Papers

Streamflow forecasting is crucial for water resource management and risk mitigation. While deep learning models have achieved strong predictive performance, they often overlook underlying physical processes, limiting interpretability and generalization. Recent causal learning approaches address these issues by integrating domain knowledge, yet they typically rely on fixed causal graphs that fail to adapt to data. We propose CauStream, a unified framework for causal spatiotemporal streamflow forecasting. CauSTream jointly learns (i) a runoff causal graph among meteorological forcings and (ii) a routing graph capturing dynamic dependencies across stations. We further establish identifiability conditions for these causal structures under a nonparametric setting. We evaluate CauSTream on three major U.S. river basins across three forecasting horizons. The model consistently outperforms prior state-of-the-art methods, with performance gaps widening at longer forecast windows, indicating stronger generalization to unseen conditions. Beyond forecasting, CauSTream also learns causal graphs that capture relationships among hydrological factors and stations. The inferred structures align closely with established domain knowledge, offering interpretable insights into watershed dynamics. CauSTream offers a principled foundation for causal spatiotemporal modeling, with the potential to extend to a wide range of scientific and environmental applications.

This paper presents a structured and comprehensive dataset corresponding to the 2025 Asia Cup T20 cricket tournament, designed to facilitate data-driven research in sports analytics. The dataset comprises records from all 19 matches of the tournament and includes 61 variables covering team scores, wickets, powerplay statistics, boundary counts, toss decisions, venues, and player-specific highlights. To demonstrate its analytical value, we conduct an exploratory data analysis focusing on team performance indicators, boundary distributions, and scoring patterns. The dataset is publicly released through Zenodo under a CC-BY 4.0 license to support reproducibility and further research in cricket analytics, predictive modeling, and strategic decision-making. This work contributes an open, machine-readable benchmark dataset for advancing cricket analytics research.

Monte Carlo studies of item response theory (IRT) methods often leave the information level implicit in the choice of item parameters. Designs with the same sample size and test length can therefore represent quite different measurement conditions. We develop a calibration procedure that makes the information level an explicit design choice. The target is an information-based reliability index derived from population mean test information. Before generating responses, we solve for a common multiplier on item discriminations, keeping difficulties, test length and the reference population fixed. The R package IRTsimrel implements the procedure, allowing researchers to compare methods across chosen information levels or compare designs at a common target. In an item-level treatment-effect simulation, power increases across targets, while excess rejection from ignoring item-effect variation persists. These comparisons show how targeting helps distinguish findings that depend on the chosen information level from those that persist across the studied range.

It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting interpretable features, however, is that they exist in superposition. In this work, we study the question of extracting features in superposition from a learning theoretic perspective. We start with the following fundamental setting: we are given query access to a function \[ f(x)=\sum_{i=1}^n \sigma_i(v_i^\top x), \] where each unit vector $v_i$ encodes a feature direction and $\sigma_i:\R\to\R$ is an arbitrary response function and our goal is to recover the $v_i$ and the function $f$. In learning-theoretic terms, superposition refers to the overcomplete regime, when the number of features is larger than the underlying dimension (i.e. $n > d$), which has proven especially challenging for typical algorithmic approaches. Our main result is an efficient query algorithm that, from noisy oracle access to $f$, identifies all feature directions whose responses are non-degenerate and reconstructs the function $f$. Crucially, our algorithm works in a significantly more general setting than all related prior results. We allow for essentially arbitrary superpositions, only requiring that $v_i, v_j$ are not nearly identical for $i \neq j$, and allowing for general response functions $\sigma_i$. At a high level, our algorithm introduces an approach for searching in Fourier space by iteratively refining the search space to locate the hidden directions $v_i$.

One strategy to scale up ML-driven science is to increase wet lab experiments' information density. We present a method based on a neural extension of compressed sensing to function space. We measure the activity of multiple different molecules simultaneously, rather than individually. Then, we deconvolute the molecule-activity map during model training. Co-design of wet lab experiments and learning algorithms provably leads to orders-of-magnitude gains in information density. We demonstrate on antibodies and cell therapies.

