Papers

Flow Matching (FM) has emerged as a powerful paradigm for continuous normalizing flows, yet standard FM implicitly performs an unweighted $L^2$ regression over the entire ambient space. In high dimensions, this leads to a fundamental inefficiency: the vast majority of the integration domain consists of low-density “void” regions where the target velocity fields are often chaotic or ill-defined. In this paper, we propose {$\gamma$-Flow Matching ($\gamma$-FM)}, a density-weighted variant that aligns the regression geometry with the underlying probability flow. While density weighting is desirable, naive implementations would require evaluating the intractable target density. We circumvent this by introducing a Dynamic Density-Weighting strategy that estimates the target density directly from training particles. This approach allows us to dynamically downweight the regression loss in void regions without compromising the simulation-free nature of FM. Theoretically, we establish that $\gamma$-FM minimizes the transport cost on a statistical manifold endowed with the $\gamma$-Stein metric. Spectral analysis further suggests that this geometry induces an implicit Sobolev regularization, effectively damping high-frequency oscillations in void regions. Empirically, $\gamma$-FM significantly improves vector field smoothness and sampling efficiency on high-dimensional latent datasets, while demonstrating intrinsic robustness to outliers.

The balanced loss is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are not overlooked. However, directly minimizing the balanced classification loss is typically intractable, which makes the design of effective surrogate losses a central question. This paper introduces and studies two advanced surrogate loss families: Generalized Logit-Adjusted (GLA) loss functions and Generalized Class-Aware weighted (GCA) losses. GLA losses generalize Logit-Adjusted losses, which shift logits based on class priors, to the broader general cross-entropy loss family. GCA loss functions extend the standard class-weighted losses, which scale losses inversely by class frequency, by incorporating class-dependent confidence margins and extending them to the general cross-entropy family. We present a comprehensive theoretical analysis of consistency for both loss families. We show that GLA losses are Bayes-consistent, but only $H$-consistent for complete (i.e., unbounded) hypothesis sets. Moreover, their $H$-consistency bounds depend inversely on the minimum class probability, scaling at least as $1/\mathsf p_{\min}$. In contrast, GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings. We report the results of experiments demonstrating that, empirically, both the GCA losses with calibrated class-dependent confidence margins and GLA losses can greatly outperform straightforward class-weighted losses as well as the LA losses. GLA generally performs slightly better in common benchmarks, whereas GCA exhibits a slight edge in highly imbalanced settings.

U.S. discrimination law can impose liability on firms that fail to adopt a less discriminatory alternative (LDA): a decision policy that achieves the same business objectives while reducing disparate impact on legally protected groups. Recent scholarship argues that this doctrine has direct implications for algorithmic decision-making in high-stakes domains such as employment, lending, and housing, potentially obligating firms to search for "less discriminatory algorithms" (Black et al., 2024). Regulators have at times encouraged proactive LDA searches, reinforcing the expectation of a good-faith effort to identify equally performant models with lower disparate impact. Model multiplicity makes such searches plausible: retraining with different random seeds can yield models with comparable predictive performance but materially different disparate impacts. Yet firms cannot retrain indefinitely, raising a central question: when is the search sufficient to demonstrate good faith? We formalize LDA search under multiplicity as an optimal stopping problem in which a developer seeks to produce evidence that further search is unlikely to yield meaningful improvements. Our main contribution is an adaptive stopping algorithm that provides a high-probability upper bound on the best disparate-impact gains attainable through continued retraining, enabling developers to certify (e.g., to a court) that additional search is unlikely to help. We also show how stronger distributional assumptions over the model space can yield tighter bounds, and we validate the approach on real-world credit and housing datasets.

