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**A**: (2022, 2023), the last of which proposed a novel factor model based bias correction approach for multivariate response linear regression with hidden variables, which is a special case of GLMs. However, their approach is only applicable to linear regression. The challenge of extending their approach to GLMs is de...
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**A**: government bonds with maturities of 2 to 5 years between January 1980 and December 2003, containing 288 data points. The tt-year risk premium is calculated as the excess log return as the subtraction of the log holding period return of a tt-year bond and the log yield of the 1-year discount bond (Cochrane and Pi...
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**A**: This stands in contrast to the traditional BOP2 design, in which the type I error rate is fixed and does not vary with SS**B**: This dependence necessitates additional care in controlling the type I error across the plausible range of SS. **C**: Lemma 1 implies that under the null hypothesis (H0H_{0}), the propo...
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**A**: The distortion is substantial, with coverage as low as 0.88 for extreme parameter values**B**: Fig. 2 indicates that, when the nuisance parameter h22h_{2}^{2} is near one, the score-based confidence interval for h12h_{1}^{2} is invalid**C**: By contrast, the proposed confidence interval, while conservative, is e...
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**A**: Probit BART, or pBART, is shown in pink. Probit monotone BART, or pmBART, is shown in blue. The solid lines are the posterior mean curves and the transparent region shows the 90% pointwise posterior credible region, for each model.**B**: Figure 1: Comparison of probit BART to probit monotone BART for fitting a ...
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**A**: Finally, they take 15 minutes to return home. When at home and at work, the individual moves around the area according to a zero-drift Brownian motion σ​B​(t)\sigma B(t) with standard deviation σ=0.1\sigma=0.1. When in public space, the individual moves similarly with σ=0.2\sigma=0.2. The travel between these th...
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**A**: In this paper we propose a new version of signal lasso based on two kinds of penalty function to estimate the signal parameter and uncovering network topology in complex network with a small amount of observations**B**: We find the tuning parameter can be set to a large enough values such that the signal parame...
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**A**: This was probably not realized in [6] since it was not stated in the description/manual of [10]**B**: On the other hand, [6] gives an interpretation of the fixed point iteration for ψα\psi_{\alpha} as a Newton-Raphson method under additional assumptions.**C**: (a version of the fixed point iteration for ψα\psi_...
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**A**: In the last section, the basic idea is carried over to the two-sided alternative H1∗:F≠GH_{1}^{*}:F\neq G. For the corresponding transformation, we also determine the limit distribution. **B**: Moreover, we report on the results of a small Monte Carlo simulation study. Here, the VV-test proves to be superior to ...
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**A**: However, in a finite sample scenarios, these bounds are too high in practice.**B**: [24], [14]. These upper bounds can serve as an upper bound on mm while keeping the the approximation error in a compact interval under some value**C**: The literature provides upper bounds on the number of hidden units required t...
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**A**: Specifically, Xie and Xu, (2023) proposed a one-step estimator (OSE) that absorbs the network likelihood information and established that OSE improves upon ASE**B**: Recently, Xie and Xu, (2023) discovered a striking fact: Spectral estimators are sub-optimal for estimating the latent positions due to the neglige...
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**A**: NHANES assesses the health and nutrition status of U.S. adults and children through comprehensive interviews and physical examinations**B**: Behavioral scientists are interested in analyzing the association between cardiovascular risk factors (such as systolic blood pressure and total cholesterol) and physical ...
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**A**: Low-ℛ\mathcal{R} concepts are prioritized for spaced retrieval; low-MM/CC concepts trigger targeted drills. **B**: The vector (M,C,ℛ,P,V,E)(M,C,\mathcal{R},P,V,E) and blueprint weights act as state features for schedulers and item selection**C**: Inputs to EDGE
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**A**: It is especially stable in evaluating random policies, where treatment assignment varies stochastically. Only when ranking PresPM methods for the time contact HQ intervention is considered, the ensemble is not the top performer, though it still remains in the top 2/3**B**: In contrast, individual learners perfor...