The double machine learning (DML) method combines the predictive power of machine learning with statistical estimation to conduct inference about the structural parameter of interest. This paper presents the R package `xtdml`, which implements DML methods for partially linear panel regression models with low-dimensional fixed effects, high-dimensional confounding variables, proposed by Clarke and Polselli (2025). The package provides functionalities to: (a) learn nuisance functions with machine learning algorithms from the `mlr3` ecosystem, (b) handle unobserved individual heterogeneity choosing among first-difference transformation, within-group transformation, and correlated random effects, (c) transform the covariates with min-max normalization and polynomial expansion to improve learning performance. We showcase the use of `xtdml` with both simulated and real longitudinal data.

I describe and compare procedures for binary eye-tracking (ET) data. The basic GLM model is a logistic mixed model combined with random effects for persons and items. Additional models address error correlation in eye-tracking serial observations. In particular, three novel approaches are illustrated that address serial without the use of an observed lag-1 predictor: a first-order autoregressive model and a first-order moving average models obtained with generalized estimating equations, and a recurrent two-state survival model used with run-length encoded data. Altogether, the results of five different analyses point to unresolved issues in the analysis of eye-tracking data and new directions for analytic development. A more traditional model incorporating a lag-1 observed outcome for serial correlation is also included.

In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix algorithms proceed by first collecting information about a matrix and then processing that data to perform some computational task. This thesis addresses the following question: How can one design algorithms that use this information as efficiently as possible, reliably achieving the greatest possible speed and accuracy for a limited data budget? The first part of this thesis focuses on low-rank approximation for positive-semidefinite matrices. Here, the goal is to compute an accurate approximation to a matrix after accessing as few entries of the matrix as possible. This part of the thesis explores the randomly pivoted Cholesky (RPCholesky) algorithm for this task, which achieves a level of speed and reliability greater than other methods for the same problem. The second part of this thesis considers the task of estimating attributes of an implicit matrix accessible only by matrix-vector products. This thesis describes the leave-one-out approach to developing matrix attribute estimation algorithms and develops optimized trace, diagonal, and row-norm estimation algorithms. The third part of this thesis considers randomized algorithms for overdetermined linear least squares problems. Randomized algorithms for linear-least squares problems are asymptotically faster than any known deterministic algorithm, but recent work has raised questions about the accuracy of these methods in floating point arithmetic. This thesis shows these issues are resolvable by developing fast randomized least-squares problem achieving backward stability, the gold-standard stability guarantee for a numerical algorithm.

The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the second problem, it is assumed to be a Gaussian random variable. The main problem is the computation of adaptive Kalman filters and the discussion of their asymptotic optimality. The realization of this program for both models is done in several steps. First, a preliminary estimator of the unknown parameter is constructed by observations on some learning interval. Then, this estimator is used for the calculation of recurrent one-step MLE estimators, which are subsequently substituted in the equations of Kalman filtration.

Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its behavior in high-dimensional regimes remains limited. In this paper, we study a data integration model in which two high-dimensional data matrices share a low-rank common latent structure while also containing individual-specific components. We analyze the singular vectors of the associated cross-covariance matrix using tools from random matrix theory and derive asymptotic characterizations of the alignment between estimated and true latent directions. These results provide a quantitative explanation of the reconstruction performance of the PLS variant based on Singular Value Decomposition (PLS-SVD) and identify regimes where the method exhibits counter-intuitive or limiting behavior. Building on this analysis, we compare PLS-SVD with principal component analysis applied separately to each dataset and show its asymptotic superiority in detecting the common latent subspace. Overall, our results offer a comprehensive theoretical understanding of high-dimensional PLS-SVD, clarifying both its advantages and fundamental limitations.

