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Compared to the analysis of the identifiability of PBP_{B} in linear regression (Bing et al., 2022), our argument differs in the following two ways. First, the decomposition in (8) is applied to the covariance of the inverse variance weighted residual, rather than the residual itself. Again, this reweighting approach i... | We consider three variants of our G-hive algorithm. data driven G-hive is the proposed method that uses a data driven estimate of KK mentioned in Remark 1. The other two are oracle type estimators, Oracle(K) G-hive, corresponding to the algorithm with the true value of KK given and Oracle(P) G-hive, the algorithm with ... | Theoretically, our first key result shows that the approximation bias satisfies ‖F∗−Θ‖F/M=O(1/p)\|F^{*}-\Theta\|_{F}/\sqrt{M}=O(1/\sqrt{p}) and ‖PB⟂F∗−Θ‖F/M=O(1/p)\|P_{B}^{\perp}F^{*}-\Theta\|_{F}/\sqrt{M}=O(1/p). An interesting implication of this result is that collecting more observed covariates can mitigate the ... | In this work, we propose a unified framework for parameter estimation and statistical inference called G-hive, short for Generalized - HIdden Variable adjusted Estimation. Since the hidden variable ZZ is random and unobserved, the coefficient matrix Θ\Theta is generally not identifiable. To make Θ\Theta (asymptotically... | Recall that given nn i.i.d. observations (Y(i),X(i))(Y^{(i)},X^{(i)}) of (Y,X)(Y,X), i=1,…,ni=1,...,n, our goal is to estimate and do inference on Θ\Theta. In this section, we present our estimation and inference procedure called G-hive, short for Generalized - HIdden Variable adjusted Estimation. The algorithm, inspir... | D |
In the context of news text data for stock prediction, neural networks can capture complex interactions between terms—such as "interest rates," "central bank," and "market volatility"—that individually provide limited information but together reveal important market signals. By modeling such nonlinear word combinations... | As has been shown by Figure 9, for classifications, factors extracted from neural networks, 𝑭^fnn\widehat{\bm{F}}_{\mathrm{fnn}} and 𝑭^cnn\widehat{\bm{F}}_{\mathrm{cnn}}, are the most powerful ones. For example, in the MNIST database using Lasso, while directly estimating with 𝑿\bm{X} has a high testing error of aro... | Moreover, as the method is widely applicable, when considering image data, we may also use convolutional neural networks (CNN), and extract 𝑿cnn{\bm{X}}_{\mathrm{cnn}} from its last hidden layer. | Figure 9: Ratio of the classification error (ERR) of each model to that without feature augmentation (ERR(𝑿)\mathrm{ERR}(\bm{X}), benchmark). The CNN factor 𝑭^cnn\widehat{\bm{F}}_{\mathrm{cnn}} is only available for the images. | As for neural networks, we draw the last hidden layer of an FNN applied to 𝑿\bm{X} and obtain 𝑿fnn{\bm{X}}_{\mathrm{fnn}}. Shallow neural networks with one or two layers of convolution with ReLU activation with a wide enough last hidden layer output is enough to be combined by PCA to derive the factors. | B |
Lemma 1 implies that under the null hypothesis (H0H_{0}), the proposed decision rule is explicitly dependent on the value of SS, and as a result, the type I error rate becomes a function of SS. This stands in contrast to the traditional BOP2 design, in which the type I error rate is fixed and does not vary with SS. Thi... | Lemma 1 implies that under the null hypothesis (H0H_{0}), the proposed decision rule is explicitly dependent on the value of SS, and as a result, the type I error rate becomes a function of SS. This stands in contrast to the traditional BOP2 design, in which the type I error rate is fixed and does not vary with SS. Thi... | Given that the separation timepoint SS is uncertain and modeled as a random variable within a pre-specified range, it is more appropriate to control the average type I error and average power, rather than these metrics at a fixed SS. This marginal approach naturally accounts for the variability in SS, offering robust o... | Moreover, we find that the power is primarily governed by the ratio of the median survival times before and after the separation point, rather than their absolute values, offering robustness and interpretability across a range of clinical scenarios. | To assess how reliably the calibrated design controls error across the entire prior range of the separation time, we investigated the type-I error and power curves of DTE-BOP2 as functions of the true SS. Particular attention was paid to the effect of boundary control – that is, re-optimising the decision boundary (λ,γ... | B |
The three methods in Fig. 4 include a naive method that implements the split likelihood ratio test as described in Sec. 2.1, without using the fact that the KmK_{m} can be jointly diagonalized. The second considered method uses this fact only when calculating θ^0\hat{\theta}_{0}, emulating a setting where diagonalizati... | In the following section, we discuss special cases of interest where computation can be made more efficient by using additional structure. | Assuming (8), OTYO^{\mathrm{\scriptscriptstyle T}}Y has the multivariate normal distribution in (1), but with Λm\Lambda_{m} in place of KmK_{m}, m∈{1,…,M}m\in\{1,\dots,M\}. Thus, replacing YY by OTYO^{\mathrm{\scriptscriptstyle T}}Y if needed, we may assume every Km=ΛmK_{m}=\Lambda_{m} is diagonal. We make this assum... | Because the critical value for the randomized test in general is different each time it is implemented, pp-values and widths of confidence intervals also vary from implementation to implementation. In Figure 7 we examine the distribution of the widths of the confidence intervals in this data example. Because the non-ra... | The simulation results, along with those of the data example in the next section, can be reproduced using code at https://github.com/koekvall/univ_vc_suppl. | D |
In this paper, we introduce an implementation of monotone BART for binary outcomes. This is done with a probit link, implemented using the ideas of normal latent variables/data augmentation from Albert and Chib, (1993), akin to how Chipman et al., (2010) created the probit-variant of original BART. | We fit both probit BART and probit monotone BART with default settings. The posterior mean curve and 90% pointwise credible bands for each model are shown in Figure 1. We see that when the mean function is truly monotonic, imposing monotonic constraints improves both the estimation and its precise, as shown by how clos... | The paper proceeds as follows. We first review the original, probit, and monotone BART models from the literature. In Section 3 we propose probit monotone BART, including the model set up and some details on the code implementation. In Section 4 we demonstrate the proposed method with a simulation study. Section 5 conc... | Before we proposal our model in Section 3, we first define original BART as well as the two variants of BART that our model proposal uses as cornerstones. | Likewise, this implies two main changes to monotone BART: introduce the normal latent variables and change the likelihood of the outcome from normal to Bernoulli, thus removing σ\sigma from the model. Here we enumerate all parts of the proposed model, reiterating some of the Equations from the previous section. | B |
A characteristic quality of human mobility is the frequent use of particular spaces or activity regions. Many people tend to travel to a specific region or along specific routes for work, return home on a daily basis, and frequent the same region to buy food, utilities, or clothing. In the literature on human mobility,... | We give an overview of the statistical frameworks used in the development of human mobility models. These models are treated as stochastic processes, subject to variability due to local movement and more extensive habitual travel. They are frequently modeled as structured random walks, a method that borrows concepts de... | This provides a novel approach to human mobility to data anonymization. By simulating the spatial mobility patterns of individuals with the LFCM, researchers can fit accurate models of human mobility based on the resulting synthetic data while preserving the privacy of the individuals involved. | Characterizations of human mobility using non-Gaussian random-walk models have also been explored. For example, studies by Gonzalez et al. (2008) and Rhee et al. (2011) have highlighted that human mobility often shows heavy-tailed travel distances similar to a Lévy flight process. Song et al. (2010) employed a modified... | A separate body of research prominent in animal telemetry attempts to recover the latent position process that underlies the observed locations of individuals (see Hooten et al. (2017) for an extensive review). By modeling the latent position process, they addressed the temporal dependence present in the observed data.... | A |