Fitted \(Q\)-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability under function approximation often relies on Bellman completeness, which requires Bellman images of the fitted class to remain in the class. We study Kullback–Leibler (KL)-regularized, or soft, FQI relative to a fixed reference policy without this assumption. Our key insight is that soft control locally inherits the contraction of policy evaluation in a discounted-occupancy norm. At the soft-optimal fixed point, the linearization of the soft Bellman operator is exactly the Bellman operator for the soft-optimal policy, which contracts in its discounted-occupancy norm; projection in the same norm preserves this contraction. Standard soft FQI instead projects under the offline state-action distribution and need not preserve this property. Motivated by this observation, we propose occupancy-reweighted soft FQI, which retains standard Bellman targets and least-squares updates while reweighting regressions by discounted-occupancy ratios induced by the current soft policy. Under \(Q\)-function realizability and local regularity, we establish local contraction and finite-sample convergence with estimated ratios, without Bellman completeness. We then use temperature annealing to convert the local result into global convergence from arbitrary initialization: sufficiently high temperature provides a globally contractive starting regime, while gradual cooling connects successive local contraction regions to any prescribed positive target temperature. Under an action-gap margin condition, switching at a fixed positive temperature to hard FQI with refreshed occupancy weights also yields population and finite-sample convergence to the unregularized optimum.

Machine learning has achieved remarkable success across a wide range of applications, yet many of its most effective methods rely on access to large amounts of labeled data or extensive online interaction. In practice, acquiring high-quality labels and making decisions through trial-and-error can be expensive, time-consuming, or risky, particularly in large-scale or high-stakes settings. This dissertation studies interactive machine learning, in which the learner actively influences how information is collected or which actions are taken, using past observations to guide future interactions. We develop new algorithmic principles and establish fundamental limits for interactive learning along three dimensions: active learning with noisy data and rich model classes, sequential decision making with large action spaces, and model selection under partial feedback. Our results include the first computationally efficient active learning algorithms achieving exponential label savings without low-noise assumptions; the first efficient, general-purpose contextual bandit algorithms whose guarantees are independent of the size of the action space; and the first tight characterizations of the fundamental cost of model selection in sequential decision making. Overall, this dissertation advances the theoretical foundations of interactive learning by developing algorithms that are statistically optimal and computationally efficient, while also providing principled guidance for deploying interactive learning methods in large-scale, real-world settings.

The Dynamic Nelson–Siegel (DNS) model is a widely used framework for term structure forecasting. We propose a novel extension that models DNS residuals as a Gaussian random field, capturing dependence across both time and maturity. The residual field is represented via a stochastic partial differential equation (SPDE), enabling flexible covariance structures and scalable Bayesian inference through sparse precision matrices. We consider a range of SPDE specifications, including stationary, non-stationary, anisotropic, and nonseparable models. The SPDE–DNS model is estimated in a Bayesian framework using the integrated nested Laplace approximation (INLA), jointly inferring latent DNS factors and the residual field. Empirical results show that the SPDE-based extensions improve both point and probabilistic forecasts relative to standard benchmarks. When applied in a mean–variance bond portfolio framework, the forecasts generate economically meaningful utility gains, measured as performance fees relative to a Bayesian DNS benchmark under monthly rebalancing. Importantly, incorporating the structured SPDE residual substantially reduces cross-maturity and intertemporal dependence in the remaining measurement error, bringing it closer to white noise. These findings highlight the advantages of combining DNS with SPDE-driven residual modeling for flexible, interpretable, and computationally efficient yield curve forecasting.

We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy confidence intervals. These intervals are compared with methods described in the literature for well-known distributions such as normal, binomial, and Poisson. The results show that in high-variance situations, the new intervals provide better performance. Furthermore, through these intervals, it is possible to compute a lower bound for the expected length, demonstrating that they achieve the minimal maximum expected length for a Bernoulli trial observation.

Denoising and score estimation are classically linked through Tweedie's formula, which relates the posterior mean under Gaussian noise to the Stein score of the noisy marginal. In this work, we extend this perspective beyond Gaussian noise to a broad class of Gibbs (energy-based) noise distributions, with the generalized Gaussian family as the running example. We derive the Energy-Tweedie identity: when the denoising posterior is viewed through the lens of scoring rules, the path derivative of a kernel scoring rule defined by the noise potential recovers the Stein score of the noisy marginal. The rule's propriety is determined by the noise potential alone. Thus, the familiar correspondence between Gaussian noise, posterior means, squared loss, and Tweedie's formula is lifted to a distributional correspondence between Gibbs noise distributions, full posterior laws, kernel scoring rules, and the Energy-Tweedie identity, yielding one Tweedie-style relation for each noise potential. Among its consequences, this identity gives a posterior-samples-to-score route to score estimation, yields a principled criterion for estimating unknown noise parameters, and enables diffusion-style sampling along user-chosen paths through the noise-parameter space, supplying the score-based perspective on recent generative methods trained with scoring rules.