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**A**: To validate the effectiveness of our approach, we evaluated Causal SHAP on both synthetic data with known causal structures and real-world datasets**B**: We demonstrate that our method not only provides more accurate feature attributions but also better reflects the causal structure of the underlying datasets**...
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**A**: This process is analogous to the role of average-pooling filters in convolutional neural networks [72]. As we can see, several pixel values (greyscale colours) are very frequently repeated; thus any model would not need to memorize a new value for each pixel but would rather need to first group pixels according ...
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**A**: An edge connects a document node to a topic node if that document is assigned to that topic. Each topic node acts as a hub, with its associated document nodes forming a subgraph around it**B**: Node2Vec learns embeddings by performing random walks on this graph. These walks frequently transition from a document,...
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**A**: Post-hoc error control: E-values allow a variation of valid Type-I error control even when the significance level is chosen after observing the data [25]**B**: Specifically, if ee is the observed e-value, then rejecting the null hypothesis at level 1/e1/e preserves a Type I risk bound despite this level being da...
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**A**: In this case, AUC-ROC performs the worst and cannot accurately evaluate USAD’s capability, because AUC-ROC cannot accurately reflect situations where USAD’s anomaly detection capability is not prominent enough, as point-based evaluation is too strict**B**: In ECG, the models with better performance are LSTMAD, U...
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**A**: In this nonlinear dataset, performative effects influence both features and labels, presenting a more complex scenario than in synthetic datasets. Existing methods, based on rigorous, uncontrollable conditions, underestimate the complexity of real-world applications**B**: However, in this 𝒟​(θ)\mathcal{D}(\thet...
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**A**: These paradigms are also compared to the single-task training setting to evaluate which approach most closely mimics the classical GCN under single-task training. The best multi-task results for each dataset are bolded.**B**: Table 1**C**: Comparison of ADMP-GCN training paradigms ALM and ST
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**A**: The observed phase transitions, particularly the k=4k=4 inflection points in both winning and losing streaks, suggest that momentum follows complex systems principles rather than simple linear relationships**B**: These nonlinear dynamics demonstrate that tennis momentum operates through threshold-dependent psyc...
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**A**: The indices of columns with the highest NN correlations are selected for the estimated support set 𝚲k\mathbf{\Lambda}^{k}**B**: When NN equals 11, gOMP reverts to OMP. The chosen indices define the extended support set at each iteration. The least-square solution is computed as:**C**: It involves comparing cor...
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**A**: For example, simulation studies in previous works and our paper find that with sparse outcomes resulting from asymmetric censoring, Poisson PML can outperform the gamma PML in terms of mean squared error, even when gamma PML is most efficient. This phenomenon reveals the importance of sparsity when modeling non-...
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**A**: The results are presented on the logit scale and include both point estimates and the associated credible intervals**B**: Figure 6: Model-based prevalence estimates obtained from the spatially correlated Gaussian-process time-series model for the weekly average prevalence of insufficient food consumption in fou...
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**A**: That is, we use Dirichlet priors to generate categorical distributions for both variables**B**: The Dirichlet distributions, in turn, are specified by parameter vectors 𝜶1\bm{\alpha}_{1} and 𝜶2\bm{\alpha}_{2} that determine their shape**C**: We set these parameters to
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**A**: Figure 3: Performance comparison of model variants for the Advection equation**B**: The horizontal axis shows the average per-iteration training time ratio relative to the modified DeepONet, averaged over multiple random seeds (lower is faster), while the vertical axis shows the mean relative L2L^{2} error (low...
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**A**: In high dimensions, computing the posterior mean is intractable, and is usually estimated**B**: While it is possible to consider the convergence of the algorithm to the posterior mean by applying a Metropolis–Hastings correction step [16], this would compare the algorithms against an estimator with a-priori unkn...
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**A**: We further used a modified cross-validation scheme to avoid trial-level overfitting**B**: Repeating this process yields cross-validated predictions for all trials, which serve as inputs to the meta-learner. Finally, all candidate methods are refitted on the full data set, and their predictions are combined using...