This result indicates that we can set λ\lambda by a large enough values and without tuning λ\lambda using cross validation, and the signal parameter can be shrunk to 0 or 1 which achieve the purpose of complete classification. The overall iterative coordinate descent algorithm to find the solution can be obtained using... | 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. We find the tuning parameter can be set to a large enough values such that the signal parameter can be co... | Although lasso method, have ability of shrink the parameter estimates toward to zero under the natural sparsity in complex network, the existent links between nodes can not be shrunk to its true value of 1, which will inevitably decrease the estimation accuracy in most cases. For this reason, Shi et al. (2021) proposed... | In Eq. (17), β\beta contains the elements of the connectivity matrix A=[aij]A=[a_{ij}], representing a signal parameter where a value of 1 indicates a connection between two nodes, and 0 indicates no connection. To evaluate the accuracy of the estimator for β\beta, we plot various metrics as a function of Δ=L/N\Delta=... | To measure the accuracy of network reconstruction, we have to define some metrics for assessing the efficiency of proposed method. | D |
(a version of the fixed point iteration for ψα\psi_{\alpha}) is also used by the codes in [10] to compute the empirical expectiles. This was probably not realized in [6] since it was not stated in the description/manual of [10]. On the other hand, [6] gives an interpretation of the fixed point iteration for ψα\psi_{\al... | – a direct proof for the convergence of a one-sided fixed point iteration via Banach’s fixed point theorem, | (a version of the fixed point iteration for ψα\psi_{\alpha}) is also used by the codes in [10] to compute the empirical expectiles. This was probably not realized in [6] since it was not stated in the description/manual of [10]. On the other hand, [6] gives an interpretation of the fixed point iteration for ψα\psi_{\al... | To the best of our knowledge, there is no general convergence proof yet for the fixed point iteration via (2.6) although the algorithm works very well. Under additional assumptions (the distribution has a continuous density function), [6, Thm. 2.2, Cor. 2.3] provides quadratic convergence as expected from a Newton-type... | Theorem 2.2 in [6] provides a result on quadratic convergence for the fixed point iteration for ψ^α\hat{\psi}_{\alpha} for continuous distributions, not for a discrete data set. In the discrete case, the convergence follows from the general case in Theorem 2.7. | C |
H(τ)∈(G(τ),F(τ))H(\tau)\in(G(\tau),F(\tau)), because λ∈(0,1).\lambda\in(0,1). Consequently, H(τ)∈(0,1)H(\tau)\in(0,1), whence the limit in (16) lies in | Recall that (Rnm,Dnm)(R_{nm},D_{nm}) is distribution free under H0H_{0}, whence we can assume that FF and GG both are equal to the distribution function of U(0,1)U(0,1), the uniform distribution on the | G=ℝ×(0,1).G=\mathbb{R}\times(0,1). Recall the function hh in the proof of Theorem 3, which is continuous on GG. | Obviously hh is continuous on GG. Moreover, a(B)∈(0,1)a(B)\in(0,1) almost surely. (Indeed, a(B)a(B) is uniformly distributed on (0,1)(0,1).) Thus (11) and another application of the CMT gives | Let h:ℝ×(0,1]→ℝh:\mathbb{R}\times(0,1]\rightarrow\mathbb{R} be defined by h(x,y):=x/y(1−y)h(x,y):=x/\sqrt{y(1-y)} for (x,y)∈ℝ×(0,1)=:G(x,y)\in\mathbb{R}\times(0,1)=:G and h(x,y):=0h(x,y):=0 otherwise. | B |
Y~α:=Yα−αr−1+αr+−αr−.\tilde{Y}_{\alpha}:=\frac{Y_{\alpha}-\alpha r_{-}}{1+\alpha r_{+}-\alpha r_{-}}. | Now consider an integer n≥2n\geq 2 integer and α:=1n\alpha:=\frac{1}{n} Eq. (1). With a slight abuse of notation, we write YnY_{n} instead of Y1nY_{\frac{1}{n}}, and define the following ANM model | Assumption 2 is satisfied for both models from Eq. (2) and Eq. (3) due to the density of the class of cubic splines in C([0,1])C([0,1]) with an arbitrary number of knots mm. | With a slight abuse of notation and for simplicity we do not write Y~n\tilde{Y}_{n} but Y={y1,…,yn}Y=\{y_{1},\dots,y_{n}\} for a cubic spline regression on set | Y~α:=Yα−αr−1+αr+−αr−.\tilde{Y}_{\alpha}:=\frac{Y_{\alpha}-\alpha r_{-}}{1+\alpha r_{+}-\alpha r_{-}}. | A |
This random formulation of the latent positions introduces implicit homogeneity and is connected to the infinite exchangeable random graphs (Janson and Diaconis,, 2008). | Given an n×dn\times d matrix 𝐗=[𝐱1,…,𝐱n]T\mathbf{X}=[\mathbf{x}_{1},\ldots,\mathbf{x}_{n}]^{\mathrm{T}}, where 𝐱1,…,𝐱n∈ℝd\mathbf{x}_{1},\ldots,\mathbf{x}_{n}\in\mathbb{R}^{d}, with first pp columns orthogonal to last qq columns, such that 𝐱iT𝐈p,q𝐱j∈[0,1]\mathbf{x}_{i}^{\mathrm{T}}{\mathbf{I}}_{p,q}\mathbf{x}_... | The latter Glivenko–Cantelli type condition is also relaxed in the current work, as we only require that σd(𝐗)>0\sigma_{d}(\mathbf{X})>0 (see Remark 1 below). | The same homogeneity condition was retained in Xie and Xu, (2023) using a Glivenko–Cantelli type condition when 𝐱1,…,𝐱n\mathbf{x}_{1},\ldots,\mathbf{x}_{n} are deterministic. | In this paper, we consider the latent positions 𝐱1,…,𝐱n\mathbf{x}_{1},\ldots,\mathbf{x}_{n} to be deterministic parameters to be estimated. | C |
μX(t)=E{X(t)} and CXX(s,t)=E[{X(s)−μX(s)}{X(t)−μX(t)}].\mu_{X}(t)=E\{X(t)\}\text{ and }C_{XX}(s,t)=E[\{X(s)-\mu_{X}(s)\}\{X(t)-\mu_{X}(t)\}]. | The Radon-Nikodym theorem (Ash and Doléans-Dade, 2000) ensures the existence of a measurable function w(t)=dν(t)/dtw(t)=d\nu(t)/dt, t∈𝒯t\in\mathcal{T}, which we refer to as weight function. The weight function ww is assumed to reside in the space | By Mercer’s Theorem (see Theorem 4.6.5 in Hsing and Eubank (2015)), the spectral decomposition of the covariance function CXX(s,t)C_{XX}(s,t) is | where ZZ has E(Z(t))=0E(Z(t))=0 and covariance function CZZ(s,t)=E{Z(s)Z(t)}C_{ZZ}(s,t)=E\{Z(s)Z(t)\}. The spectral decomposition of the covariance CZZC_{ZZ} with respect to Lebesgue measure is | μX(t)=E{X(t)} and CXX(s,t)=E[{X(s)−μX(s)}{X(t)−μX(t)}].\mu_{X}(t)=E\{X(t)\}\text{ and }C_{XX}(s,t)=E[\{X(s)-\mu_{X}(s)\}\{X(t)-\mu_{X}(t)\}]. | B |
Let 𝒞\mathcal{C} denote design constraints (e.g., minimum emphasis on mastery and coverage, fairness caps per section), and J(α)J(\alpha) a strictly convex penalty (e.g., quadratic deviation from a prior α0\alpha^{0} and entropy regularization for spread). Consider | We presented a blueprint-aware, axiomatic readiness index with theoretical guarantees: monotonicity, Lipschitz stability, bounded drift under re-weighting, unique weight design under convex constraints, and compatibility with prerequisite-admissible recommendations. The framework is deployment-ready and can later accom... | If JJ is strictly convex and 𝒞\mathcal{C} is convex and nonempty, the solution α⋆\alpha^{\star} to (2) exists and is unique. | Let 𝒞\mathcal{C} denote design constraints (e.g., minimum emphasis on mastery and coverage, fairness caps per section), and J(α)J(\alpha) a strictly convex penalty (e.g., quadratic deviation from a prior α0\alpha^{0} and entropy regularization for spread). Consider | Boundedness and monotonicity follow from nonnegativity and normalization. Blueprint coherence follows by linearity and separability. Scale-invariance holds as each component is normalized to [0,1][0,1]. | B |