Fitted \(Q\)-evaluation (FQE) is a standard regression-based method for off-policy evaluation, but under distribution shift, value-function realizability alone does not ensure convergence, and existing analyses often require Bellman completeness. We trace this instability to a geometric mismatch: standard FQE projects Bellman targets in the norm induced by the offline distribution, which need not preserve Bellman contraction. We therefore study occupancy-weighted FQE, which changes only the regression weights. Weighting by a target-policy discounted occupancy ratio aligns the projection norm with the target-policy dynamics and restores contraction of the population projected Bellman operator. We derive finite-sample guarantees with estimated occupancy ratios and function-class misspecification, separating finite-iteration, statistical, approximation, and ratio-estimation errors. Exact occupancy weighting removes the need for Bellman completeness; with estimated weights, approximate completeness and value-function realizability reduce sensitivity to ratio-estimation error, with exact realizability yielding higher-order dependence. Combining occupancy-weighted FQE with fitted occupancy-ratio evaluation gives an end-to-end guarantee governed by the complexities and direct approximation errors of the value-function and occupancy-ratio classes. Under coverage, joint realizability of these two classes suffices for consistent estimation without Bellman or critic-side completeness. Controlled experiments illustrate the projection-norm mechanism and the finite-sample tradeoff between contraction and coverage.

We present TabMixNN, a flexible PyTorch-based deep learning framework that synthesizes classical mixed-effects modeling with modern neural network architectures for tabular data analysis. TabMixNN addresses the growing need for methods that can handle hierarchical data structures while supporting diverse outcome types including regression, classification, and multitask learning. The framework implements a modular three-stage architecture: (1) a mixed-effects encoder with variational random effects and flexible covariance structures, (2) backbone architectures including Generalized Structural Equation Models (GSEM) and spatial-temporal manifold networks, and (3) outcome-specific prediction heads supporting multiple outcome families. Key innovations include an R-style formula interface for accessibility, support for directed acyclic graph (DAG) constraints for causal structure learning, Stochastic Partial Differential Equation (SPDE) kernels for spatial modeling, and comprehensive interpretability tools including SHAP values and variance decomposition. We demonstrate the framework's flexibility through applications to longitudinal data analysis, genomic prediction, and spatial-temporal modeling. TabMixNN provides a unified interface for researchers to leverage deep learning while maintaining the interpretability and theoretical grounding of classical mixed-effects models.

In this paper, we model the locations of five major banks in mainland France, two lucrative and three cooperative institutions based on socio-economic considerations. Locations of banks are collected using web scrapping and constitute a bivariate spatial point process for which we estimate nonparametrically summary functions (intensity, Ripley and cross-Ripley's K functions). This shows that the pattern is highly inhomogenenous and exhibits a clustering effect especially at small scales, and thus a significant departure to the bivariate (inhomogeneous) Poisson point process is pointed out. We also collect socio-economic datasets (at the living area level) from INSEE and propose a parametric modelling of the intensity function using these covariates. We propose a group-penalized bivariate composite likelihood method to estimate the model parameters, and we establish its asymptotic properties. The application of the methodology to the banking dataset provides new insights into the specificity of the cooperative model within the sector, particularly in relation to the theories of institutional isomorphism.