Subgroup selection in clinical trials is essential for identifying patient groups that react differently to a treatment, thereby enabling personalised medicine. In particular, subgroup selection can identify patient groups that respond particularly well to a treatment or that encounter adverse events more often. However, this is a post-selection inference problem, which may pose challenges for traditional techniques used for subgroup analysis, such as increased Type I error rates and potential biases from data-driven subgroup identification. In this paper, we present two methods for subgroup selection in regression problems: one based on generalised linear modelling and another on isotonic regression. We demonstrate how these methods can be used for data-driven subgroup identification in the analysis of clinical trials, focusing on two distinct tasks: identifying patient groups that are safe from manifesting adverse events and identifying patient groups with high treatment effect, while controlling for Type I error in both cases. A thorough simulation study is conducted to evaluate the strengths and weaknesses of each method, providing detailed insight into the sensitivity of the Type I error rate control to modelling assumptions.

Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized quantum circuits to the mathematical nature of the functions they can actually learn. Within this framework, we show how fundamental properties, like circuit depth and non-Clifford gate count, directly determine whether a model's output leads to efficient classical simulation or surrogation. We argue that this analysis uncovers common pathways to dequantization that underlie many existing simulation methods. More importantly, it reveals critical distinctions between models that are fully simulatable, those whose function space is classically tractable, and those that remain robustly quantum. This perspective provides a conceptual map of this landscape, clarifying how different models relate to classical simulability and pointing to where opportunities for quantum advantage may lie.

Spatial boundaries, such as ecological transitions or climatic regime interfaces, capture steep environmental gradients, and shifts in their structure can signal emerging environmental changes. Quantifying uncertainty in spatial boundary locations and formally testing for temporal shifts remains challenging, especially when boundaries are derived from noisy, gridded environmental data. We present a unified framework that combines heteroskedastic Gaussian process (GP) regression with a scaled Maximum Absolute Difference (MAD) Global Envelope Test (GET) to estimate spatial boundary curves and assess whether they evolve over time. The heteroskedastic GP provides a flexible probabilistic reconstruction of boundary lines, capturing spatially varying mean structure and location specific variability, while the test offers a rigorous hypothesis testing tool for detecting departures from expected boundary behaviors. Simulation studies show that the proposed method achieves the correct size under the null and high power for detecting local boundary shifts. Applying our framework to the Sahel Sahara transition zone, using annual Koppen Trewartha climate classifications from 1960 to 1989, we find no statistically significant decade scale changes in the arid and semi arid or semi arid and non arid interfaces. However, the method successfully identifies localized boundary shifts during the extreme drought years of 1983 and 1984, consistent with climate studies documenting regional anomalies in these interfaces during that period.

In this work, inspired by machine learning techniques, we propose a new Bayesian model for Small Area Estimation (SAE), the Fay-Herriot model with Spectral Clustering (FH-SC). Unlike traditional approaches, clustering in FH-SC is based on spectral clustering algorithms that utilize external covariates, rather than geographical or administrative criteria. A major advantage of the FH-SC model is its flexibility in integrating existing SAE approaches, with or without clustering random effects. To enable benchmarking, we leverage the theoretical framework of posterior projections for constrained Bayesian inference and derive closed form expressions for the new Rao-Blackwell (RB) estimators of the posterior mean under the FH-SC model. Additionally, we introduce a novel measure of uncertainty for the benchmarked estimator, the Conditional Posterior Mean Square Error (CPMSE), which is generalizable to other Bayesian SAE estimators. We conduct model-based and data-based simulation studies to evaluate the frequentist properties of the CPMSE. The proposed methodology is motivated by a real case study involving the estimation of the proportion of households with internet access in the municipalities of Colombia. Finally, we also illustrate the advantages of FH-SC over existing Bayesian and frequentist approaches through our case study.

