Papers

Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.

Irreversible perturbations accelerate the convergence of Langevin dynamics, breaking detailed balance while preserving the invariant measure. The design of optimal irreversible perturbations has been studied in the continuous-time Gaussian setting, but extensions to non-Gaussian target distributions, and the impact of time discretization on the design of optimal perturbations, have not been well understood. Numerical discretizations of Langevin dynamics introduce bias, which is typically exacerbated by irreversible perturbations; handling this interaction demands a joint treatment of acceleration and accuracy. This paper develops a systematic framework for optimizing position-independent irreversible perturbations of the unadjusted Langevin algorithm (ULA). We formulate a constrained optimization problem that simultaneously accounts for mixing efficiency and discretization bias, where the former is characterized by a spectral gap analogue and the latter is quantified via a weighted expected squared jump distance. Within this framework, we derive an explicit characterization of the optimal position-independent irreversible perturbation. Extensive numerical experiments demonstrate that our design yields faster convergence with controlled bias, and improves mean squared estimation errors compared to other choices of irreversible perturbation.

Motivated by upper-tail quantile-domain summaries, we study the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. We derive statistical properties of this measure and consider a rational (Möbius) specification of the quantilebased effectiveness persistence function. Under natural boundary conditions, this specification reduces to a canonical form. The resulting canonical family defines a two-parameter class of nonnegative distributions through its quantile function. Various properties, including descriptive measures, L-moments, and quantile-based reliability concepts, are derived for this class. Estimation of the model parameters using maximum likelihood is also developed. The proposed family is illustrated using a real survival dataset.

With PRECISE, we extended Prediction-Powered Inference to produce bias-corrected estimates of ranking evaluation metrics by combining a small human-labeled set with a large LLM-judged set. PPI is provably unbiased regardless of the LLM judge's error profile. We make it applicable to hierarchical metrics like Precision@K, where annotations are per-document but the metric is per-query, by reducing the output-space computation from O(2^|C|) to O(2^K). On the ESCI benchmark, augmenting 30 human annotations with Claude 3 Sonnet judgments reduces the standard error of Precision@4 estimates from 4.45 to 3.50 (a 21% relative reduction). In a production system, our framework correctly identified the best of three system variants from 100 human labels and 2 hours of domain-expert annotation; A/B testing confirmed this ranking with +407 bps in daily sales.

We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.

Transfer learning is a natural strategy when a target population has limited data but multiple related auxiliary sources are available. A central difficulty is source heterogeneity: auxiliary sources may not be equally useful, and their usefulness may vary in a structured, cluster-like fashion. Existing transfer-learning methods often reduce source selection to a binary informative/non-informative decision, overlooking subgroups of sources with differential transferability. Motivated by a suicide-risk study using data from the Connecticut Hospital Information Management Exchange (CHIME), comprising 636,758 patients across 27 hospitals, we propose Trans-GLMC, a cluster-structured transfer-learning procedure for generalized linear models. The CHIME setting illustrates the core challenge: hospital-specific risk models are unstable because suicide attempts are rare at any single facility, whereas indiscriminate pooling across hospitals can obscure facility-level differences in patient mix and risk profiles. Trans-GLMC first constructs a coefficient-based distance among the target and candidate sources to recover latent source clusters. It then combines global fusion, within-cluster refinement, and target debiasing to produce an estimator that adapts to the detected structure. We establish a non-asymptotic error bound that improves over its unclustered counterpart whenever a meaningful target cluster exists and matches the unclustered rate up to constants otherwise. In simulations and in the CHIME study, Trans-GLMC improves facility-specific prediction, identifies interpretable communities of hospitals with mutual transferability, and recovers clinically coherent suicide-risk factors.

Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints. Existing hard constraint methods often impose structural restrictions on the constraint set or introduce substantial computational overhead for large-scale nonlinear problems. Here, we propose DiffSlack, a differentiable projection layer for nonlinear inequality-constrained neural prediction. DiffSlack reformulates inequalities as equalities with learnable slack variables, which are predicted as part of the augmented network output and provide a data-driven warm start for damped Gauss-Newton projection. The projection layer maps raw predictions onto the augmented feasible manifold while preserving end-to-end differentiability. A two-stage curriculum further stabilizes training and improves constraint satisfaction. We evaluate DiffSlack on vehicle path planning with 200 nonlinear inequality constraints from collision avoidance, curvature limits, and waypoint spacing. Compared with existing learning-based baselines, DiffSlack achieves a higher planning success rate and stronger geometric constraint satisfaction under a comparable inference budget. Ablation studies further show that the hard projection layer reduces sensitivity to supervision quality. Closed-loop tracking in CARLA and real-world vehicle experiments confirms the executability of the generated trajectories. These results demonstrate that DiffSlack provides a practical and scalable approach to embedding hard inequality constraints into neural networks for engineering applications.

Stochastic gradient Langevin algorithms often use tamed denominators to stabilize superlinear drifts. This paper shows that when the denominator depends on the current stochastic gradient, the transformed update can have a biased conditional mean even if the original stochastic gradient is unbiased. This creates a stationary mean-shift channel that is absent for deterministic denominators.We propose a structure-preserving framework for designing tamed denominators. The construction keeps the denominator deterministic given the current state, and uses localized deterministic envelopes to avoid unnecessary taming in typical regions. These kernels retain the stabilizing effect of taming while avoiding the bias introduced by a gradient-dependent denominator. Our theory bounds the stationary bias through Euler, envelope, and stochastic-gradient residuals. The analysis also shows why purely local taming rules can lose control in the far tail and motivates a hybrid construction with additional tail protection. Experiments confirm the stationary distortions of random denominators, the bias reduction of deterministic-envelope designs, and the stabilizing effect of the hybrid construction.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose HyFAD, a Hybrid time-frequency Diffusion model with Frequency-Aware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

We study the McKean–Vlasov free energy on the unit sphere associated with the unnormalized self-attention (USA) model for noisy transformer dynamics. We prove a sharp global-minimizer dichotomy in every dimension $d\ge2$. There is a unique $\beta_*^{(d)}>0$ such that \begin{equation*} \frac{I_{d/2+1}(\beta_*^{(d)})}{I_{d/2}(\beta_*^{(d)})}=\frac1d, \end{equation*} where $I_\nu$ is the modified Bessel function of the first kind. For $0<\beta\le \beta_*^{(d)}$, the uniform density remains the unique global minimizer up to the linear-stability threshold \begin{equation*} K_\#^{(d)}(\beta)=\frac{\beta^{d/2}}{2^{d/2}\Gamma(d/2)I_{d/2}(\beta)}, \end{equation*} and the phase transition is continuous. For $\beta>\beta_*^{(d)}$, the uniform density is not globally minimizing at $K_\#^{(d)}(\beta)$, so the critical coupling satisfies $K_c<K_\#^{(d)}(\beta)$ and the transition is discontinuous. This result generalizes the authors' recent $d=2$ work arXiv:2604.16288 to arbitrary dimension. The proof uses the sharp Beckner–Onofri/logarithmic Hardy-Littlewood-Sobolev (HLS) inequality on the sphere, together with a Funk–Hecke/Bessel coefficient computation and a degree-two quartic obstruction.

Sensitivity analysis asks how strong unmeasured confounding needs to be to explain away an observational study's conclusion. The conventional approach in matched studies conducts inference conditional upon the potential outcomes as well as both observed and unobserved confounders, and then finds the worst-case distribution for the conditional treatment assignments across all possible realizations of the unobserved confounder. The resulting worst-case allocation imagines strong, near perfect, correlations between the potential outcomes and hidden bias. We propose a stochastic sensitivity analysis that instead targets inference conditional upon potential outcomes and observed confounders while treating the hidden confounders as random with unknown conditional laws. Rather than finding the worst-case realizations for the hidden confounders, we instead determine the worst-case conditional law over a broad class of distributions. This preserves the adversarial spirit of sensitivity analysis while allowing for imperfect alignment between hidden bias and potential outcomes to a degree controlled by a scalar sensitivity parameter. We consider restrictions to both an interpretable class with no parametric assumptions and a Bernoulli class of conditional laws. Design sensitivity calculations and real-data demonstrations illustrate that allowing for even a small degree of stochasticity can materially increase reported robustness to hidden bias relative to the conventional approach.