In epidemiological research, modeling the cumulative effects of time-dependent exposures on survival outcomes presents a challenge due to their intricate temporal dynamics. Conventional spline-based statistical methods, though effective, require repeated data transformation for each spline parameter tuning, with survival analysis computations relying on the entire dataset, posing difficulties for large datasets. Meanwhile, existing neural network-based survival analysis methods focus on accuracy but often overlook the interpretability of cumulative exposure patterns. To bridge this gap, we introduce CENNSurv, a novel deep learning approach that captures dynamic risk relationships from time-dependent data. Evaluated on two diverse real-world datasets, CENNSurv revealed a multi-year lagged association between chronic environmental exposure and a critical survival outcome, as well as a critical short-term behavioral shift prior to subscription lapse. This demonstrates CENNSurv's ability to model complex temporal patterns with improved scalability. CENNSurv provides researchers studying cumulative effects a practical tool with interpretable insights.

Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman completeness or realizability. We introduce Bellman calibration, a weak reliability criterion requiring that states assigned similar predicted values have average Bellman targets that agree with those predictions. This criterion yields a scalar calibration error for diagnosing systematic numerical miscalibration, which we estimate from off-policy data using doubly robust Bellman target estimates. We then propose Iterated Bellman Calibration, a model-agnostic post-hoc procedure that recalibrates any learned value predictor by fitting a one-dimensional map of its original prediction, with histogram and isotonic variants. We prove finite-sample guarantees showing that Bellman calibration error is controlled at one-dimensional nonparametric rates without Bellman completeness or value-function realizability. Our value-error bounds separate statistical estimation, finite-iteration, and approximation errors, clarifying when calibration improves value prediction and when its gains are limited by the information in the original predictor or insufficient coverage.

We develop an online method that guarantees calibration of quantile forecasts at multiple quantile levels simultaneously. In this work, a sequence of quantile forecasts is said to be calibrated provided that its $\alpha$-level predictions are greater than or equal to the target value at an $\alpha$ fraction of time steps, for each level $\alpha$. Our procedure, called the multi-level quantile tracker (MultiQT), is lightweight and wraps around any point or quantile forecaster to produce adjusted quantile forecasts that are guaranteed to be calibrated, even against adversarial distribution shifts. Critically, it does so while ensuring that the quantiles remain ordered, e.g., the 0.5-level quantile forecast will never be larger than the 0.6-level forecast. Moreover, the method has a no-regret guarantee, implying it will not degrade the performance of the existing forecaster (asymptotically), with respect to the quantile loss. In our experiments, we find that MultiQT significantly improves the calibration of real forecasters in epidemic and energy forecasting problems, while leaving the quantile loss largely unchanged or slightly improved.

We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping input paths to rich representations. Only a linear readout layer is trained, resulting in fast, scalable models with strong inductive bias. Building on this foundation, we propose two variants: (i) Random Fourier CDEs (RF-CDEs): these lift the input signal using random Fourier features prior to the dynamics, providing a kernel-free approximation of RBF-enhanced sequence models; (ii) Random Rough DEs (R-RDEs): these operate directly on rough-path inputs via a log-ODE discretization, using log-signatures to capture higher-order temporal interactions while remaining stable and efficient. We prove that in the infinite-width limit, these model induces the RBF-lifted signature kernel and the rough signature kernel, respectively, offering a unified perspective on random-feature reservoirs, continuous-time deep architectures, and path-signature theory. We evaluate both models across a range of time-series benchmarks, demonstrating competitive or state-of-the-art performance. These methods provide a practical alternative to explicit signature computations, retaining their inductive bias while benefiting from the efficiency of random features.

We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of dimensionality. Moreover, we establish approximation guarantees for derivatives of any prescribed order, extending beyond the commonly considered first-order setting.

Joint modeling of longitudinal and survival data has become increasingly important in medical research, particularly for understanding disease progression in chronic conditions where both repeated biomarker measurements and time-to-event outcomes are available. Traditional two-stage methods, which analyze longitudinal and survival components separately, often result in biased estimates and suboptimal predictions due to failure to account for their interdependence. In this study, we propose a Bayesian hierarchical joint modeling framework with an emphasis on predictive evaluation and clinical interpretability. The model simultaneously characterizes the longitudinal trajectory of a biomarker and the associated survival outcome through shared random effects, capturing the intrinsic association between disease dynamics and event risk. The Bayesian formulation allows flexible incorporation of prior information, accommodates irregular measurement times and missing data, and provides full posterior distributions for uncertainty quantification via credible intervals. We evaluate the proposed framework using both simulated data designed to mimic realistic patient trajectories and a real-world clinical dataset involving patients with chronic liver disease. Results demonstrate that the Bayesian joint model consistently outperforms conventional two-stage approaches in terms of parameter estimation accuracy and predictive performance, as measured by time-dependent area under the curve and Brier scores. The proposed approach provides a robust and interpretable tool for dynamic, patient-specific prognosis, supporting clinical decision-making in personalized medicine.