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**A**: This pattern is common in environmental and geostatistical data, where smooth spatial variation is a natural prior belief.**B**: Assumption˜3 encodes the idea that nearby points in space have similar expected responses**C**: Intuitively, it rules out arbitrarily sharp changes in ff across very small spatial dis...
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**A**: For simplicity, we only discuss the sublinear sparsity regime, defined by s=o​(p)s=o\left({p}\right)**B**: Phase transition**C**: Previous works on sparse recovery in the dense case (reeves2019all ,gamarnik2022sparse ) have shown the existence of an information-theoretic threshold:
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**A**: While less detailed than coalescent models, which use information from the complete sequence, our choice enables the study of different surveillance planning scenarios by varying the substitution rate without needing to specify complete sequences**B**: This carries the additional benefit of simpler computations ...
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**A**: One of the earliest contributions is by Hauser and Bühlmann (2014), who proposes an optimal algorithm for the case where each experiment intervenes on a single node**B**: Their algorithm minimizes the number of unresolved edges remaining in the causal graph after a fixed number of interventions.**C**: Research ...
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**A**: For patients who do not complete the evaluation process, there is no information on psychosocial review or listing outcomes, so our estimates of the NIE and NDE can only be based on the 361361 out of 497497 patients with complete data**B**: We assume that selection into the analysis sample may be caused by some ...
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**A**: Therefore an elaboration of the Gompertz growth model that allows spatio-temporal intrinsic rates of growth, 𝝂​(t)\bm{\nu}(t), to be described by covariates is implemented in the DSTSOM as follows. **B**: Temporal-varying inputs may also be hypothesised to impact density independent rates of mortality, such as ...
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**A**: URSS allows for greater flexibility by permitting unequal allocations across strata, enabling more efficient sampling when strata exhibit higher variability or measurement difficulty. For example, if the population of interest has strata with differing levels of variability in measurements, allocating more sampl...
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**A**: a judge’s denial rate in other cases is not a direct cause of the studied treatment. Rather, the treatment and the instrument share a common cause, the latent ‘leniency’ of the judge. Recent work by Blandhol et al. (2022) demonstrates that in settings involving control covariates, the identified quantity retains...
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**A**: (1.5)) and Pennec (2019) for details), denoted by mn\textsf{m}_{n},**B**: Suppose that (C2) holds and ℙX\mathbb{P}_{X} has finite variance**C**: Then, (4) implies that the variance modulation of Fréchet mean (see, for examples, (Hundrieser, Eltzner and Huckemann, 2024, eq
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**A**: Our approach features a smoothed weighted Youden index estimator and its penalized variant, leveraging the SCAD penalty for robust variable selection and sparsity**B**: To overcome the nonconvex nature of the objective function and the additional nonsmoothness imposed by the penalty term, we propose a specialize...
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**A**: Recent proposals of regularized methods for categorical data include hypothesis tests [Wang and Li (2023)], clustering [Baek and Park (2023)], logistic regression models [Ming and Yang (2024)], or monitoring categorical processes [Wang et al**B**: The connection of regularization and Bayesian estimation was inve...
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**A**: A basic semialgebraic cone CC in ℝn\mathbb{R}^{n} is a subset defined by homogeneous equations and inequalities**B**: A semialgebraic set in real projective space ℙℝm\mathbb{P}_{\mathbb{R}}^{m} is the image of a semialgebraic cone under π.\pi.**C**: A semialgebraic cone is a finite boolean combination of basic ...
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**A**: They reliably encode identity and age of the crying baby**B**: In addition, their application to cry classification revealed that these latent representations also capture information about the tension in the vocal signal source. These results encourage the broader use of these models to study baby cries.**C**: ...
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**A**: This view is inspired by the outcome indistinguishability framework of [7].333That work does not consider calibration per se, it instead considers more general notions such as multicalibration from [17]**B**: This naturally motivates an alternate view of calibration as a notion of correctness for predictors base...