The Nancy Grace Roman Space Telescope (Roman), set for launch as early as September 2026, will conduct wide-field infrared imaging surveys with unprecedented spatial resolution and cadence, enabling the discovery of millions of astronomical transients. Hence, it is necessary to have automated pipelines for generating alerts in place so that the telescope can begin discovering reliable transients and variable objects soon after it is launched. However, no real Roman data currently exist, making the development of such pipelines difficult. In this work, we present a machine learning model $RuBR$ and a general methodology for distinguishing genuine transient and variable detections from spurious (bogus) detections within the RAPID pipeline. In particular, we present three models using this methodology: $RuBR_{comb}$ trained and tested on combined locally injected and OpenUniverse2024 transients, $RuBR_{loc}$ trained on locally injected transients and tested on OpenUniverse2024 transients, and $RuBR_{DA}$ that combines locally injected transients with a fraction of OpenUniverse2024 transients in domain-adaptation mode for training. This paves the way for strategies to adapt the $RuBR_{comb}$ model to real observations in the absence of any ground-truth labels during the early phases of the Roman mission. While the image differencing pipeline continues to be improved, our experimental results demonstrate the effectiveness of the proposed approach and its promise for robust real-bogus classification in the Roman era.

This paper studies the problem of detecting a change in the distribution of a sequence of independent observations when the post-change distribution is unknown. We propose a novel change detection algorithm, termed Predictive-Mixture CuSum (PM-CuSum), which combines predictive distributions constructed from sliding windows of different lengths within a CuSum recursion. The predictive distributions are aggregated using adaptive weights based on their recent predictive performance. We show that PM-CuSum achieves first-order asymptotic optimality under mild conditions, and that its asymptotic delay bound has a smaller remainder order than what is achieved procedures using a single fixed (even oracle) window. Numerical simulations demonstrate that PM-CuSum performs well compared to existing methods. Moreover, it is demonstrated that forming likelihood ratios using full predictive distributions can substantially improve performance compared to plug-in likelihoods.

We introduce Graph Cascades, a mesoscopic rewiring strategy for Graph Neural Networks (GNNs) and Graph Transformers (GTs) that captures intermediate-scale graph structure beyond purely local edges or fully global attention. Using contagion-based diffusion processes, Graph Cascades constructs, in O(|V|+|E|) time, an auxiliary graph where node pairs supported by repeated multi-hop reinforcement are promoted to direct neighbors. We theoretically characterize when reinforcement-based rewiring helps: sufficient conditions under which reinforcement-based edge selection is more label-aligned than direct adjacency, an SBM witness in which two-hop reinforcement is perfectly homophilic, and a formalization of mesoscopic connectivity via graph effective resistance. Empirically, across node-classification benchmarks, Graph Cascades improves multiple GNN and sparse-GT backbones, with the most reliable gains observed on heterophilic and moderate- to high-degree homophilic graphs. The theoretical conditions also identify regimes where mesoscopic rewiring is unlikely to be beneficial – low-degree regular graphs and graphs with structural bottlenecks – and these predictions match the observed failures. We additionally observe tight correlations between performance and structural properties in the rewired graphs.