Distribution shift is the defining challenge of real-world machine learning. The dominant paradigm–Unsupervised Domain Adaptation (UDA)–enforces feature invariance, aligning source and target representations via symmetric divergence minimization [Ganin et al., 2016]. We demonstrate that this approach is fundamentally flawed: when domains are unequally informative (e.g., high-quality vs degraded sensors), strict invariance necessitates information destruction, causing "negative transfer" that can be catastrophic in safety-critical applications [Wang et al., 2019]. We propose a decision-theoretic framework grounded in Le Cam's theory of statistical experiments [Le Cam, 1986], using constructive approximations to replace symmetric invariance with directional simulability. We introduce Le Cam Distortion, quantified by the Deficiency Distance $\delta(E_1, E_2)$, as a rigorous upper bound for transfer risk conditional on simulability. Our framework enables transfer without source degradation by learning a kernel that simulates the target from the source. Across five experiments (genomics, vision, reinforcement learning), Le Cam Distortion achieves: (1) near-perfect frequency estimation in HLA genomics (correlation $r=0.999$, matching classical methods), (2) zero source utility loss in CIFAR-10 image classification (81.2% accuracy preserved vs 34.7% drop for CycleGAN), and (3) safe policy transfer in RL control where invariance-based methods suffer catastrophic collapse. Le Cam Distortion provides the first principled framework for risk-controlled transfer learning in domains where negative transfer is unacceptable: medical imaging, autonomous systems, and precision medicine.

Does more data improve return prediction? In non-stationary financial markets, longer training windows improve prediction of complex models but incorporate outdated economic regimes, whereas simpler models require less data and are less vulnerable to changes in economic conditions. We formally characterize this nonstationarity-complexity tradeoff, showing that model complexity and training window length must be jointly optimized. We propose an adaptive selection procedure with formal performance guarantees. Over three decades of U.S. equity markets, our method improves out-of-sample $R^2$ on industry portfolios by 14% relative to fixed-window and regime-switching benchmarks, with large gains during recessions.

We propose a novel Bayesian optimization (BO) procedure aimed at identifying the "profile optima" of a deterministic black-box computer simulation that has a single control parameter and multiple nuisance parameters. The profile optima capture the optimal response values as a function of the control parameter. Our objective is to identify these optima across the entire plausible range of the control parameter. Classic BO, which targets a single optimum over all parameters, does not explore the entire control parameter range. Instead, we develop a novel two-stage acquisition scheme to balance exploration across the control parameter and exploitation of the profile optima, leveraging deep and shallow Gaussian process surrogates to facilitate uncertainty quantification. We are motivated by a computer simulation of a diffuser in a rotating detonation combustion engine, which returns the energy lost through diffusion as a function of various design parameters. We aim to identify the lowest possible energy loss as a function of the diffuser's length; understanding this relationship will enable well-informed design choices. Our "profile Bayesian optimization" procedure outperforms traditional BO and profile optimization methods on a variety of benchmarks and proves effective in our motivating application against state-of-the-art multi-objective optimization.

Bayesian profile regression mixture models (BPRM) allow to assess a health risk in a multi-exposed population. These mixture models cluster individuals according to their exposure profile and their health risk. However, their results, based on Monte-Carlo Markov Chain (MCMC) algorithms, turned out to be unstable in different application cases. We suppose two reasons for this instability. The MCMC algorithm can be trapped in local modes of the posterior distribution and the choice of post-treatment procedures used on the output of the MCMC algorithm leads to different clustering structures. In this work, we propose improvements of the MCMC algorithms proposed in previous works in order to avoid the local modes of the posterior distribution while reducing the computation time. We also carry out a simulation study to compare the performances of the MCMC algorithms and different post-processing in order to provide guidelines on their use. An application in radiation epidemiology is considered.