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**A**: Results on m/z in specific CCs**B**: These CCs are reported in the left panels of Figure 6. Two correspond to distinct areas within the tumor nodule, depicted in the top (Cluster A) and bottom (Cluster C) panels.**C**: To highlight the type of inference enabled by the Poseidon formulation, we focus on the resul...
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**A**: The complexity and opacity of modern systems, due to hidden components or limited monitoring, pose significant challenges for traditional RCA methods that rely on correlations between monitored signals [2, 13]. Unobserved factors (latent confounders) frequently obscure the true causal relationships, complicating...
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**A**: Furthermore, it drastically increases the computational time by a factor ∝M\propto M. **B**: Finally, the middle panel of Fig. 4 compares our results against repeated unitary expansions, that is, expanding the LHS MM times with one new sample at a time, instead of performing a direct one-step expansion of size M...
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**A**: We propose using ensemble learning for constructing control variates**B**: This technique consists of combining multiple weak learners to construct a stronger learner and is commonly used in many machine learning applications (Mienye & Sun, 2022)**C**: An example of ensemble learning in control variates is SECF...
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**A**: [9].**B**: GLMs are used to model the relationships between the number of NMEs in a given period and driver profile attributes, assuming that the number of NMEs follows a Poisson distribution**C**: This method follows the methodology positioned by Gullien et al
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**A**: Section 4 describes the simulation scenarios and the applied analysis of the ovarian dataset. Section 5 reports the simulation and applied results, and Section  5.2 introduces the performance metrics (ISE, IBS, and coverage). Section 6 discusses the implications and limitations of this study and suggests future ...
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**A**: In this context, we introduced a novel count data model, the Poisson-Copoun distribution, along with its regression framework and a three inflated version. The model combines the Poisson and Copoun distributions, offering a flexible alternative for count data analysis. Estimation methods, including maximum likel...
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**A**: In the context of estimation by DNN, the smoothness of the true functions affects the error rate of estimation**B**: Thus, the above assumptions give the weakest condition regarding the smoothness of G​(⋅,⋅)G(\cdot,\cdot), FY|X​(y)F_{Y|X}(y), etc**C**: In practice, these functions may be smoother than what we a...
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**A**: As spatial resolution increases, data distributions can be conceptualized as measures over function spaces. Developing generative models directly in this infinite-dimensional setting hold the promise of resolution-independent behavior, a perspective that has proven successful in Bayesian inverse problems [55] an...
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**A**: After accumulating n​τn\tau iterations across all workers, synchronization occurs to compute the LSAM score according to Equation˜5 and deliver the resulting gradient to the optimizer. This forms the complete workflow of distributed LSAM, detailed in Algorithm˜2.**B**: Each worker independently generates samples...
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**A**: If δ\delta is too large, the resampled distribution becomes smeared out, less accurate, and eventually unstable**B**: Conversely, if δ\delta is too small, too few frequencies are activated, leading to inefficient frequency sampling and slow convergence of the resampling iterations, as illustrated in Figure 7.2. ...
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**A**: In particular, its ERR correctly increases as the sample size does, but with a smaller rate in comparison to the others. **B**: A similar pattern in EC of SBW is also seen in scenarios S11 and S14, where the treatment effect is small and there is a strong influence of the covariates on the outcome (see Figure 2)...
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Selection 2
**A**: The third dataset (ROAD) contains physiological data collected during driving under externally induced stress, with stress labels based on observer-rated continuous scores. The self-reported datasets provide only point events, highlighting limitations of current metrics in real-world settings. In contrast, the e...
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**A**: We propose an alternate method that consists of first clustering the data, then embedding each cluster individually, and finally finding rigid transformations to align the clusters in a global embedding so that there is meaningful organization of all clusters together. By embedding each cluster individually, we ...
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**A**: The review of prior work highlights two critical and interconnected gaps**B**: First, the use of undirected graphs in missing data problems remains underexplored, despite their importance in statistical modeling and machine learning**C**: Second, most existing imputation methods lack a rigorous theoretical found...