In structural health monitoring (SHM) systems, data is collected from a multitude of sensors measuring, for example, vibration or strain in the structure, along with additional features that capture environmental or operational information. It is well known that changes in the measured sensor outputs do not necessarily originate from structural damage but are often induced by environmental changes. One popular approach to account for these effects is regressing the system outputs on the confounding factors, also known as "response surface modeling". Afterward, the predicted values are subtracted from the observed ones to obtain corrected data with the environmental effects (supposedly) removed. However, the evaluation of real-world SHM data shows that environmental conditions may affect not only the expected output values but also higher-order statistical moments, particularly the variances of and the covariances and correlations between the output quantities, such as eigenfrequencies of different modes or strain sensors at different locations. By construction, the (supervised) machine learning techniques commonly used for response surface modeling cannot account for those higher-order effects. To address these issues, we present and discuss several approaches for identifying and quantifying multivariate confounding effects on output covariances and correlations: a nonparametric, kernel-based estimator, a random forest, a semiparametric additive model, and a deep learning approach. Furthermore, we show how the resulting conditional covariance matrices can be used in an SHM pipeline. We compare the competing methods on both artificial data and real-world load test data from the Vahrendorfer Stadtweg bridge in Hamburg, Germany, as well as eigenfrequency data from the railway bridge KW51 near Leuven, Belgium.

Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman operator theory, which states that nonlinear dynamics can be represented as linear transitions in an infinite-dimensional space. Building upon finite-dimensional approximations of this operator, we present AdaKoop, an efficient streaming algorithm for modeling nonlinear dynamics over nonstationary data streams. Our approach utilizes a probabilistic framework grounded in Koopman operator theory, treating both raw observations and reproducing kernel Hilbert space (RKHS) features as emissions from latent vectors. This dual-view formulation allows nonlinear dynamics to be expressed as a tractable linear system. Therefore, AdaKoop enables the efficient and stable modeling of nonlinear dynamics in a streaming fashion, avoiding the prohibitive computational costs of iterative nonlinear optimization. Furthermore, to address nonstationarity in data streams, AdaKoop adaptively detects the switching of patterns via statistical hypothesis testing for abrupt pattern shifts and incrementally updates model parameters to handle continuous changes. Extensive experiments on a total of 71 practical benchmark datasets across various domains demonstrate that AdaKoop outperforms state-of-the-art methods in terms of real-time forecasting accuracy and computational efficiency.

Worker utility is not observed – only its consequence is. Each gig transaction produces a single bit: accepted or rejected. We argue this structure points directly to the Preisach hysteresis model as the natural representation of latent worker preferences. The Preisach operator models aggregate output as an integral over a population of binary threshold elements – precisely the structure that emerges when heterogeneous workers each carry a private acceptance wage. We estimate two latent utility surfaces: acceptance utility U_1(X) and rejection utility U_0(X), via a dual-output neural network (shared layers 256->128, margin loss enforcing U_1 >= U_0). Classification reduces to the Preisach gap U_1(X) - U_0(X), passed into an XGBoost classifier alongside clip-stabilised price-to-threshold encodings. On 36,891 gig transactions, this pipeline achieves Jaccard = 0.827 and ROC AUC = 0.799. The price-to-threshold encoding accounts for +11.0 pp AUC over raw utility features. The model confirms the directional asymmetry hysteresis predicts: price decreases depress completion rates more than equivalent increases raise them. Applied to the full dataset, the model's recommendations simultaneously reduce the total wage bill by 21.3% and increase expected fill rate by 9.7 pp. For 74.2% of transactions, P(accept) already exceeds 0.80; reducing the wage keeps it above threshold (mean post-cut P = 0.972), releasing cost savings (median 31%). For the remaining 25.4%, a median 7% wage increase recovers +43 pp acceptance. A model without an explicit indifference zone cannot execute both moves simultaneously.

Probabilistic forecasts are essential for inventory management, where decisions depend on the full distribution of future demand. While probabilistic forecast combination is widely used to improve statistical accuracy, most existing approaches optimize statistical loss alone and overlook operational objectives. However, in inventory settings, higher forecast accuracy does not necessarily translate into better decision performance, especially under nonlinear cost structures and multiple, potentially conflicting, decision targets. To address this gap, we propose a multi-objective probabilistic forecast combination framework that simultaneously considers forecast accuracy and inventory decision performance. The framework formulates forecast combination as a multi-objective optimization problem and derives a set of Pareto-optimal combinations, enabling explicit trade-offs between forecasting and operational goals. Empirical studies using Walmart retail data and Royal Air Force spare parts data demonstrate that the proposed approach achieves more balanced and robust performance than individual models, simple averaging, and single-objective optimization. Our results provide a practical and flexible framework for aligning probabilistic forecasting with inventory decision-making.