One key research direction in PresPM involves leveraging techniques from CI. The objective is to estimate the effect of an intervention using offline observational data. This avoids the need for potentially costly and risky randomized experiments, such as A/B testing a loan assignment strategy in a bank or setting up a... | CI learners are designed to address the challenges of observational data in estimating causal effects. Broadly, they fall into two categories: model-agnostic and model-based. Model-agnostic learners, or meta-learners, define general estimation strategies that are independent of the base model family (e.g., neural netwo... | Second, it only implements the TARNet architecture, which may not yield reliable counterfactual estimates across all datasets, as described in Section II. More critically, selecting the most appropriate learner depends on identifying certain data characteristics (e.g., effect heterogeneity, see Section II), which is in... | While observational data offers clear advantages, it also presents challenges. Since the data reflects an existing policy, e.g., a bank’s current loan strategy, treatment assignment is not random, unlike in controlled trials. A non-random treatment assignment policy can complicate causal estimation. For example, there ... | One key research direction in PresPM involves leveraging techniques from CI. The objective is to estimate the effect of an intervention using offline observational data. This avoids the need for potentially costly and risky randomized experiments, such as A/B testing a loan assignment strategy in a bank or setting up a... | C |
All results are averaged over 5 runs with different random seeds. μ\mu represents the mean and σ\sigma represents the standard deviation. | Bold values indicate the best performance and underline values indicate second best for each dataset and metric. | On IBS dataset: Best AUROC (0.8594) and second-best Cross Entropy (0.4645) and Brier scores (0.1464) | On Colorectal Cancer dataset: Best performance across all metrics (AUROC: 0.6271, Cross Entropy: 0.6735, Brier: 0.2397) | We compared Causal SHAP against five baseline methods using the insertion test [15], which sequentially adds features from most to least important based on each method’s attributions, measuring AUROC, Cross Entropy and Brier scores at each step. High AUROC, lower Cross Entropy and Brier scores indicate better performan... | A |
Our combinatorial symmetries offer a complementary form of regularity that neural networks can exploit—distinct from the strong smoothness assumptions commonly used in scientific computing inspired deep learning [4, 19, 27], and more amenable to practical verification than compositional assumptions on the target functi... | We note that when provided with noiseless training data our algorithm implies a randomized polynomial-time procedure for constructing a three-layer MLP capable of memorizing any finite regression dataset. Unlike the result of [34], our approach is not restricted to binary classification. Moreover, unlike [78, 110], thi... | . We exhibit a neural network architecture and propose a concrete, architecture-specific, randomized end-to-end training algorithm that learns network parameters implementing a uniform approximator of the ground truth function; even when trained on noisy data. Unlike RFN and NTK approaches, our training procedure (Algo... | We now specify the initialization scheme used for the weights and biases of our 33-layer MLP encoder. Our procedure largely follows standard random initialization protocols, with a mild but deliberate modification: we adjust the variance of the random weight matrices and choose non-random biases, following insights fro... | Leveraging these results, we show that a sample complexity of 𝒪(1/Nr)≪𝒪(1/N)\mathcal{O}(1/N^{r})\ll\mathcal{O}(1/N) is achievable for any OOD regression task that shares the same combinatorial symmetries as the pre-training task (Corollary 5.1). This yields strictly faster rates than those obtainable via classical ... | A |
In contrast, the LDA projection displays significantly more overlap and less defined cluster structures. The topics do not form tight congregations but are instead scattered in diffuse, often intersecting arrangements. For instance, the “laws state governed” topic, which was a compact cluster in the NMF projection, is ... | To understand the prevalence and balance of the topics discovered within the corpus, a topic distribution bar chart, conceptualized as Figure 3 for the ACORD dataset, is highly instructive. This chart shows the number of documents assigned to each topic cluster identified by the hybrid | By concatenating the Top2Vec and Node2Vec embeddings, we leverage both textual and network information to obtain richer representations. This combination aims to produce interpretable topic clusters that are not only semantically cohesive but also structurally well-separated in the latent embedding space. We demonstrat... | To evaluate the effectiveness of the proposed topic modeling and representation learning pipeline, we conducted a series of experiments on the ACORD dataset, a well-established benchmark for legal-clause retrieval focused on contract drafting. Prior to modeling, the dataset underwent preprocessing to remove redundant a... | We have introduced a sophisticated hybrid methodology that synergizes semantic embeddings from Top2Vec with graph-based structural learning from Node2Vec to achieve robust unsupervised clustering of complex legal documents. Through comprehensive evaluations on the ACORD dataset of legal clauses and the CUAD dataset of ... | C |
In the current example, we can go further: let wpseudo,02w^{2}_{\textrm{pseudo},0} be the continuous convolution of the independent priors w1aw^{a}_{1} and w1bw^{b}_{1}. Applying Theorem 1 to ℳ0\mathcal{M}_{0} with this density shows that the induced distribution Vpseudo,02(m)V_{\text{pseudo},0}^{2(m)} on 𝐬0(m)/m\mat... | i.e., the GRO-optimal prior on the null is the distribution induced on the null sufficient statistics by the alternative prior, or equivalently, the marginal distribution of 𝐜0\mathbf{c}_{0} induced by W1W_{1}. | The above ‘duality’ between canonical and microcanonical models implies that, alternatively, canonical models can also be parameterized using the expected value of the sufficient statistics. Given parameters 𝜽\bm{\theta}, define the mean value vector: | In the reasoning above, we invoked Theorem 1 several times to go back and forth between prior distributions on mean-value parameters and marginal distributions on sufficient statistics. Specifically: (a) at the level of | Figure 2: In the microcanonical Example A, when the prior on the alternative sufficient statistics n1an_{1}^{a} and n1bn_{1}^{b} are uniform distributions (on the left), the resulting GRO-optimal prior on the null sufficient statistic n1n_{1} is the convolution of the two uniform distributions, which results in a trian... | C |
It should be noted that AUC-ROC and VUS-ROC are not perfect metrics. Further analysis in Appendix A-D (Figs. S11c and S11d) reveals that in noisy scenarios, false positives affect the ranking capability of these metrics, as they pay more attention to the model’s anomaly prediction capability. | Property 3 (Boundedness): The final score SCCE∈[0,1]S_{\text{CCE}}\in[0,1], where 0 indicates poor performance and 1 indicates excellent performance. If we remove constraints to confidence, the CCE score has a lower bound of -1 and an upper bound of 1. | TABLE I: Comparison of ranking consistency across different indicators (the larger the Sp and Kd, the better; the smaller the MD, the better). bold indicates the best, underlined indicates the second best. | To better observe and understand anomalies in the dataset, we selected ECG and Power demand from UCR to study the performance of different models in real-world scenarios. The visualization results of model predictions are shown in Figs. 6a and 6b respectively. Table III shows the scores of these models on different met... | Figure 5 shows the visualization results of five PreQ-NegP-R models on synthetic data. Their parameters are shown in the first column of Table II, where the numbers after Q and P represent qq and pp respectively, and the noise size σ=0.1\sigma=0.1. ER represents the theoretical ranking of the model. In this case, only ... | B |
