Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity analysis methods can effectively process such complexities. Moreover, the sensitivity analysis field as a whole pays limited attention to the nature of interaction effects, whose understanding can prove to be critical for the design of safe and reliable systems. In this paper, we introduce and extensively test a simple binning approach for computing sensitivity indices and demonstrate how complementing it with the smart visualization method, simulation decomposition (SimDec), can permit important insights into the behavior of complex engineering models. The simple binning approach computes first-, second-order effects, and a combined sensitivity index, and is considerably more computationally efficient than the mainstream measure for Sobol indices introduced by Saltelli et al. The totality of the sensitivity analysis framework provides an efficient and intuitive way to analyze the behavior of complex systems containing interactions and dependencies.
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In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of joint occurrence of extremes in higher dimensions. In this paper, we propose a notion of mutual asymptotic independence to capture the behavior of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence. Furthermore, we define $k$-wise asymptotic independence which lies in between pairwise and mutual asymptotic independence. The concepts are compared using examples of Archimedean, Gaussian and Marshall-Olkin copulas among others. Notably, for the popular Gaussian copula, we provide explicit conditions on the correlation matrix for mutual asymptotic independence to hold; moreover, we are able to compute exact tail orders for various tail events.
When the target of inference is a real-valued function of probability parameters in the k-sample multinomial problem, variance estimation may be challenging. In small samples, methods like the nonparametric bootstrap or delta method may perform poorly. We propose a novel general method in this setting for computing exact p-values and confidence intervals which means that type I error rates are correctly bounded and confidence intervals have at least nominal coverage at all sample sizes. Our method is applicable to any real-valued function of multinomial probabilities, accommodating an arbitrary number of samples with varying category counts. We describe the method and provide an implementation of it in R, with some computational optimization to ensure broad applicability. Simulations demonstrate our method's ability to maintain correct coverage rates in settings where the nonparametric bootstrap fails.
A non-linear complex system governed by multi-spatial and multi-temporal physics scales cannot be fully understood with a single diagnostic, as each provides only a partial view and much information is lost during data extraction. Combining multiple diagnostics also results in imperfect projections of the system's physics. By identifying hidden inter-correlations between diagnostics, we can leverage mutual support to fill in these gaps, but uncovering these inter-correlations analytically is too complex. We introduce a groundbreaking machine learning methodology to address this issue. Our multimodal approach generates super resolution data encompassing multiple physics phenomena, capturing detailed structural evolution and responses to perturbations previously unobservable. This methodology addresses a critical problem in fusion plasmas: the Edge Localized Mode (ELM), a plasma instability that can severely damage reactor walls. One method to stabilize ELM is using resonant magnetic perturbation to trigger magnetic islands. However, low spatial and temporal resolution of measurements limits the analysis of these magnetic islands due to their small size, rapid dynamics, and complex interactions within the plasma. With super-resolution diagnostics, we can experimentally verify theoretical models of magnetic islands for the first time, providing unprecedented insights into their role in ELM stabilization. This advancement aids in developing effective ELM suppression strategies for future fusion reactors like ITER and has broader applications, potentially revolutionizing diagnostics in fields such as astronomy, astrophysics, and medical imaging.
This research presents a comprehensive approach to predicting the duration of traffic incidents and classifying them as short-term or long-term across the Sydney Metropolitan Area. Leveraging a dataset that encompasses detailed records of traffic incidents, road network characteristics, and socio-economic indicators, we train and evaluate a variety of advanced machine learning models including Gradient Boosted Decision Trees (GBDT), Random Forest, LightGBM, and XGBoost. The models are assessed using Root Mean Square Error (RMSE) for regression tasks and F1 score for classification tasks. Our experimental results demonstrate that XGBoost and LightGBM outperform conventional models with XGBoost achieving the lowest RMSE of 33.7 for predicting incident duration and highest classification F1 score of 0.62 for a 30-minute duration threshold. For classification, the 30-minute threshold balances performance with 70.84\% short-term duration classification accuracy and 62.72\% long-term duration classification accuracy. Feature importance analysis, employing both tree split counts and SHAP values, identifies the number of affected lanes, traffic volume, and types of primary and secondary vehicles as the most influential features. The proposed methodology not only achieves high predictive accuracy but also provides stakeholders with vital insights into factors contributing to incident durations. These insights enable more informed decision-making for traffic management and response strategies. The code is available by the link: //github.com/Future-Mobility-Lab/SydneyIncidents
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments.
Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming from data of unknown quality, simulated data with added noise are used to investigate practical identifiability in two distinct epidemiological models. Particular emphasis is placed on the role of initial conditions, which are assumed unknown, except those that are directly measured. Instead of just focusing on one method of estimation, we use and compare results from various broadly used methods, including maximum likelihood and Markov Chain Monte Carlo (MCMC) estimation. Among other findings, our analysis revealed that the MCMC estimator is overall more robust than the point estimators considered. Its estimates and predictions are improved when the initial conditions of certain compartments are fixed so that the model becomes globally identifiable. For the point estimators, whether fixing or fitting the that are not directly measured improves parameter estimates is model-dependent. Specifically, in the standard SEIR model, fixing the initial condition for the susceptible population S(0) improved parameter estimates, while this was not true when fixing the initial condition of the asymptomatic population in a more involved model. Our study corroborates the change in quality of parameter estimates upon usage of pre-peak or post-peak time-series under consideration. Finally, our examples suggest that in the presence of significantly noisy data, the value of structural identifiability is moot.
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various alignments of executions. Seemingly more flexible alignments can be expressed in terms of product automata based on program transition relations. A single degenerate alignment rule (self-composition), atop a complete Hoare logic, comprises a RHL for $\forall\forall$ properties that is complete in the ordinary logical sense (Cook'78). The notion of alignment completeness was previously proposed as a more satisfactory measure, and some rules were shown to be alignment complete with respect to a few ad hoc forms of alignment automata. This paper proves alignment completeness with respect to a general class of $\forall\forall$ alignment automata, for a RHL comprised of standard rules together with a rule of semantics-preserving rewrites based on Kleene algebra with tests. A new logic for $\forall\exists$ properties is introduced and shown to be alignment complete. The $\forall\forall$ and $\forall\exists$ automata are shown to be semantically complete. Thus the logics are both complete in the ordinary sense. Recent work by D'Osualdo et al highlights the importance of completeness relative to assumptions (which we term entailment completeness), and presents $\forall\forall$ examples seemingly beyond the scope of RHLs. Additional rules enable these examples to be proved in our RHL, shedding light on the open problem of entailment completeness.
One of the hallmark achievements of the theory of graphical models and Bayesian model selection is the celebrated greedy equivalence search (GES) algorithm due to Chickering and Meek. GES is known to consistently estimate the structure of directed acyclic graph (DAG) models in various special cases including Gaussian and discrete models, which are in particular curved exponential families. A general theory that covers general nonparametric DAG models, however, is missing. Here, we establish the consistency of greedy equivalence search for general families of DAG models that satisfy smoothness conditions on the Markov factorization, and hence may not be curved exponential families, or even parametric. The proof leverages recent advances in nonparametric Bayes to construct a test for comparing misspecified DAG models that avoids arguments based on the Laplace approximation. Nonetheless, when the Laplace approximation is valid and a consistent scoring function exists, we recover the classical result. As a result, we obtain a general consistency theorem for GES applied to general DAG models.
We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of neurons in the hidden layer is replaced by a continuous ensemble. We show that the problem can be phrased as global minimization of a free energy functional on the space of (finite-length) paths over probability measures on the weights. This functional trades off the $L^2$ approximation risk of the terminal measure against the KL divergence of the path with respect to an isotropic Brownian motion prior. We characterize the unique global minimizer and examine the dynamics in the space of probability measures over weights that can achieve it. In particular, we show that the optimal path-space measure corresponds to the F\"ollmer drift, the solution to a McKean-Vlasov optimal control problem closely related to the classic Schr\"odinger bridge problem. While the F\"ollmer drift cannot in general be obtained in closed form, thus limiting its potential algorithmic utility, we illustrate the viability of the mean-field Langevin diffusion as a finite-time approximation under various conditions on entropic regularization. Specifically, we show that it closely tracks the F\"ollmer drift when the regularization is such that the minimizing density is log-concave.
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.
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