Shapes of objects in images are often complex, high-dimensional, and vary in ways not captured by standard Euclidean geometry and statistics. Statistical shape analysis encompasses methods for flexible and interpretable measurement of intrinsic shape and shape variability in geometric objects. Elastic Shape Analysis (ESA) is one such method that measures shape differences between objects, represented by contours, in a way that is invariant to rotation, scale, translation, and parameterization. Although ESA is useful for quantifying shape of objects in many image applications, formal methods for statistical inference in image-based ESA remain limited. This work introduces a hypothesis test procedure based on empirical confidence intervals for the elastic shape distance (ESD) between a proposed underlying true shape and an estimated shape. The confidence intervals are created using a bootstrap procedure for non-smooth functionals, which accounts for the non-differentiability of the ESD. The effectiveness of the method is illustrated through both numerical studies and real world image examples from inertial confinement fusion (ICF).

Multidimensional Gaussian Process (multi-GP) regression is widely used to disentangle stellar and planetary signals in radial velocities (RVs) by jointly modelling ancillary activity indicators. However, identifying the combination of indicators that best constrains the stellar signal in the RVs is non-trivial, as classical model comparison methods are not directly applicable when multi-GPs involve different time series combinations. In this work, we present an information criterion to compare multi-GP models based on their ability to explain the RV component, $\mathrm{MGIC}_{\rm rv}$. This metric combines the conditional RV likelihood with an effective parameter count that accounts for the regularisation imposed by the multi-GP model on the RV component. We demonstrate that $\mathrm{MGIC}_{\rm rv}$ provides a quantitative and robust framework for multi-GP model comparison, identifying the activity indicators that most effectively constrain the RV signal. Although developed in the context of RV analysis, the proposed criterion is general and applicable to multi-GP problems in which the inference focuses on a specific observable.

In this work, we develop Stein's method for the Wishart distribution on the cone of positive definite matrices. We establish the basic ingredients of a Wishart Stein framework: we derive an extended-generator-based Stein characterization from the Wishart diffusion process, identify the corresponding transition semigroup through the noncentral Wishart law, provide an explicit semigroup representation for the solution of the Stein equation, and obtain regularity estimates for the solution. The new methodology is demonstrated in four applications: (i) an order $n^{-1}$ bound, for smooth test functions, for the Wishart approximation of uncentered group-mean scatter matrices in MANOVA; (ii) a quantitative multivariate Satterthwaite approximation; (iii) local/integrated De Bruijn identities and logarithmic Sobolev inequalities for the Wishart measure; and (iv) Stein's method of moments for the shape and scale parameters, including structured scale estimation.

Sequential decision-making problems are often modelled as a Markov decision process (MDP). We focus on the stochastic shortest path (SSP) problem, which is an infinite-horizon undiscounted MDP with absorbing terminal states. We develop a Bayesian framework to learn the optimal decision strategy through interactions with the decision-making task. Specifically, we learn the optimal action-value function $Q^*$, but unlike many existing Bayesian approaches, we do not rely on unrealistic modelling assumptions and ad-hoc approximations. Our approach is to directly construct the posterior beliefs for $Q^*$ through Bellman's optimality equations. For deterministic rewards, we characterise the posterior as a distribution with a manifold density. To facilitate simpler inference, we relax the likelihood so that a Lebesgue density exists. The flip side is to create unidentifiability issues. Specifically, the relaxed posterior can have significant mass on improper decision rules, while the exact posterior will not. We also calculate the exact posterior probabilities for optimal action selections for the tabular parametrisation of $Q^*$, a Gaussian likelihood relaxation and a Gaussian prior, which is useful in benchmarking studies. Numerical studies on variants of the Deep Sea benchmark verify our findings. We demonstrate that our framework faithfully quantifies uncertainty and, compared to other temporal-difference-based Bayesian methodologies, is more data efficient. We conclude with recommendations for future work.