Table 6: Performance comparison in terms of model consistency (MC) for the proposed NP2M2 and six baseline approaches on the Company Bankruptcy Prediction dataset. Here, dd denotes the parameter in 𝒟(θ)\mathcal{D}(\theta). For each method under each setting, the average result and standard deviation over 1010 trials ... | Tables 4 and 4 present the accuracy and model consistency, respectively, of all methods on the nonlinear synthetic dataset. Our method consistently ranks first across all settings in terms of both accuracy and model consistency, demonstrating its superior performance on the complex nonlinear dataset. Notably, NP2M2 ach... | First, we collect initial data {𝐗0,𝐲0}\{\mathbf{X}_{0},\mathbf{y}_{0}\} from the base distribution 𝒟0\mathcal{D}_{0}. At each time step tt, we train and deploy model θt\theta_{t}, then collect new data {𝐗t,𝐲t}\{\mathbf{X}_{t},\mathbf{y}_{t}\} from the distribution 𝒟(θt)\mathcal{D}(\theta_{t}). We evaluate the ac... | Tables 6 and 6 report the accuracy and model consistency, respectively, of all methods on the Company Bankruptcy Prediction dataset. | Tables 2 and 2 present the accuracy and model consistency, respectively, of all methods on the linear synthetic dataset. Our method, NP2M2, achieves the highest accuracy in 4 out of 6 settings and ranks the second in the remaining two, as shown in Tables 2. For model consistency, NP2M2 outperforms all baselines across ... | C |
To identify the optimal multi-task training configuration, we evaluate how much of a performance drop we incur at each layer compared to the single-task setting in GNNs. The comparative analysis of the three strategies for both GCN is detailed in Tables 1 and 8. Our findings indicate that ADMP-GNN ST outperforms ADMP-G... | To identify the optimal multi-task training configuration, we evaluate how much of a performance drop we incur at each layer compared to the single-task setting in GNNs. The comparative analysis of the three strategies for both GCN is detailed in Tables 1 and 8. Our findings indicate that ADMP-GNN ST outperforms ADMP-G... | The training setup ST, where we sequentially train the deep ADMP-GNN, incurs relatively higher time costs due to the need for L+1L+1 training iterations. However, in each iteration, backpropagation is performed on a limited number of parameters, approximately equivalent to those in a single message passing layer. Conse... | Table 1. Comparison of ADMP-GCN training paradigms ALM and ST. 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. | We have studied an alternative training setup where we progressively train one GNN layer at a time, subsequently freezing each layer after training. More formally, the problem in (1) can be tackled using dynamic programming as follows, | B |
The alternating pattern of positive and negative change points reveals frequent shifts in momentum advantage between the two players, indicating a dynamic and varied competitive landscape with changing control over the match. To further analyze the distribution and impact of change points, the identified positive and n... | Assuming momentum is present, we subsequently address the quantification challenge. Prior research has predominantly treated momentum as a qualitative construct or resorted to simplified correlation models, which frequently fell short in capturing the multifaceted and dynamic essence of momentum within competitive spor... | To analyze the intensity of momentum shifts, we calculate the relative distance VtV_{t} according to the definition in Section 2.4. See Figure 7. | The series VtV_{t} exhibits significant fluctuations throughout the course of the final match. The sharp spikes in the graph represent the intensity of momentum shifts at change points. Positive peaks (Vt>0V_{t}>0) indicate strong momentum shifts in favor of Carlos Alcaraz at these change points, with larger peaks corr... | To quantify dynamic momentum transitions and evaluate the intensity of shift events during a match, we propose a relative distance metric, denoted by VtV_{t}, which captures both the direction and the magnitude of momentum shifts. | B |
It is noteworthy that in the case of JS-gOMP, we have utilized an ensemble of p=5p=5 noise-corrupted 𝐲\mathbf{y}-values in our analysis. | In Figure.1, we provide the recovery performance as a function of the sparsity level KK. A higher level of critical sparsity indicates improved empirical reconstruction performance. The simulation results reveal that the critical sparsity of JS-gOMP algorithms is much larger compared to OMP and gOMP algorithms. As the ... | To observe the empirical performance of the modified gOMP algorithm (JS-gOMP), we performed computer simulations using MATLAB (R2023a). In our experiment, we employ a testing strategy to measure the effectiveness of recovery algorithms by examining the empirical frequency of exact reconstruction in noisy environments. ... | Due to this noise corruption, most of the sparse classification algorithms falsely identify lots of unnecessary signal components (faulty atoms from dictionary 𝚽\mathbf{\Phi}) and as a result the recovered signal lost its required sparsity. This is one of the major drawbacks of the pursuit algorithms like the OMP & gO... | As a cost-effective solution for recovering sparse signals from compressed measurements, the OMP algorithm has received much attention in recent years. And the generalized version of the OMP algorithm i.e. gOMP is more efficient in reconstructing sparse signals. Since multiple indices can be identified with no addition... | A |
Our results in this section demonstrate that the out-of-sample RMSE can be used as a general cross validation metric to determine the optimal κ\kappa when modeling data with non-negative outcomes. For example, when estimating a gravity model on trade data, we can generate a plot similar to that in Figure˜9, and use it ... | As a main contribution of this paper, we show that the optimal modeling choice depends on the relative prominence of each feature in the data, and could diverge considerably from the Poisson estimator. Furthermore, we provide a simple data-driven procedure that empirical researchers can employ to determine the optimal ... | We summarize the preceding three sets of simulation results in the phase transition plot in Figure˜7. We see that, as heteroskedasticity decreases or sparsity increases, the optimal κ\kappa decreases, and vice versa. Therefore, we advocate for a more systematic modeling of non-negative dependent variables based on asse... | To determine the degree α\alpha of heteroskedasticity, we can employ hypothesis tests discussed in Manning and Mullahy (2001). To determine | It may appear that under heteroskedasticity, one should always use the estimator that best captures the conditional variance as a function of the conditional mean, by determining the value of α\alpha. Previous works have proposed these types of methods to determine the dispersion using regression-based tests (Park, 196... | C |
Table 1 presents the average ECP for the five different models (M1 to M5) evaluated on both the training and test sets across multiple districts. We observe that ECP values in the test set exhibit greater variability and are generally lower for several districts and models compared to the training set, highlighting a d... | Table 2: Comparison of model performance on the training set and test set for Food insecurity in Cameroon, using the Empirical Coverage Probability (ECP), averaged by region. M1: Knorr-Held (2000), M2: first-order Rushworth et al. (2014), M3: second-order Rushworth et al. (2014), M4: independent Gaussian-process, M5: s... | Table 1: Comparison of model performance on the training set and test set for Malaria incidence in Niassa, Mozambique, using the Empirical Coverage Probability (ECP), averaged by district. M1: Knorr-Held (2000), M2: first-order Rushworth et al. (2014), M3: second-order Rushworth et al. (2014), M4: independent Gaussian-... | Figure 7: Comparison of model performance on the training set and test set for food insecurity in Cameroon, using the Continuous Ranked Probability Score (CRPS). M1: Knorr-Held (2000), M2: first-order Rushworth et al. (2014), M3: second-order Rushworth et al. (2014), M4: independent Gaussian-process, M5: spatially corr... | Figure 4: Comparison of model performance on the training set and test set for Malaria incidence in Niassa, Mozambique, using the Continuous Ranked Probability Score (CRPS). M1: Knorr-Held (2000), M2: first-order Rushworth et al. (2014), M3: second-order Rushworth et al. (2014), M4:independent Gaussian-process, M5: spa... | B |