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction error and strongly influence engineering decisions. Because distinguishing and representing each source separately is often infeasible, their combined effect is typically analyzed using a unified model-error framework. Model error directly affects model credibility and predictive reliability; yet its characterization remains challenging. To address this need, we introduce a bootstrap-based stochastic subspace model for characterizing model error in the stochastic reduced-order modeling framework. Given a snapshot matrix of state vectors, the method leverages the empirical data distribution to induce a sampling distribution over principal subspaces for reduced order modeling. The resulting stochastic model enables improved characterization of model error in computational mechanics compared with existing approaches. The method offers several advantages: (1) it is assumption-free and leverages the empirical data distribution; (2) it enforces linear constraints (such as boundary conditions) by construction; (3) it requires only one hyperparameter, significantly simplifying the training process; and (4) its algorithm is straightforward to implement. We evaluate the method's performance against existing approaches using numerical examples in computational mechanics and structural dynamics.

Near an optimal learning point of a neural network, the learning performance of gradient descent dynamics is dictated by the Hessian matrix of the loss function with respect to the network parameters. We characterize the Hessian eigenspectrum for some classes of teacher-student problems, when the teacher and student networks have matching weights, showing that the smaller eigenvalues of the Hessian determine long-time learning performance. For linear networks, we analytically establish that for large networks the spectrum asymptotically follows a convolution of a scaled chi-square distribution with a scaled Marchenko-Pastur distribution. We numerically analyse the Hessian spectrum for polynomial and other non-linear networks. Furthermore, we show that the rank of the Hessian matrix can be seen as an effective number of parameters for networks using polynomial activation functions. For a generic non-linear activation function, such as the error function, we empirically observe that the Hessian matrix is always full rank.

Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning. Building upon this bijection, we derive the equivalence between supervised learning of ARMs and EBMs. Furthermore, we analyze the distillation of EBMs into ARMs by providing theoretical error bounds. Our results provide insights into the ability of ARMs to plan ahead, despite being based on the next-token prediction paradigm.

Panels with large time $(T)$ and cross-sectional $(N)$ dimensions are a key data structure in social sciences and other fields. A central question in panel data analysis is whether to pool data across individuals or to estimate separate models. Pooled estimators typically have lower variance but may suffer from bias, creating a fundamental trade-off for optimal estimation. We develop a new inference method to compare the forecasting performance of pooled and individual estimators. Specifically, we propose a confidence interval for the difference between their forecasting errors and establish its asymptotic validity. Our theory allows for complex temporal and cross-sectional dependence in the model errors and covers scenarios where $N$ can be much larger than $T$-including the independent case under the classical condition $N/T^2 \to 0$. The finite-sample properties of the proposed method are examined in an extensive simulation study.

In many real-world contexts, such as social or transport networks, data exhibit both structural connectivity and node-level attributes. For example, roads in a transport network can be characterized not only by their connectivity but also by traffic flow or speed profiles. Understanding such systems therefore requires jointly analyzing the network structure and node attributes, a challenge addressed by attributed graph partitioning, which clusters nodes according on both connectivity and attributes. In this work, we adapt transport-based approaches based on Gromov–Wasserstein (GW) discrepancy. We investigate how GW methods, traditionally used for general-purpose tasks such as graph matching, can be specifically adapted for node partitioning, an area that has been relatively underexplored. In the context of node-attributed graphs, we introduce an adaptation of the Fused GW method, offering theoretical guarantees and the ability to handle heterogeneous attribute types. Additionally, we propose to incorporate distance-based embeddings to enhance performance. The proposed approaches are systematically evaluated using a dedicated simulation framework and illustrated on a real-world transportation dataset. Experiments investigate the influence of target choice, assess robustness to noise, and provide practical guidance for attributed graph clustering. In the context of road networks, our results demonstrate that these methods can effectively leverage both structural and attribute information to reveal meaningful clusters, offering insights for improved network understanding.

We propose using an adaptive sampling method to detect changes for a system with multiple lines. The adaptive sampling utilizes the information in responses to learn on which line is more likely to have a change thus allocating more units to the line. The learning process is formatted as a Markov decision process by integrating sampling information with likelihood ratio for changes to define rewards and the optimal sampling is approximated by using the Bellman operator iteratively based on the average reward criterion. We demonstrate the performance of the proposed method for binary responses using the exact distribution method for adaptive sampling. Our numeric results show that the adaptive sampling samples more often the line that has a change and the statistical power to detect a change is better than those with the equal randomization for sample sizes of 20 or higher. When sample sizes increase or the difference between out-of-control and in-control probabilities increases, the adaptive sampling allocates higher proportion of units averagely to the line with a change and the statistical power to detect a change increases.