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**A**: (betlei2024maximizing, 2) introduce an optimization problem to directly maximize the probability of success of a test by assigning buckets of user populations to policies**B**: At the difference to our work, (betlei2024maximizing, 2) only consider the thresholding criteria, use a finite set of policies, and rely...
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**A**: Even POTEC, a state-of-the-art method designed for large action spaces, is surpassed by the much simpler and easier-to-optimize cLPI**B**: This supports our central claim: optimization stability is key to effective OPL. **C**: This robustness leads to better final policies: PWLL-based methods outperform OPE-base...
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**A**: We have developed and analyzed a causal model for impact factors. While this model is plausible and straight-forward, and we believe in it, the model is not part of our conclusions**B**: Given the nature of our study, several of the widely known threats to validity simply do not apply. Take internal validity as...
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**A**: Although statistical validation is strengthened by approaches like CUBV and SAR, results remain sensitive to sample size and potential biases in the data. Furthermore, correlations between latent components and anatomical regions do not imply causality or direct clinical relevance, and may be affected by spatial...
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**A**: The Variable Bandpass Periodic Block Bootstrap (VBPBB) extends PBB by treating time series as signals composed of additive periodically correlated (PC) components [11]. Each PC component is associated with a specific frequency of interest and its harmonics. Harmonic frequencies are integer multiples of a fundam...
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**A**: The top-ranked passages are combined with the query to create an enriched prompt**B**: This retrieval-augmented setup enhances factual grounding and reduces hallucinations while keeping the model compact. **C**: In fusion-in-decoder architectures, passages are encoded separately, and the decoder attends to all i...
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**A**: Co-authorship and collaboration networks describe which pairs of researchers work together (Ji et al**B**: 2022). In neuroscience, networks arise in the form of connectome data, in which nodes correspond to brain regions or individual neurons and edges encode strength of connections between brain regions or form...
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**A**: An example of the training data is shown in figure 9**B**: In order to construct the mapping SS, we fit a normal distribution to the training data and construct an affine mapping from this directly, in the same spirit as the example in section 4.1. An example of the result of the mapping applied to the validatio...
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**A**: In this section, we illustrate Prob-GParareal and its performance on five different ODE systems with deterministic initial conditions (except in Section˜5.4, with random initial conditions), four of which were considered for GParareal (Pentland et al., 2023b), allowing for a direct comparison. These include the...
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**A**: Leading search ad platforms, such as Google Ads and Microsoft Advertising, optimize these auctions to maximize revenue while balancing user experience and advertiser value. These platforms play a crucial role in digital marketing, driving targeted traffic to businesses while generating significant revenue for se...
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**A**: Now Ω∖B¯δ⊂Ω∖Bδ′\Omega\setminus\overline{B}_{\delta}\subset\Omega\setminus B_{\delta^{\prime}}, so G​(Ω∖B¯δ′)⊂G​(Ω∖Bδ′)G(\Omega\setminus\overline{B}_{\delta^{\prime}})\subset G(\Omega\setminus B_{\delta^{\prime}})**B**: Thus**C**: set G​(Ω∖Bδ′)G(\Omega\setminus B_{\delta^{\prime}}) is also compact and thus contai...
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**A**: Note that this assumption implies the total boundedness of the space 𝒳\mathcal{X}.**B**: Our main result in this section is a quantitative version of Lemma 3.2**C**: To this end, we employ 1.3 and introduce an additional dimensionality constraint on the domain, which we formalize in terms of covering numbers a...
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**A**: In medical imaging, however, we deal with a wide range of dataset characteristics stemming from the use of various imaging modalities, different patient populations, clinical tasks, diagnostic processes and workflows, each contributing to the underlying causal processes with different potential sources of bias [...
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**A**: Thus we can focus on the uplift curve reconstruction in our discussion as we assume random treatment allocation.**B**: When the treatment groups are randomly allocated, the Qini curve will be mostly proportional to the uplift curve as NkT=1/kN^{T=1}_{k}/k shall be nearly a constant across different selection siz...