An asymmetry in distributions can lead to an asymmetry in the learning signals to a gradient-based causal discovery method. In the bivariate categorical case we find that the spikier distribution with ΔHi,j<0\Delta H_{i,j}<0 is easier to learn. | Figure 3: Bias 1 (Section 5.1) and Bias 2 (Section 5.2) for different values of ε\varepsilon and λ\lambda on the bivariate categorical setup with Dirichlet priors. Interventions happen in random order in Figure 3(b). | Distribution asymmetry can be controlled for by a suitable choice of conditional P(Xj|Xi)P(X_{j}|X_{i}), at least in a synthetic setup. In the categorical case with Dirichlet prior, we present the Bayesian Dirichlet equivalence prior (see Section 4.1) as an example. For clarity, we provide the definition for (conditio... | We define Bias 1 as the difference in entropy between marginal distributions and show how it can be controlled, in the bivariate categorical setup, by parameterized deviations from a Bayesian Dirichlet equivalence (BDe) prior. Likewise, we define Bias 2 as the difference of Kullback-Leibler Divergences between distribu... | To achieve symmetry of marginal distributions in our generated synthetic data, at least for an observational case, we borrow the Bayesian Dirichlet equivalence (BDe) prior from the classical literature of structure learning (Koller & Friedman, 2009, Section 18.3.6.3). This allows us to control the extent of Bias 1: Mar... | B |
A non-parametric TOST for equivalence, with a margin of ±0.06%\pm 0.06\%, confirms that the two models are statistically equivalent in predictive accuracy, while the error patterns remain strongly correlated (Spearman ρ=0.869\rho=0.869). | At ν=10−2\nu=10^{-2} (Figure˜15), the Variant TF exhibits a median relative L2L^{2} error slightly higher than that of the modified DeepONet. | Figures˜15, 16 and 17 show the distributions of the relative L2L^{2} error over all test instances for selected variants at viscosities ν=10−2\nu=10^{-2}, 10−310^{-3}, and 10−410^{-4}, respectively. | At ν=10−4\nu=10^{-4} (Figure˜17), both Variants TF and BxTF achieve lower median relative L2L^{2} errors than the modified DeepONet, with overall error distributions shifted downward relative to the modified DeepONet. | At ν=10−3\nu=10^{-3} (Figure˜16), the Variant TF attains a median relative L2L^{2} error comparable to that of the modified DeepONet. | C |
We compare the mean and (norm of the channel-wise) standard deviation of the TV-regularized objective. In addition, we compute the PSNR of the finite-particle posterior mean to the true TV-regularized solution, equivalent to running a fixed number of parallel chains for the Langevin methods. We do this to compare the s... | In this section, we present various two-dimensional toy examples to demonstrate the effects of adding a preconditioning matrix on the sampling behavior, followed by high-dimensional Bayesian total-variation regularized image deconvolution, and Bayesian neural network training. We compare against the MCMC-based baseline... | Figure 9: Evolution of the high-dimensional modifications for the 50-dimensional Gaussian, at convergence in 1000 iterations. Evaluated with 50 particles, step-size η=0.1\eta=0.1 and regularizations T=0.02,0.2,0.9T=0.02,0.2,0.9 in the top, middle and bottom rows respectively. We observe little difference when using the... | We compare against ULA, MLA, and MYULA [11]. We note that the acceptance probability for MALA is almost degenerate for this high-dimensional problem and requires extremely small step-sizes, and is thus omitted due to slow convergence. MYULA takes the following form: for a composite potential of the form exp(−f(x)+g(... | where AA is a convolution operator, yy is a corrupted image, and TV(x)=‖Dx‖1\mathrm{TV}(x)=\|Dx\|_{1} denotes the discrete total variation functional. For image deconvolution, the forward operator AA takes the form A=ℱ∗ΛℱA={\mathcal{F}}^{*}\Lambda{\mathcal{F}}, where ℱ{\mathcal{F}} is the (complex, unitary) matrix ... | C |
Still, this approach may already be meaningfully applied if XX is a baseline risk score, which is likely to be available in most trials. If the trial populations are similar, one could even apply this approach without any covariates; this may still lead to higher trial-level correlations than the canonical MA framework... | In the canonical MA framework, the observed-data model ℳ\mathcal{M} is often parametric; the parameter of interest then simply is a function of the model parameters. | For instance, one could define an alternative full-data parameter in terms of a projection onto the parametric model (used in the canonical MA framework) based on the Kullback-Leibler divergence. Such a projection parameter would be easier to estimate [97], but it may be more difficult to interpret when the parametric ... | Hence, the full-data parameter cannot rely on parametric assumptions about the distribution of (αg,β)′(\alpha^{g},\beta)^{\prime}. The bivariate normal model used in the canonical MA framework is nonetheless convenient as the model parameters (i.e., the mean and covariance of a bivariate normal distribution) have a sim... | We have focused on a particular full-data parameter that reduces to the target parameter of the canonical MA framework when the parametric model is correctly specified. However, one may define different full-data parameters that are identical to the target parameter of the canonical MA framework when the parametric mod... | D |
Results. We summarize the results across the two simulations in Fig.˜2. Our method consistently achieves coverage at or above the nominal 0.950.95 level and does not produce false positives. By contrast, the baseline methods frequently fall far short of nominal coverage: in the second simulation, all baselines achieve ... | We evaluate methods along four complementary dimensions. Our primary focus is on empirical coverage and the proportion of false positives, since failure on either dimension undermines the reliability of statistical conclusions. Empirical coverage measures the proportion of confidence intervals that contain the true par... | The strength of our method lies in its reliability: it avoids misleading conclusions even in challenging extrapolation regimes. The cost of this conservativeness is wider confidence intervals and, consequently, a smaller proportion of true positives compared to the baselines. This trade-off is expected, as our method p... | Figure 2: From left to right, coverage average confidence interval width, proportion of false positives and proportion of true positives for each method on the first simulation (top) and the second simulation (bottom). Coverage should be above the nominal level (dashed line in first column), and the proportion of false... | Overview of Inference Strategy. A desirable property for an estimator is consistency: with enough training data, the estimator should converge to the estimand, the true underlying quantity of interest. In our spatial setting, however, it is not just the amount of training data that matters, but also where the data are ... | B |
We show that this result holds under a mild uniform-integrability conjecture. The statement of the conjecture is deferred to appendix B (Conjecture B.1) as it requires delving into technical details of the proof. | We call X=[Xij]i∈[n],j∈[p]∈ℝn×pX=\left[{X_{ij}}\right]_{i\in[n],j\in[p]}\in\mathbb{R}^{n\times p} a sparse Gaussian matrix with parameter dd if for all i∈[n],j∈[p]i\in[n],j\in[p] we have: | We expect it to follow from standard concentration bounds as all relevant random terms are sub-Gaussian, and verification is work in progress. | Let XX be a sparse Gaussian random matrix of parameter dd, and ZZ be a random vector in ℝn\mathbb{R}^{n} such that Z∼𝒩(0,σ2In)Z\sim\mathcal{N}\left({0,\sigma^{2}I_{n}}\right), with σ>0\sigma>0 a fixed constant. Let β⋆∈{0,1}p\beta^{\star}\in\left\{{0,1}\right\}^{p} be a deterministic vector such that ‖β⋆‖0=s\left\|{\... | Traditionally, XX is considered to be a dense random matrix with sub-Gaussian entries. Previous works have shown that the complexity of the problem in terms of required sample size exhibits two phase transitions at two thresholds nINF<nALGn_{\text{INF}}<n_{\text{ALG}}, yielding three regimes: | B |