Physical systems are naturally parameterized in terms of geometric entities and their transformations. While exact equivariance can be a powerful inductive bias, real-world applications frequently exhibit approximate or broken symmetries in practice. We introduce object-centric world models that provide a soft geometric inductive bias without enforcing exact symmetries. By embedding object states as Clifford multivectors, our models encourage physically meaningful transformations while retaining the expressivity needed to handle asymmetric dynamics. We evaluate our approach on 2D rigid-body dynamics, 3D charged-particle systems, and real-world driving trajectories. Compared to both unstructured baselines and strictly equivariant models, our soft Clifford transformer achieves better long-horizon fidelity, particularly in regimes with broken symmetries. These results suggest that geometric algebra offers an effective middle ground, delivering sample-efficient dynamics without the inflexibility of hard mathematical constraints.

We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. PaLD is best known for unsupervised, parameter-free clustering, but its robustness is based on triples of data points, making exact analysis computationally expensive. Research is ongoing to improve the scalability of the underlying discrete algorithm and expand the breath of PaLD's applications. The new algorithm we present, online PaLD, is well-suited to situations where it is possible to pre-compute a cohesion network from a reference dataset. After $O(n^3)$ steps to construct a queryable data structure, online PaLD can extend the cohesion network to a new data point in $O(n^2)$ time. Our approach complements previous speed up approaches based on approximation and parallelism. In practical terms, online PaLD makes larger datasets accessible to exact analysis with a relatively simple implementation. We present applications to online anomaly detection and semi-supervised classification for health-care datasets as initial illustrations of online PaLD's potential to expand applications of the PaLD framework.

Modelling block maxima using the generalised extreme value (GEV) distribution is a classical and widely used method for studying univariate extremes. It allows for theoretically motivated estimation of return levels, including extrapolation beyond the range of observed data. A frequently overlooked challenge in applying this methodology comes from handling datasets containing missing values. In this case, one cannot be sure whether the true maximum has been recorded in each block, and simply ignoring the issue can lead to biased parameter estimators and, crucially, underestimated return levels. We propose an extension of the standard block maxima approach to overcome such missing data issues. This is achieved by explicitly accounting for the proportion of missing values in each block within the GEV model. Inference is carried out using likelihood-based techniques, and we propose an update to commonly used diagnostic plots to assess model fit. We assess the performance of our method via a simulation study, with results that are competitive with the "ideal" case of having no missing values. The practical use of our methodology is demonstrated on sea surge data from Brest, France, and air pollution data from Plymouth, U.K.

Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus, this study investigates the statistical properties of min-max normalized eigenvalues in random matrices. Previously, the effective distribution for such normalized eigenvalues has been proposed. In this study, we apply it to evaluate a scaling law of the cumulative distribution. Furthermore, we derive the residual error that arises during matrix factorization of random matrices. We conducted numerical experiments to verify these theoretical predictions.

We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model and guarantees finite-sample coverage. It is computationally efficient and yields informative prediction intervals even with limited data. The core idea is a novel coordinate-wise standardization procedure that makes residuals across output dimensions directly comparable, estimating suitable scaling parameters using the calibration data themselves. This does not require modeling of cross-output dependence nor auxiliary sample splitting. Implementing this idea requires overcoming technical challenges associated with transductive or full conformal prediction. Experiments on simulated and real data demonstrate this method can produce tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.