We tackle the challenge of estimating grouping structures and factor loadings in asset pricing models, where traditional regressions struggle due to sparse data and high noise. Existing approaches, such as those using fused penalties and multi-task learning, often enforce coefficient homogeneity across cross-sectional units, reducing flexibility. Clustering methods (e.g., spectral clustering, Lloyd's algorithm) achieve consistent recovery under specific conditions but typically rely on a single data source. To address these limitations, we introduce the Panel Coupled Matrix-Tensor Clustering (PMTC) model, which simultaneously leverages a characteristics tensor and a return matrix to identify latent asset groups. By integrating these data sources, we develop computationally efficient tensor clustering algorithms that enhance both clustering accuracy and factor loading estimation. Simulations demonstrate that our methods outperform single-source alternatives in clustering accuracy and coefficient estimation, particularly under moderate signal-to-noise conditions. Empirical application to U.S. equities demonstrates the practical value of PMTC, yielding higher out-of-sample total $R^2$ and economically interpretable variation in factor exposures.

How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments that apply only to conservative systems, limiting the range of dynamics they can recover. Here, we present a new framework that reconciles these two perspectives by reformulating inference as a stochastic control problem. Our method uses geometry-driven path augmentation, guided by the geometry in the system's invariant density to reconstruct likely trajectories and infer the underlying dynamics without assuming specific parametric models. Applied to overdamped Langevin systems, our approach accurately recovers stochastic dynamics even from extremely undersampled data, outperforming existing methods in synthetic benchmarks. This work demonstrates the effectiveness of incorporating geometric inductive biases into stochastic system identification methods.

Machine Learning (ML) has been a foundational topic in artificial intelligence (AI), providing both theoretical groundwork and practical tools for its exciting advancements. From ResNet for visual recognition to Transformer for vision-language alignment, the AI models have achieved superior capability to humans. Furthermore, the scaling law has enabled AI to initially develop general intelligence, as demonstrated by Large Language Models (LLMs). To this stage, AI has had an enormous influence on society and yet still keeps shaping the future for humanity. However, distribution shift remains a persistent “Achilles' heel”, fundamentally limiting the reliability and general usefulness of ML systems. Moreover, generalization under distribution shift would also cause trust issues for AIs. Motivated by these challenges, my research focuses on Trustworthy Machine Learning under Distribution Shifts, with the goal of expanding AI's robustness, versatility, as well as its responsibility and reliability. We carefully study the three common distribution shifts into: (1) Perturbation Shift, (2) Domain Shift, and (3) Modality Shift. For all scenarios, we also rigorously investigate trustworthiness via three aspects: (1) Robustness, (2) Explainability, and (3) Adaptability. Based on these dimensions, we propose effective solutions and fundamental insights, meanwhile aiming to enhance the critical ML problems, such as efficiency, adaptability, and safety.

We study how organizations should select among competing AI models when user utility, deployment costs, and compliance requirements jointly matter. Widely used capability leaderboards do not translate directly into deployment decisions, creating a capability – deployment gap; to bridge it, we take a systems-level view in which model choice is tied to application outcomes, operating constraints, and a capability-cost frontier. We develop ML Compass, a framework that treats model selection as constrained optimization over this frontier. On the theory side, we characterize optimal model configurations under a parametric frontier and show a three-regime structure in optimal internal measures: some dimensions are pinned at compliance minima, some saturate at maximum levels, and the remainder take interior values governed by frontier curvature. We derive comparative statics that quantify how budget changes, regulatory tightening, and technological progress propagate across capability dimensions and costs. On the implementation side, we propose a pipeline that (i) extracts low-dimensional internal measures from heterogeneous model descriptors, (ii) estimates an empirical frontier from capability and cost data, (iii) learns a user- or task-specific utility function from interaction outcome data, and (iv) uses these components to target capability-cost profiles and recommend models. We validate ML Compass with two case studies: a general-purpose conversational setting using the PRISM Alignment dataset and a healthcare setting using a custom dataset we build using HealthBench. In both environments, our framework produces recommendations – and deployment-aware leaderboards based on predicted deployment value under constraints – that can differ materially from capability-only rankings, and clarifies how trade-offs between capability, cost, and safety shape optimal model choice.

