization unique to the RL setting, might be achieved not through specialized algorithms (temporal difference learning) but rather through the same recipe that has provided generalization in other machine learning settings (via scale). Project website: https://michalbortkiewicz.github.io/golden-standard/

Novelty detection in large scientific datasets faces two key challenges: the noisy and high-dimensional nature of experimental data, and the necessity of making statistically robust statements about any observed outliers. While there is a wealth of literature on anomaly detection via dimensionality reduction, most methods do not produce outputs compatible with quantifiable claims of scientific discovery. In this work we directly address these challenges, presenting the first step towards a unified pipeline for novelty detection adapted for the rigorous statistical demands of science. We introduce AutoSciDACT (Automated Scientific Discovery with Anomalous Contrastive Testing), a general-purpose pipeline for detecting novelty in scientific data. AutoSciDACT begins by creating expressive low-dimensional data representations using a contrastive pre-training, leveraging the abundance of high-quality simulated data in many scientific domains alongside expertise that can guide principled data augmentation strategies. These compact embeddings then enable an extremely sensitive machine learning-based two-sample test using the New Physics Learning Machine (NPLM) framework, which identifies and statistically quantifies deviations in observed data relative to a reference distribution (null hypothesis). We perform experiments across a range of astronomical, physical, biological, image, and synthetic datasets, demonstrating strong sensitivity to small injections of anomalous data across all domains.

Causal inference identifies cause-and-effect relationships between variables. While traditional approaches rely on data to reveal causal links, a recently developed method, assimilative causal inference (ACI), integrates observations with dynamical models. It utilizes Bayesian data assimilation to trace causes back from observed effects by quantifying the reduction in uncertainty. ACI advances the detection of instantaneous causal relationships and the intermittent reversal of causal roles over time. Beyond identifying causal connections, an equally important challenge is determining the associated causal influence range (CIR), indicating when causal influences emerged and for how long they persist. In this paper, ACI is employed to develop mathematically rigorous formulations of both forward and backward CIRs at each time. The forward CIR quantifies the temporal impact of a cause, while the backward CIR traces the onset of triggers for an observed effect, thus characterizing causal predictability and attribution of outcomes at each transient phase, respectively. Objective and robust metrics for both CIRs are introduced, eliminating the need for empirical thresholds. Computationally efficient approximation algorithms to compute CIRs are developed, which facilitate the use of closed-form expressions for a broad class of nonlinear dynamical systems. Numerical simulations demonstrate how this forward and backward CIR framework provides new possibilities for probing complex dynamical systems. It advances the study of bifurcation-driven and noise-induced tipping points in Earth systems, investigates the impact from resolving the interfering variables when determining the influence ranges, and elucidates atmospheric blocking mechanisms in the equatorial region. These results have direct implications for science, policy, and decision-making.