Let R denote the class of all computable, causal functionals that are rate-independent in the classical sense (invariant under monotone time reparametrizations), and let Pi_n be the Preisach extremum stack of an input sequence u_{0:n}. We prove a characterization theorem establishing that every F in R satisfies Fu = f(Pi_n) for a computable f, and derive two information-theoretic results. First, under any probability measure on u_{0:n}, the equality I(u_{0:n}; Fu) = I(Pi_n; Fu) holds for every F in R and is an immediate corollary of the characterization theorem. Second, the main result: Pi_n is a Shannon-minimal sufficient statistic in the sense that I(u_{0:n}; Pi_n) <= I(u_{0:n}; S) for every random variable S from which all R-queries are computable. The proof uses the finite indicator family of [Frydrych, 2026] to reconstruct Pi_n from any sufficient S. As a corollary, online maintenance of Pi_n suffices for rate-independent estimation: the NNLS estimator of the Preisach measure mu can be assembled from the incremental stack process (Pi_t)_{t=0}^n in O(k * L^2) memory per step, where k = |Pi_t| and L is the grid resolution.

We study the problem of estimating smooth optimal transport (OT) maps between two probability distributions under differential privacy (DP) constraints. Leveraging wavelet-based density estimators and recent stability bounds for smooth OT maps, we propose differentially private estimators that apply to both central and local DP models. Our main estimator achieves near-minimax optimal rates in dimension $d \geq 2$, and we complement it with a quantile-based estimator that attains minimax optimal rates in dimension $d = 1$ under central DP. We further establish matching minimax lower bounds, confirming the near-optimality of our approach. To the best of our knowledge, this constitutes the first differentially private procedure for OT map estimation with minimax optimality guarantees.

In target trial emulation (TTE), marginal structural models (MSMs) can be used to characterise per-protocol treatment effects over time. The MSM parameters are often estimated by inverse probability weighting (IPW), with weights estimated by maximum likelihood. However, IPW-based estimators can be unstable in small samples and are sensitive to misspecification of the weight models. An alternative method for estimating the MSM parameters is longitudinal targeted maximum likelihood estimation (LTMLE). LTMLE is double robust and potentially more efficient than IPW. Nevertheless, LTMLE also relies on inverse probability weights and may therefore share the instability of IPW-based estimators. We propose joint calibrated LTMLE, which integrates LTMLE with joint calibrated weights tailored for per-protocol effect estimation in TTE. This calibration of weights improves finite-sample performance by enforcing covariate balance in both the treatment and censoring processes simultaneously. Simulations show that the proposed method has improved efficiency and robustness to weight model misspecification, compared to standard LTMLE. We illustrate the method using a case study to evaluate the effect of highly active antiretroviral therapy on CD4 cell count among HIV-positive women.

Background: Stepped wedge trials are longitudinal randomised evaluations, usually cluster-randomised, in which the experimental intervention is introduced in a staggered fashion. Incomplete stepped wedge designs focus the effort of data collection on particular periods in particular sequences. Methods: We suppose there is a cost for every period in every cluster where we collect data, and that there are a fixed number of individuals, m, with data available in each period in each cluster. If we are willing to pay the cost of data collection in that cluster-period then we collect the data on all m individuals, and if we are not willing to pay the cost then we collect no data in that cluster-period. We consider the problem of designing a trial to minimise the total number of cluster-periods of data collection needed to achieve given precision for the treatment effect estimator, or equivalently, to maximise precision for a given number of cluster-periods of data collection. Results: We present the solution for two-period trials, which has two distinct forms, depending on the correlation between two cluster-period means from the same cluster in different periods. We also present a conjecture on the form of the solution for multi-period trials, informed by results from a greedy search of the design space. Conclusions: A real-life stepped wedge design problem will involve trading off the costs of various design elements subject also to constraints on the scale of data collection. Nevertheless, the solutions to the problem considered here add significantly to our understanding of the optimal design of incomplete stepped wedge trials.