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**A**: Secondly, one attempts to derive a policy aimed at maximizing the learned reward, while in the meantime ensuring that the derived policy does not deviate much from the reference policy π𝗋𝖾𝖿\pi_{\mathsf{ref}}**B**: Firstly, the collected human feedback is utilized to train a reward model — denoted by rϕr_{\phi...
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**A**: Third, early training behavior can be highly misleading. Validation-loss curves during this initial phase tend to exaggerate performance gaps (Figure˜1, bottom right) and, in some cases, even reverse the eventual ranking, (Figure˜5, right)**B**: Many optimizers exhibit rapid early descent followed by plateauing...
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**A**: To examine whether LLMs express coherent trait structures similar to those observed in humans, we test whether self-regulation scores are predicted by the Big Five traits**B**: We fit linear regression models for each training phase (pre- vs post-alignment), regressing standardized self-regulation on the five p...
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**A**: (2016) proposed an IZ-free procedure for selecting the best system, using the Law of Iterated Logarithm (Durrett 2010) to maintain statistical validity without the IZ. Meanwhile, Cheng et al. (2025) adapted the IZ-free procedures from Fan et al. (2016) to identify feasible systems without a tolerance level and e...
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**A**: These sets are then analysed using the selected metrics and compared with the model’s accuracy to yield a final assessment of classifier safety.**B**: This process involves training models on a dataset as usual**C**: During validation, classification outcomes are recorded and stored in a suitable format (e.g., ...
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**A**: Machine-readable certainly meant something very different in 1954 than in 2025. In his reflections, Meehl (1986) notes that character recognition is still barely functional. He doesn’t rule out the possibility of more sophisticated pattern recognition methods emerging if computers improve**B**: Obviously, such ...
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**A**: The results are shown in Figure 4**B**: It can be observed how an optimal incentive for a younger patient with higher risk is larger than for an older patient, as the latter will be participating more willingly than the former due to its CRC probability perception. Also, notice how the lower the probability, the...
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**A**: Instead, the model provides CATE estimates and variance estimates per covariate profile and study. Therefore, for a given covariate profile 𝑿∗\boldsymbol{X}^{*} in the target setting, we can calculate estimated means and variances of their treatment effect if they were in each trial:**B**: The causal forest is ...
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**A**: Note that these bounds do not assume anything about the underlying predictor, and therefore do not show any dependence on the number of training samples mm. The underlying method might as well have access to the underlying distributions P​(Y|X)P(Y|X).**B**: We call the term σ\sigma, the dispersion following a si...
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**A**: Data Generation**B**: In clustered populations, spatial coordinates were randomly sampled from a bivariate Gaussian distribution:**C**: In the CSR populations, spatial coordinates for each individual in the population were randomly sampled from independent uniform distributions, x,y∼𝒰​(0,30)x,y\sim\mathcal{U}(...
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**A**: While the corrected score estimator for Poisson surrogates proposed by Li et al**B**: (2004) can be applied in this context, its application is limited to linear regression**C**: In contrast, SIMEX can be applied more broadly, but it has yet to be developed for conditionally Poisson-distributed surrogates. In ad...
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**A**: This is necessary because the data assimilation update and contraction of the system often cause the particles to become very similar**B**: Inflation is utilized to prevent filter collapse by ensuring diversity among the particles. Furthermore, since these systems are often not fully resolved, for example with r...
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**A**: However, both methods fail to address the inefficiency of the estimator for μ\mu, and concerns have been raised about the finite sample performance of the plug-in MLE. Adenstedt (1974) proposed an efficient but infeasible estimator for μ\mu. **B**: The first approach maximizes the likelihood assuming μ\mu is kno...
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**A**: For the first step, the idea is to check some overarching properties and commonalities across datasets, windows, and factors**B**: Since there are no specific hypotheses to be tested, we sweep over a large collection of volatility specifications and innovation distributions that can assess a variety of propertie...
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**A**: We introduce a truncation scheme specifically designed to handle unbounded density ratios**B**: This scheme enables spectral algorithms to achieve near-optimal convergence rates when the regression problem is well-specified (Corollary 2.7)**C**: Notably, fast convergence rates for misspecified scenarios are also...
