Working with multiple variables they usually contain difficult to control complex dependencies. This article proposes extraction of their individual information, e.g. $\overline{X|Y}$ as random variable containing information from $X$, but with removed information about $Y$, by using $(x,y) \leftrightarrow (\bar{x}=\textrm{CDF}_{X|Y=y}(x),y)$ reversible normalization. One application can be decoupling of individual information of variables: reversibly transform $(X_1,\ldots,X_n)\leftrightarrow(\tilde{X}_1,\ldots \tilde{X}_n)$ together containing the same information, but being independent: $\forall_{i\neq j} \tilde{X}_i\perp \tilde{X}_j, \tilde{X}_i\perp X_j$. It requires detailed models of complex conditional probability distributions - it is generally a difficult task, but here can be done through multiple dependency reducing iterations, using imperfect methods (here HCR: Hierarchical Correlation Reconstruction). It could be also used for direct mutual information - evaluating direct information transfer: without use of intermediate variables. For causality direction there is discussed multi-feature Granger causality, e.g. to trace various types of individual information transfers between such decoupled variables, including propagation time (delay).
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High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior computation are inefficient as $n$ and/or $p$ increase due to worsening time per step and mixing rates. One strategy is to use a gradient-based sampler to improve mixing while using data sub-samples to reduce per-step computational complexity. However, usual sub-sampling breaks down when applied to imbalanced data. Instead, we generalize piece-wise deterministic Markov chain Monte Carlo algorithms to include importance-weighted and mini-batch sub-sampling. These approaches maintain the correct stationary distribution with arbitrarily small sub-samples, and substantially outperform current competitors. We provide theoretical support and illustrate gains in simulated and real data applications.
Frequent and intensive disasters make the repeated and uncertain post-disaster recovery process. Despite the importance of the successful recovery process, previous simulation studies on the post-disaster recovery process did not explore the sufficient number of household return decision model types, population sizes, and the corresponding critical transition conditions of the system. This paper simulates the recovery process in the agent-based model with multilayer networks to reveal the impact of household return decision model types and population sizes in a toy network. After that, this paper applies the agent-based model to the five selected counties affected by Hurricane Harvey in 2017 to check the urban-rural recovery differences by types of household return decision models. The agent-based model yields three conclusions. First, the threshold model can successfully substitute the binary logit model. Second, high thresholds and less than 1,000 populations perturb the recovery process, yielding critical transitions during the recovery process. Third, this study checks the urban-rural recovery value differences by different decision model types. This study highlights the importance of the threshold models and population sizes to check the critical transitions and urban-rural differences in the recovery process.
Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data generating processes when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These methods typically require that all the confounders are observed to ensure identification of the effects. We contribute by showing how valid semiparametric inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We propose uncertainty intervals which allow for unobserved confounding, and show that the resulting inference is valid when the amount of unobserved confounding is small relative to the sample size; the latter is formalized in terms of convergence rates. Simulation experiments illustrate the finite sample properties of the proposed intervals and investigate an alternative procedure that improves the empirical coverage of the intervals when the amount of unobserved confounding is large. Finally, a case study on the effect of smoking during pregnancy on birth weight is used to illustrate the use of the methods introduced to perform a sensitivity analysis to unobserved confounding.
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem, we employ a damped Zarantonello iteration, which leads to a linear Poisson-type equation that is symmetric and positive definite. The resulting system is solved by a contractive algebraic solver such as a multigrid method with local smoothing. We formulate a fully adaptive algorithm that equibalances the various error components coming from mesh refinement, iterative linearization, and algebraic solver. We prove that the proposed adaptive iteratively linearized finite element method (AILFEM) guarantees convergence with optimal complexity, where the rates are understood with respect to the overall computational cost (i.e., the computational time). Numerical experiments investigate the involved adaptivity parameters.