Accurate spatial interpolation of the air quality index (AQI), computed from concentrations of multiple air pollutants, is essential for regulatory decision-making, yet AQI fields are inherently non-Gaussian and often exhibit complex nonlinear spatial structure. Classical spatial prediction methods such as kriging are linear and rely on Gaussian assumptions, which limits their ability to capture these features and to provide reliable predictive distributions. In this study, we propose deep classifier kriging (DCK), a flexible, distribution-free deep learning framework for estimating full predictive distribution functions for univariate and bivariate spatial processes, together with a data fusion mechanism that enables modeling of non-collocated bivariate processes and integration of heterogeneous air pollution data sources. Through extensive simulation experiments, we show that DCK consistently outperforms conventional approaches in predictive accuracy and uncertainty quantification. We further apply DCK to probabilistic spatial prediction of AQI by fusing sparse but high-quality station observations with spatially continuous yet biased auxiliary model outputs, yielding spatially resolved predictive distributions that support downstream tasks such as exceedance and extreme-event probability estimation for regulatory risk assessment and policy formulation.

Gaussian process-based models are attractive for estimating heterogeneous treatment effects (HTE), but their computational cost limits scalability in causal inference settings. In this work, we address this challenge by extending Patchwork Kriging into the causal inference framework. Our proposed method partitions the data according to the estimated propensity score and applies Patchwork Kriging to enforce continuity of HTE estimates across adjacent regions. By imposing continuity constraints only along the propensity score dimension, rather than the full covariate space, the proposed approach substantially reduces computational cost while avoiding discontinuities inherent in simple local approximations. The resulting method can be interpreted as a smoothing extension of stratification and provides an efficient approach to HTE estimation. The proposed method is demonstrated through simulation studies and a real data application.

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression models (partial least-squares regression, PLS, principal component regression, PCR) along with their kernelized versions (kernel partial least-squares regression, K-PLS, kernel principal component regression, K-PCR), do not incorporate uncertainty quantification as part of their output. In this study, we propose a method inspired by conformal inference to estimate and calibrate the uncertainty of multivariate statistical models. The result of this method is a point prediction accompanied by prediction intervals that depend on the input data. We tested the proposed method on both traditional and kernelized versions of PLS and PCR. The method is demonstrated using synthetic data, as well as laboratory near-infrared (NIR) and airborne hyperspectral regression models for estimating functional plant traits. The model was able to successfully identify the uncertain regions in the simulated data and match the magnitude of the uncertainty. In real-case scenarios, the optimised model was not overconfident nor underconfident when estimating from test data: for example, for a 95% prediction interval, 95% of the true observations were inside the prediction interval.

This paper develops a general approach for deep learning for a setting that includes nonparametric regression and classification. We perform a framework from data that fulfills a generalized Bernstein-type inequality, including independent, $\phi$-mixing, strongly mixing and $\mathcal{C}$-mixing observations. Two estimators are proposed: a non-penalized deep neural network estimator (NPDNN) and a sparse-penalized deep neural network estimator (SPDNN). For each of these estimators, bounds of the expected excess risk on the class of Hölder smooth functions and composition Hölder functions are established. Applications to independent data, as well as to $\phi$-mixing, strongly mixing, $\mathcal{C}$-mixing processes are considered. For each of these examples, the upper bounds of the expected excess risk of the proposed NPDNN and SPDNN predictors are derived. It is shown that both the NPDNN and SPDNN estimators are minimax optimal (up to a logarithmic factor) in many classical settings.

Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you can answer any causal inference question within the realm of probabilistic modelling and inference, without causal-specific tools or notation. Through concrete examples, we demonstrate how causal questions can be tackled by writing down the probability of everything. Lastly, we reinterpret causal tools as emerging from standard probabilistic modelling and inference, elucidating their necessity and utility.