Choose with equal probability (1/21/2) the change scenario to be proposed: from chain to offspring or vice-versa. | Choose with equal probability (1/21/2) the change scenario to be proposed: from chain to offspring or vice-versa. | where No′N_{o}^{\prime} is the number of nodes that can be rewired from offspring to chain scenario in 𝒯′\mathcal{T}^{\prime} and kjk_{j} is the out-degree of host jj. | Choose with equal probability a host ii that can be rewired according to the selected change scenario. We denote by NcN_{c} (NoN_{o}) the number of different hosts for which the chain to offspring (offspring to chain) scenario can be applied. | Taking these steps into account, the ratio of proposal probabilities (“from chain to offspring” divided by “from offspring to chain”) is | C |
Simple SCMs always have uniquely defined observational, interventional, and counterfactual distributions. | In the remainder of this paper, we only consider simple SCMs. The same assumption is also used in Mokhtarian et al. (2023). | The proof of Proposition 36 in Mokhtarian et al. (2023) is constructive. This allows us to obtain a colored separating system on (𝐕,𝒞)(\mathbf{V},\mathcal{C}) with at most 2⌈log2(χ)⌉2\lceil\log_{2}(\chi)\rceil elements. | In this section, we introduce step 1.1 of our algorithm for learning the descendant sets {De𝒢(X)}X∈𝐕\{De_{\mathcal{G}}(X)\}_{X\in\mathbf{V}} and SCCs 𝒮={𝐒1,…,𝐒s}\mathcal{S}=\{\mathbf{S}_{1},\dots,\mathbf{S}_{s}\} of 𝒢\mathcal{G}. This part is similar to Mokhtarian et al. (2023), but we consider the presence of ... | The experiment design problem has been studied extensively in the context of DAGs (Shanmugam et al., 2015; Choo and Shiragur, 2023b; Squires et al., 2020; Agrawal et al., 2019). Some prior work has also addressed settings involving either latent confounders (Kocaoglu et al., 2017b; Addanki et al., 2020) or cycles (Mokh... | A |
No element in ZZ is a descendant in GX¯G_{\overline{X}} of any W∉XW\not\in X lying on a proper causal path from XX to YY | All backdoor paths between MM and YY are blocked by ZZ and SS, i.e., (M⟂Y∣Z,S)G(X,M),Ypbd(M\perp Y\mid Z,S)_{G^{pbd}_{(X,M),Y}} | All backdoor paths between XX and YY are blocked by ZZ and SS, i.e., (X⟂Y∣Z,S)GX,Ypbd(X\perp Y\mid Z,S)_{G^{pbd}_{X,Y}} | All backdoor paths between Mi∈MM_{i}\in M and YY are blocked by ZZ and SS, i.e., (Mi⟂Y∣Z,S)G(X,Mi),Ypbd(M_{i}\perp Y\mid Z,S)_{G^{pbd}_{(X,M_{i}),Y}} for all MiM_{i}, where MM contains all nodes along proper causal paths from XX to YY. | ZTZ^{T} m-separates YY from SS in the proper backdoor graph, i.e., (Y⟂S∣ZT)GX,Ypbd(Y\perp S\mid Z^{T})_{G^{pbd}_{X,Y}} | B |
The parameter b=ρ−1b=\rho-1 is the strength of density dependent growth of the population in the Gompertz model of population growth (Dennis et al.,, 2006). As the density dependence parameter aa approaches zero then the Gompertz model approaches a density independent model of exponential growth. | For certain model structures there is an equivalence between the cumulative and sequential model. In an ordinal GLM with the complementary log-log link function of Eq. (13) and covariates with global effects, the sequential model is equivalent to the popular grouped Cox model (Laara and Matthews,, 1985) that is also kn... | The contributions of the paper are as follows. The dynamic spatio-temporal sequential ordinal model (DSTSOM) is defined in Section 3. This ordinal model formulation extends dynamic generalised linear models to account for the multivariate ordinal response data in spatio-temporal models. The spatial autoregressive struc... | The objective of this study is to propose the dynamic spatio-temporal sequential ordinal model (DSTSOM) for spatio-temporal applications. This spatio-temporal model for ordinal data can be fit using standard procedures developed for Bayesian spatio-temporal models of univariate data, for example, using the popular inte... | The sign reversal convention is often used for covariates with global effects in ordinal GLMs (McCullagh,, 1980; Laara and Matthews,, 1985; Armstrong and Sloan,, 1989; Berridge and Whitehead,, 1991; McCullagh and Nelder,, 1989; Tutz,, 1991), though not always (Fahrmeir and Tutz,, 1994; Tutz,, 2012). It is also possible... | A |
In MAHMC, the KLD from the target discrete distribution to the sample distribution was 0.13410.1341, the maximum value of the KS test value at 10510^{5} samples was 0.37910.3791, and the ESS per sample was 1.9×10−61.9\times 10^{-6} (9×1059\times 10^{5} samples for each 1616 independent Markov chain). | However, taking into account the time for tuning the hyperparameters, the computation time of BPS and BPS-PT was not longer than that of MAHMC. | Although the hyperparameters may not have been optimized, the performance was generally comparable to BPS. | Table 3: Comparison of computation time, maximum KS value, MSE, and ESS per sample is shown. Although BPS-PT was superior to BPS, the increase in computation time was not worth it. | Since the hyperparameters were optimized in Ref. [10], the performance was superior to BPS and BPS-PT in this model. | B |
The NHANES dataset originally contains BMI records for approximately 10,000 subjects. However, due to duplicated entries, only the first observation per subject is retained, resulting in a final dataset of 6,779 unique individuals. We treat this pre-processed dataset as the underlying population for our analysis. | The true mean of BMI is 26.488 and the correlation between the auxiliary variable Weight and the outcome variable BMI is 0.903, indicating high-ranking quality. The histogram of the BMI in Figure 2 shows a skewed distribution, suggesting that URSS may be more efficient than SRS. | In practice, we first generate BRSS data using the auxiliary variable (Weight) to rank and select samples without measuring BMI. The outcome variable is then measured for the selected samples as described in Section 2. | We demonstrate the RSS sampling and inference procedures by estimating the mean body mass index (BMI) and testing the hypothesis H0:μ=μ0H_{0}:\mu=\mu_{0}. The BMI is a widely used indicator of body fat based on weight and height, commonly employed to assess an individual’s health status. | The ranking accuracy in the simulated data is controlled through a linear ranking model defined as Xi=Yi+ϵiX_{i}=Y_{i}+\epsilon_{i} for i=1,2,⋯,ni=1,2,\cdots,n, where ϵi\epsilon_{i} represents independent normal random variables with mean 0 and variance chosen to achieve a specific correlation ρ=Corr(X,Y)\rho=Corr(... | A |
“[…] we find that counties with more historical immigration have higher income, less poverty, less unemployment, higher rates of urbanization, and greater educational attainment today.” (Sequeira et al., 2020) | “We […] find support for a causal interpretation of the relationship between legal change, human capital, and growth.” (Dittmar and Meisenzahl, 2020) | As a first example, consider Sequeira et al. (2020), whose abstract begins: “We study the effects of European immigration to the U.S. during the Age of Mass Migration (1850–1920) on economic prosperity.” While the authors do not seem to have held a particular interest in ΨLATE\Psi_{LATE}, they targeted this paramete... | “We also find little difference between IV and OLS estimates […], indicating that the effects of potential endogeneity of inflation expectations with respect to firms’ price setting decisions are limited.” (Coibion et al., 2020) | In IV analyses, identity slippage occurs when a study mistakenly suggests that its results represent estimates of ΨATE\Psi_{ATE} instead of ΨLATE\Psi_{LATE}. Arguably, if ΨLATE\Psi_{LATE} is a good approximation of ΨATE\Psi_{ATE}, meaning that the difference between the true values of the two parameters is sm... | C |