Kernel-based methods such as Rocket are among the most effective default approaches for univariate time series classification (TSC), yet they do not perform equally well across all datasets. We revisit the long-standing intuition that different representations capture complementary structure and show that selectively fusing them can yield consistent improvements over Rocket on specific, systematically identifiable kinds of datasets. We introduce Fusion-3 (F3), a lightweight framework that adaptively fuses Rocket, SAX, and SFA representations. To understand when fusion helps, we cluster UCR datasets into six groups using meta-features capturing series length, spectral structure, roughness, and class imbalance, and treat these clusters as interpretable data-structure regimes. Our analysis shows that fusion typically outperforms strong baselines in regimes with structured variability or rich frequency content, while offering diminishing returns in highly irregular or outlier-heavy settings. To support these findings, we combine three complementary analyses: non-parametric paired statistics across datasets, ablation studies isolating the roles of individual representations, and attribution via SHAP to identify which dataset properties predict fusion gains. Sample-level case studies further reveal the underlying mechanism: fusion primarily improves performance by rescuing specific errors, with adaptive increases in frequency-domain weighting precisely where corrections occur. Using 5-fold cross-validation on the 113 UCR datasets, F3 yields small but consistent average improvements over Rocket, supported by frequentist and Bayesian evidence and accompanied by clearly identifiable failure cases. Our results show that selectively applied fusion provides dependable and interpretable extension to strong kernel-based methods, correcting their weaknesses precisely where the data support it.

We consider estimation of the drift parameter $\vartheta>0$ in a partially observed Ornstein–Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of \cite{BrousteKleptsyna2010} to the mixed case. We construct the canonical innovation representation, derive the associated Kalman filter and Riccati equations, and analyse the asymptotic behaviour of the filtering error covariance. Within the Ibragimov–Khasminskii LAN framework we prove that the MLE of $\vartheta$, based on continuous observation of the partially observed system on $[0,T]$, is consistent and asymptotically normal with rate $\sqrt{T}$ and the Fisher Information is the same as in \cite{BrousteKleptsyna2010} or the standard Brownian motion case.

We consider the problem of ranking objects from noisy pairwise comparisons, for example, ranking tennis players from the outcomes of matches. We follow a standard approach to this problem and assume that each object has an unobserved strength and that the outcome of each comparison depends probabilistically on the strengths of the comparands. However, we do not assume to know a priori how skills affect outcomes. Instead, we present an efficient algorithm for simultaneously inferring both the unobserved strengths and the function that maps strengths to probabilities. Despite this problem being under-constrained, we present experimental evidence that the conclusions of our Bayesian approach are robust to different model specifications. We include several case studies to exemplify the method on real-world data sets.

The lack of GPS data limits the ability to reconstruct the actual routes taken by cyclists in urban areas. This article introduces an inference method based solely on trip durations and origin-destination pairs from bike-sharing system (BSS) users. Travel time distributions are modeled using log-normal mixture models, allowing us to identify the presence of distinct behaviors. The approach is applied to 3.8 million trips recorded in 2022 in the Toulouse metropolitan area, with observed durations compared against travel times estimated by OpenStreetMap (OSM). Results show that, for many station pairs, trip durations align closely with the fastest route suggested by OSM, reflecting a dominant and routine practice. In other cases, mixture models reveal more heterogeneous behaviors, including longer trips, detours, or intermediate stops. This approach highlights both the stability and diversity of cycling practices, providing a robust tool for usage analysis in data-limited contexts, and offering new insights into urban mobility dynamics without relying on spatially explicit data.

We consider causal inference in dynamic settings where treatment is assigned by thresholding a state variable that can change over time. There is a large literature on regression-discontinuity methods building on the fact that, in the static setting, treatment assignment via threshold crossing induces a quasi-experimental design that enables pragmatic causal inference. But dynamic settings involve challenges not present in the static setting, e.g., past treatments may affect current state and thus future treatments, and so existing regression-discontinuity methods do not apply. Here, we show that dynamic thresholding designs identify a marginal policy effect that nests the classical regression-discontinuity parameter in the static setting; and propose a tailored local linear regression estimator that is consistent for this marginal policy effect. We demonstrate our approach using an experiment that emulates real-world optimization of thresholds for continuous glucose monitoring using data generated from an FDA-approved simulator.