Approximate Nearest Neighbour search indices form the backbone of real-world recommender systems, enabling real-time candidate retrieval over million-item catalogues. Typically, a single point estimate embedding is learnt for every user and every item. At serving time, the user embedding queries the index for relevant items. Since these representations are learnt from sparse interaction data, they are noisy and might fail to capture all the nuances that contribute to “relevance” – ignoring the fundamental uncertainty that is inherent to them. The result is a retrieval pipeline that is systematically biased toward the small minority of popular head items with well-estimated embeddings, at the expense of the long-tail majority of niche, diverse, and serendipitous content. We propose DINOSAUR (Distributional Approximate Nearest Neighbour Search for Uncertainty-Aware Retrieval): a simple and infrastructure-compatible framework to incorporate embedding uncertainty into candidate generation. Rather than indexing point estimates, DINOSAUR samples $S_i$ embeddings per item and constructs an index on this augmented set. Analogously, at query time, a user embedding is sampled. This two-sided stochastic retrieval process implicitly marginalises over embedding uncertainty, without requiring changes to model architecture or ANN index infrastructure. On the analytical side, we show that DINOSAUR recovers standard point-estimate retrieval as uncertainty vanishes, and we characterise how increased embedding variance expands the regions of latent space in which uncertain items are retrievable. Reproducible empirical observations align with these expectations, showing large coverage gains with small losses in offline recall.

Learning Value-at-Risk (VaR) and Expected Shortfall (ES) is important for managing financial risks effectively. Existing approaches with limited parameters are vulnerable to model misspecification in the era of big data. To address this limitation, we propose a large tail risk model, the retrieval-enhanced self-grouping autoencoder (ReSGA), which is designed with millions of parameters to exploit the rich cross-sectional dependence and long-term temporal dynamics of assets using their characteristics. Applied to monthly US equity returns from 1926 to 2023 with 153 firm characteristics, ReSGA outperforms twelve econometric and machine learning competitors in terms of out-of-sample loss and statistical backtesting. In addition, its forecast advantages can translate into significant economic gains from long-short decile portfolios that are constructed by a new size-enhanced left-side momentum strategy. To clarify the role of complexity, we further conduct a systematic scaling analysis and demonstrate that improvements in joint VaR-ES forecasting are primarily driven by data complexity rather than model complexity. Finally, our analyses of group-importance and transfer-learning exhibit the interpretability and cross-market generalizability of ReSGA.

This study aims to determine whether the application of Deep Reinforcement Learning (DRL) as a specialized execution overlay can enhance pair trading in highly volatile cryptocurrency markets. Although classical implementations of the strategy have proven successful in traditional equities, they frequently exhibit rigidity and suffer from severe divergence risks when applied to high-variance environments. To address this need, this research introduces novel concepts. To construct a robust system, we developed a hierarchical "Filter-then-Rank" pair selection methodology and a proprietary "Fixed Risk, Adaptive Mean" execution model. The system employs a Proximal Policy Optimization (PPO) agent with a Long Short-Term Memory (LSTM) layer to govern execution decisions within strict deterministic risk management boundaries. Evaluated on 1-hour interval data from the Binance USD-M Futures market, the optimized RL policy achieved an out-of-sample performance that substantially outperformed the heuristic baseline. A stationary circular block bootstrap robustness check confirms that the agent's risk-adjusted outperformance is statistically significant at the 10 percent level. Although falling marginally short of the stricter 5 percent threshold, this result highlights the extreme idiosyncratic variance characteristic of digital assets. Ultimately, this thesis contributes to the quantitative finance literature by introducing a hybrid architecture that combines statistical arbitrage with DRL execution policies. Furthermore, it delivers a novel framework for safe reinforcement learning via deterministic shielding, proving that anchoring a neural policy to statistically robust boundaries successfully mitigates severe divergence risks.