Therefore, there exists at least one probability distribution on MM satisfying the assumption in Theorem 1 for the case (ii), but 𝔼[d(X,μ)]=∞\mathbb{E}[d(X,\mu)]=\infty. | A natural question arising from the definition is that for a given distribution ℙX\mathbb{P}_{X}, if the distribution is geodesically symmetric about μ1,μ2∈M\mu_{1},\mu_{2}\in M, then is it true that μ1=μ2\mu_{1}=\mu_{2}? The answer to the question is ‘yes’ under the following non-compactness condition. | Several open problems remain. First, Theorem 2 establishes a partial converse of Theorem 1 for the case (ii) in the Euclidean case. We conjecture that this converse continues to hold for general non-compact symmetric spaces, but a proof remains elusive. The primary technical obstacle lies in controlling the geometry of... | A pertinent question is whether the converse of Theorem 1 for the case (ii) holds. We provide a partial answer below | We note that the hypothesis of Theorem 1 for the case (i) holds when (Xi)i=1∞(X_{i})_{i=1}^{\infty} does not necessarily consist of identically distributed random variables. An illustrative example with non-i.i.d. random variables in the space of symmetric positive-definite matrices is provided below. | C |
To address these limitations, we introduce a novel approach that combines practical applicability, theoretical rigor, and computational innovation. By adopting the weighted Youden index as the optimization objective, our method allows for greater flexibility in aligning with clinical priorities, such as balancing sensi... | The remainder of this paper is organized as follows. Section 2 introduces the notation and theoretical foundations of the smoothed weighted Youden index. Section 3 presents the penalized estimator and its theoretical properties. Section 4 describes the optimization algorithm, while Section 5 reports simulation results.... | In summary, the use of gradient mapping enables interpolation-based line search in nonsmooth and nonconvex settings. Unlike classical backtracking schemes that rely on fixed reduction rules, our approach adaptively selects step sizes based on function values and gradient mapping information. This reduces the number of ... | This section presents two simulation studies. The first evaluates the finite-sample performance of the proposed method in comparison with lasso-logistic regression, a widely recognized benchmark for biomarker selection and combination. Other methods were excluded due to limitations such as computational inefficiency or... | Building on the previous framework, we incorporate the SCAD penalty into the smoothed weighted Youden index estimator. This penalized formulation combines the strengths of the weighted Youden index with SCAD’s sparsity-inducing properties, ensuring effective biomarker selection while preserving the desirable statistica... | A |
Let us have vectors of non-negative values t∈IJt\in\real^{IJ}, ζ∈I\zeta\in\real^{I}, and η∈J\eta\in\real^{J}. | Let us assume another 2×22\times 2 contingency table with the test statistic (12) denoted as Z2Z_{2}. | Let us consider a given pair [i,j][i,j], for which π^ij=0\hat{\pi}_{ij}=0. Let us assume tij=0t_{ij}=0. | Let π^11,…,π^IJ\hat{\pi}_{11},\dots,\hat{\pi}_{IJ} denote maximum likelihood estimates of π11,…,πIJ\pi_{11},\dots,\pi_{IJ}. Let us consider regularized estimates of πij\pi_{ij} obtained as | Let the set of all pairs [i,j][i,j], for which π^ij=0\hat{\pi}_{ij}=0, be denoted by 𝒮.{\cal S}. Then the regularized empirical mutual information fulfils | B |
μ(y)=∫y∞e−tt𝑑t,∀y∈ℝ+.\mu(y)=\int_{y}^{\infty}\frac{e^{-t}}{t}\,dt\,,\quad\forall\,y\in\mathbb{R}_{+}\,. | Let us next recall some elementary facts about the space of CM functions. Such space is a convex cone, closed under pointwise multiplication. It is also closed under locally uniform limits. If ff is CM and Φ:[0,∞)→[0,∞)\Phi\,\colon\,[0,\infty)\rightarrow[0,\infty) is smooth AM when restricted on (0,∞)(0,\infty), then Φ... | Let f(x)=1/xf(x)=1/x on (0,∞)(0,\infty). It is immediate to check by differentiating that ff is CM. On the other hand, ff is CM by Theorem 2.4 since f(x)=∫0∞e−xy𝑑yf(x)=\int_{0}^{\infty}e^{-x\,y}dy. | Since μ\mu is non-negative on (0,∞)(0,\infty), ff is CM. Note that log(x+1)\log(x+1) is not CM, showing that if the product of two functions is CM, it is not necessarily true that also the individual factors are CM. | is in fact CM. The Bernstein-Hausdorff-Widder-Choquet (BHWC) theorem [22], see Theorem 2.4, states that also the converse is true. That is, if a function f:C→ℝf\,\colon C\rightarrow\mathbb{R} is smooth and CM on an open convex cone CC, then there exists a unique Borel measure dνd\nu supported on the dual cone C∗C^{*},... | C |
We hypothesize that the representations of pre-trained speech models can be used to analyze infant cries. Specifically, we propose that these representations encode information about the non-linear phenomena of vocalizations. To test this hypothesis, we compute latent representations from five pre-trained speech models... | We hypothesize that the representations of pre-trained speech models can be used to analyze infant cries. Specifically, we propose that these representations encode information about the non-linear phenomena of vocalizations. To test this hypothesis, we compute latent representations from five pre-trained speech models... | To assess the ability of latent representations from pre-trained speech models to classify baby cries, we consolidated eight available datasets. Each dataset comprises several cry recordings, labeled differently according to the respective study. These labels defined our probing tasks. Table 1 provides an overview of t... | In conclusion, we have shown that latent representations of speech models contain valuable information for the classification of human infant cries. They reliably encode identity and age of the crying baby. In addition, their application to cry classification revealed that these latent representations also capture info... | Although our results might suggest that these latent representations could be used to predict the cause of cries, we must remain very cautious with this possibility. The results obtained from the Donate A Cry dataset are unreliable, particularly due to the lack of information about the identity of the crying child. | B |
In Section 4.2 we give a simpler yet equivalent definition of the CFDL in (4.5), which leads to an interpretation of CDL through the lens of indistinguishability. | According to the theorem, if a predictor pp is miscalibrated, then the right-hand side of (4.2) is larger than the left-hand side for some decision task 𝒯{\mathcal{T}}. The difference between the two sides is exactly the payoff loss incurred by the decision maker who follows the best-response strategy σ𝒯\sigma_{\math... | As we will see when we prove Theorem 4.1 in Section 4.2, the CDL is zero if and only if the predictor pp is perfectly calibrated. If a predictor is not perfectly calibrated but has a small CDL, any decision maker can still trust the predictor as if it were calibrated without losing too much expected payoff. This holds ... | In this section we prove Theorem 4.1. We start by giving a characterization of the maximum expected payoff on the right-hand side of (4.2) for a general predictor pp that may or may not be calibrated, which simplifies the definition of CFDL and will be useful in the proof. | We have the following characterization of the maximum expected payoff achievable by post-processing pp: | C |