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**A**: The weights for these BOPs are estimated through a nonlinear least squares optimization technique. For unknown random traffic loading, it is shown that the variance of the second time derivative of the generalized coordinate, q¨i\ddot{q}_{i} remains almost constant over the time span of the sensor traversing the...
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**A**: – The effective rank RR of NMF was estimated via the predictability method deduced from the exact PCC; see section IV**B**: In contrast to estimates found via BIC (Bayesian Information Criteria), our estimate RcR_{c} is stable against weak data noise**C**: RcR_{c} does have a geometrical meaning related to a lim...
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Selection 1
**A**: The proposed algorithm converged reliably in all real-data and simulation settings, confirming its numerical stability. **B**: Parameters are estimated using a iterative two-stage procedure that alternates between estimating the fixed and random effects from the marginals and given these values, updating the cop...
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Selection 4
**A**: High-performance computing (HPC) is one example with such a complex design structure**B**: In modern engineering fields, however, products often come with more complex spatial structures, where physical distance alone cannot explain the entirety of the spatial correlation structure**C**: HPC sees a massive amoun...
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Selection 3
**A**: In this paper, we present an approach to calibrated recommendations using a (neural) contextual bandit that learns to prescribe the optimal distribution of content types across a slate for each user, based on their current context**B**: We apply this formulation to the calibration of music and podcasts on the Sp...
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Selection 3
**A**: In this work, we aim to show that the prediction of joint models for longitudinal and survival data measured by the Brier score (i.e., specifically, time-varying Brier score [9]), can be improved using a similarity-based approach. We use cross-validation to determine the optimal subpopulation size that produces ...
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Selection 1
**A**: For absolute monotonicity, consider two cases:**B**: We must show that H​(z)H(z) satisfies the conditions of Lemma 2.0.1**C**: It is clear that H​(1)=1H(1)=1, H​(z)H(z) is continuous on z∈[0,1]z\in[0,1], and H​(0)=0H(0)=0 (which ensures the support excludes zero) for all α∈(0,2]\alpha\in(0,2]
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Selection 3
**A**: If sex is unobserved (Table 1), there are two approaches**B**: The first is to fit a reduced model using only treatment and outcome, effectively assuming no unobserved confounders (equivalent to the assumption of ignorability)**C**: This corresponds to a marginalized hypothesis applied to marginalized data:
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Selection 1
**A**: For further discussion and guidance on optimal two-stage GSDs, see Pilz et al. (2021) and Lewis (2023). **B**: Brittain & Bailey (1993) introduced two- and three-stage GSDs that minimise the expected sample size (ESS) under a specified alternative hypothesis with respect to critical values and interim analysis t...
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Selection 1
**A**: For the KL divergence, the bandwidth in the kernel density estimation was determined using Silverman’s rule-of-thumb**B**: The initial parameter distribution ρθ0\rho_{\theta_{0}} is set to 𝒩​(0,1)\mathcal{N}(0,1), represented by 10410^{4} i.i.d. samples. We then apply the particle-based algorithm described in E...
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Selection 1
**A**: the objective function at the upper level (lower level) relies on the solutions of the lower-level inverse problem (upper-level sensor allocation). Because of the constrained inverse problem in the lower level as well as the stochastic wind condition in the upper level, the solution of this sensor allocation pro...
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Selection 3
**A**: Specifically, the central subspace, the primary target of SDR (cook1998regression), does not exist when predictors are compositional. It turns out that the CDR constraint P∈ℳm,dP\in\mathcal{M}_{m,d} resolves this non-existence problem, yielding a well-defined, identifiable target, called central compositional su...
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Selection 3
**A**: Compared to those works, our assumptions are stronger in that we require a certain star-shaped structure of ℱ\mathcal{F} in (A1)**B**: Similar assumptions were previously imposed by Gassiat, (2002), Liu and Shao, (2003) and Aza¨ıs et al., (2009) who studied the behavior of the likelihood ratio test under very g...
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Selection 1
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