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges for most conventional artificial neural network, as they are essentially implemented in a deterministic manner. In this paper, we develop an efficient probabilistic computation framework by truncating the probabilistic representation of neural activation up to its mean and covariance and construct a moment neural network that encapsulates the nonlinear coupling between the mean and covariance of the underlying stochastic network. We reveal that when only the mean but not the covariance is supervised during gradient-based learning, the unsupervised covariance spontaneously emerges from its nonlinear coupling with the mean and faithfully captures the uncertainty associated with model predictions. Our findings highlight the inherent simplicity of probabilistic computation by seamlessly incorporating uncertainty into model prediction, paving the way for integrating it into large-scale AI systems.
We present a comprehensive analysis of the implications of artificial latency in the Proposer-Builder Separation framework on the Ethereum network. Focusing on the MEV-Boost auction system, we analyze how strategic latency manipulation affects Maximum Extractable Value yields and network integrity. Our findings reveal both increased profitability for node operators and significant systemic challenges, including heightened network inefficiencies and centralization risks. We empirically validates these insights with a pilot that Chorus One has been operating on Ethereum mainnet. We demonstrate the nuanced effects of latency on bid selection and validator dynamics. Ultimately, this research underscores the need for balanced strategies that optimize Maximum Extractable Value capture while preserving the Ethereum network's decentralization ethos.
Scattering networks yield powerful and robust hierarchical image descriptors which do not require lengthy training and which work well with very few training data. However, they rely on sampling the scale dimension. Hence, they become sensitive to scale variations and are unable to generalize to unseen scales. In this work, we define an alternative feature representation based on the Riesz transform. We detail and analyze the mathematical foundations behind this representation. In particular, it inherits scale equivariance from the Riesz transform and completely avoids sampling of the scale dimension. Additionally, the number of features in the representation is reduced by a factor four compared to scattering networks. Nevertheless, our representation performs comparably well for texture classification with an interesting addition: scale equivariance. Our method yields superior performance when dealing with scales outside of those covered by the training dataset. The usefulness of the equivariance property is demonstrated on the digit classification task, where accuracy remains stable even for scales four times larger than the one chosen for training. As a second example, we consider classification of textures.
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are pressure-robust, i.e. the error estimates for the velocity do not depend on the error in the pressure. Similar considerations arise in nearly incompressible linear elastic solids. Conforming discretizations with this property are now well understood in two dimensions, but remain poorly understood in three dimensions. In this work we state two conjectures on this subject. The first is that the Scott-Vogelius element pair is inf-sup stable on uniform meshes for velocity degree $k \ge 4$; the best result available in the literature is for $k \ge 6$. The second is that there exists a stable space decomposition of the kernel of the divergence for $k \ge 5$. We present numerical evidence supporting our conjectures.
Predictions under interventions are estimates of what a person's risk of an outcome would be if they were to follow a particular treatment strategy, given their individual characteristics. Such predictions can give important input to medical decision making. However, evaluating predictive performance of interventional predictions is challenging. Standard ways of evaluating predictive performance do not apply when using observational data, because prediction under interventions involves obtaining predictions of the outcome under conditions that are different to those that are observed for a subset of individuals in the validation dataset. This work describes methods for evaluating counterfactual performance of predictions under interventions for time-to-event outcomes. This means we aim to assess how well predictions would match the validation data if all individuals had followed the treatment strategy under which predictions are made. We focus on counterfactual performance evaluation using longitudinal observational data, and under treatment strategies that involve sustaining a particular treatment regime over time. We introduce an estimation approach using artificial censoring and inverse probability weighting which involves creating a validation dataset that mimics the treatment strategy under which predictions are made. We extend measures of calibration, discrimination (c-index and cumulative/dynamic AUCt) and overall prediction error (Brier score) to allow assessment of counterfactual performance. The methods are evaluated using a simulation study, including scenarios in which the methods should detect poor performance. Applying our methods in the context of liver transplantation shows that our procedure allows quantification of the performance of predictions supporting crucial decisions on organ allocation.
The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.
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