Second, (ii) it accommodates the nested structure of multiomics MSI data by integrating multiple molecular classes into a unified framework, allowing comparisons across analyte types measured on the same tissue. Finally, (iii) to ensure scalability and efficient inference in high-dimensional settings, we implement a ta... | First, we generate a reference dataset, D(0){D}^{(0)}, with μ(0)=4\mu^{(0)}=4. This case represents a scenario where a clear separation exists among the row clusters and, consequently, among the column clusters. For the remaining datasets, D(r){D}^{(r)} with r=1,2,3,4r=1,2,3,4, we set μ(r)∈{1,0.75,0.50,0.25}\mu^{(r)}\i... | Figure S.1 shows an annotated view of the H&E-stained clear cell Renal Cell Carcinoma (ccRCC) tissue we analyzed. This image is a high-resolution version of the one reported in panel (A) of Figure 2 of the main paper. In this detailed representation, regions of interest identified by an expert pathologist are color-cod... | Our application focuses on MALDI-MSI measurements extracted from a human tissue sample diagnosed with clear cell renal cell carcinoma (ccRCC), shown in panel (A) of Figure 2. The tissue is annotated as follows: the green region indicates the healthy cortex, the blue outlines the capsule, and the red highlights the tumo... | By applying our proposed method to these data, we aim to identify molecular signatures and spatial subregions within the renal tissue that distinguish tumor from non-tumor areas, offering insights into the heterogeneity of clear cell renal cell carcinoma. Moreover, the biclustering approach aligns with our broader goal... | C |
Finding root causes is, however, a complex task. If a module fails, and its behavior depends on a sequence of previous actions, it may difficult to find the specific root source of the failure. | Traditional RCA methods often struggle under conditions of limited observability, where latent factors confound observable metrics. Probabilities of causation, with their intrinsic ability to capture counterfactual scenarios, provide a rigorous metric aligned precisely with the fundamental queries of RCA: assessing whe... | Accordingly, the consistent capability of necessity-based metrics to accurately recover the true causal paths underscores their adequacy for automated RCA in intelligent autonomous systems. From a practical perspective, the choice between PN and w-PN must consider computational and data requirements. While PN provides ... | On methodological contributions for root cause analysis (RCA), we proposed a novel approach leveraging probabilities of causation as metrics for identifying and ranking causal paths within scenarios of limited observability, such as those in microservices observability contexts. | Root Cause Analysis (RCA) range from manual, diagram-based inspections to advanced automated systems leveraging statistical or causal inference techniques [13]. These approaches are broadly employed in domains like epidemiology, medical diagnostics and, increasingly, system observability, particularly for microservices... | D |
𝒟(S)=1NP∑j=0P−1∑l=0N−1min[∑i=0N−1I[lN,l+1N)(Sij),1],\mathcal{D}(S)=\frac{1}{N\,P}\,\sum_{j=0}^{P-1}\sum_{l=0}^{N-1}\min\left[\sum_{i=0}^{N-1}I_{\left[\frac{l}{N},\frac{l+1}{N}\right)}(S_{ij}),1\right]\,, | and satisfying the one-dimensional projection property of LHS. That is, there is one and only one sample per interval if each dimension is uniformly binned into NN disjoint intervals. We wish to distribute MM new samples to obtain an extended set eLHS(P,N+M){\rm eLHS}(P,N+M). | Essentially, this procedure checks all the ii-intervals for each dimension jj. If they are populated by a sample SijS_{ij}, a weight 1/(NP)1/(NP) is assigned; otherwise, the weight is 0. The metric is the sum of all the weights. | To quantify this loss, we introduce a new metric 𝒟\mathcal{D}, which we refer to as the “LHS degree” of a sample set. Consider a generic sample set SS with NN elements in PP dimensions; this is composed of real numbers SijS_{ij} with i=0,…,N−1i=0,\dots,N-1 and j=0,…,P−1j=0,\dots,P-1. We define | After the expansion, one has 𝒟(eLHS)≤1\mathcal{D}({\rm eLHS})\leq 1. Indeed, the sums in Eq. (1) trace the presence of at least one sample per interval. An interval containing overlapping samples still contributes a weight of 1 to the weighted sum described above, due to the use of the min\min function. For each such... | B |
Semi-exact control functionals with a Gaussian kernel via median-tuned heuristic: SECFQ\text{SECF}_{Q} where (Q+dQ)<S{Q+d\choose Q}<S, Q∈{1,2}Q\in\{1,2\}. | In Experiment 1, sampling from the posterior distribution is relatively expensive. For most methods, the overall efficiency is primarily dominated by the statistical efficiency. Our proposed methods generally achieve the best overall efficiency, which improves as kk increases, with minimal differences between k=25k=25 ... | While our proposed framework is general, we primarily focus on ZVCV in this work. Performing ZVCV is equivalent to solving a multiple linear regression problem, for which various criteria can be used. A common choice is the ordinary least squares (OLS) criterion. However, as the number of polynomial coefficients JJ gro... | The methods used in the simulation study are available in the GitHub repository edelweiss611428/ZVCV, which is a forked version of the R package ZVCV (South, 2022) 222Will be available shortly. The regularised ZVCV methods utilise penalised regression solvers in the glmnet package (Friedman et al., 2021). Here, the seq... | Table 2: Brief descriptions of the experiments in the simulation study, where dd is the number of dimensions of Θ\Theta. | C |
characteristics. These variables are detailed in Section 3.0.3. They are used as predictors in stage three of the | (Graells-Garrido et al. 2021), predict socioeconomic levels (Soto et al. 2011; Blumenstock, Cadamuro, and On 2015), estimate income segregation (Moro et al. 2021), quantify | accumulating (De Heer and De Leeuw 2002; Stedman et al. 2019; Luiten, Hox, and Leeuw 2020). Dwindling | over-representing urban, wealthy and young-adult populations (Blumenstock and Eagle 2010; Wesolowski et al. 2013; Schlosser et al. 2021). | tourism activity (Raun, Ahas, and Tiru 2016) and estimate migration (Rowe et al. 2024; González-Leonardo et al. 2025) and population displacement (Rowe et al. 2022; Iradukunda, Rowe, and Pietrostefani 2025). | C |
Despite notable progress in driver behavior modeling and its applications, the extant literature still exhibits several limitations: | In driving behavior studies, certain data features pose persistent challenges. Most automobile insurance databases record a large number of policyholders with zero claims, and zero inflation may be exacerbated by reporting incentives (e.g., deductibles or bonus-malus penalties) [4, 5]. In contrast, when NMEs are captur... | Specifically, in this paper, we frame the problem of NME prediction as a time series forecasting problem (on a weekly basis). We propose a Grouped ZIP (G-ZIP) model to handle the “excess of zeros” in the weekly near-miss counts. The model gathers drivers into behaviorally homogeneous groups (e.g., by car model or drivi... | We model six individual NMEs Ci,t(e)C^{(e)}_{i,t}: harsh braking, harsh acceleration, serious speeding, forward collision, lane departure, too close distance and their combination NMEs Ni,tN_{i,t}. The exposure is the weekly total distance EiE_{i}; all models use the offset logEi\log E_{i}. The NME histograms are show... | Zero inflation and long-tail distribution. Zero counts remain frequent at the driver-week level of NMEs. Beyond the dominant zeros, most non-zero counts are small while a few cases are very large, yielding long-tailed, overdispersed outcomes. Conventional existing models yield mis-specified likelihoods and biased uncer... | D |
ℒi(μ,𝜷,κ)=S(Li∣𝒙i)−S(Ri∣𝒙i).\mathcal{L}_{i}(\mu,\bm{\beta},\kappa)=S(L_{i}\mid\bm{x}_{i})-S(R_{i}\mid\bm{x}_{i}). | The coefficient interpretation is in terms of time ratios: exp(βj)\exp(\beta_{j}) multiplies the median survival time for a one-unit increase in xjx_{j}. | Step 2 (Covariate-adjusted prediction): A Weibull AFT model was fitted with age and treatment arm as the covariates. Time ratios exp(βj)\exp(\beta_{j}) quantify the multiplicative effects on typical survival, enabling clinical interpretation. | S(t∣𝒙i)=exp[−(texp(μ+𝒙i⊤𝜷))κ].S(t\mid\bm{x}_{i})=\exp\!\left[-\left(\frac{t}{\exp(\mu+\bm{x}_{i}^{\top}\bm{\beta})}\right)^{\kappa}\right]. | Conversely, parametric AFT models introduce distributional assumptions that produce smooth curves and permit covariate adjustments. In the simulation study, when the Weibull family matched the truth, the AFT models achieved lower integrated Brier scores (IBS) than the EM or Kaplan–Meier benchmarks, demonstrating superi... | A |
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