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Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of elements, of size $O(|S^{opt}| \cdot 1/\varepsilon)$, where $S^{opt}$ denotes the optimal solution, that is guaranteed to contain a $3/2 + \varepsilon$ approximation, while guaranteeing certain robustness properties. We call such a small subset a Density Constrained Subset (DCS), which is inspired by the Edge-Degree Constrained Subgraph (EDCS) [Bernstein and Stein, 2015], originally designed for the maximum cardinality matching problem in a graph. Our proof is constructive and hinges on a greedy decomposition of matroids, which we call the density-based decomposition. We show that this sparsifier has certain robustness properties that can be used in one-way communication and random-order streaming models.

Facing climate change the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Leakage detection and localization are challenging problems due to the complex interactions and changing demands in water distribution networks. Especially small leakages are hard to pinpoint yet their localization is vital to avoid water loss over long periods of time. While there exist different approaches to solving the tasks of leakage detection and localization, they are relying on various information about the system, e.g. real-time demand measurements and the precise network topology, which is an unrealistic assumption in many real-world scenarios. In contrast, this work attempts leakage localization using pressure measurements only. For this purpose, first, leakages in the water distribution network are modeled employing Bayesian networks, and the system dynamics are analyzed. We then show how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing leakages given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios.

The propositional product logic is one of the basic fuzzy logics with continuous t-norms, exploiting the multiplication t-norm on the unit interval [0,1]. Our aim is to combine well-established automated deduction (theorem proving) with fuzzy inference. As a first step, we devise a modification of the procedure of Davis, Putnam, Logemann, and Loveland (DPLL) with dichotomous branching inferring in the product logic. We prove that the procedure is refutation sound and finitely complete. As a consequence, solutions to the deduction, satisfiability, and validity problems will be proposed for the finite case. The presented results are applicable to a design of intelligent systems, exploiting some kind of multi-step fuzzy inference.

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

We propose a model of treatment interference where the response of a unit depends only on its treatment status and the statuses of units within its K-neighborhood. Current methods for detecting interference include carefully designed randomized experiments and conditional randomization tests on a set of focal units. We give guidance on how to choose focal units under this model of interference. We then conduct a simulation study to evaluate the efficacy of existing methods for detecting network interference. We show that this choice of focal units leads to powerful tests of treatment interference which outperform current experimental methods.

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature.

To promote the generalization ability of breast tumor segmentation models, as well as to improve the segmentation performance for breast tumors with smaller size, low-contrast amd irregular shape, we propose a progressive dual priori network (PDPNet) to segment breast tumors from dynamic enhanced magnetic resonance images (DCE-MRI) acquired at different sites. The PDPNet first cropped tumor regions with a coarse-segmentation based localization module, then the breast tumor mask was progressively refined by using the weak semantic priori and cross-scale correlation prior knowledge. To validate the effectiveness of PDPNet, we compared it with several state-of-the-art methods on multi-center datasets. The results showed that, comparing against the suboptimal method, the DSC, SEN, KAPPA and HD95 of PDPNet were improved 3.63\%, 8.19\%, 5.52\%, and 3.66\% respectively. In addition, through ablations, we demonstrated that the proposed localization module can decrease the influence of normal tissues and therefore improve the generalization ability of the model. The weak semantic priors allow focusing on tumor regions to avoid missing small tumors and low-contrast tumors. The cross-scale correlation priors are beneficial for promoting the shape-aware ability for irregual tumors. Thus integrating them in a unified framework improved the multi-center breast tumor segmentation performance.

Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering method to estimate non-stationary trend of quantiles. We introduce general shrinkage priors to induce locally adaptive Bayesian inference on trends and mixture representation of the asymmetric Laplace likelihood. To quickly compute the posterior distribution, we develop calibrated mean-field variational approximations to guarantee that the frequentist coverage of credible intervals obtained from the approximated posterior is a specified nominal level. Simulation and empirical studies show that the proposed algorithm is computationally much more efficient than the Gibbs sampler and tends to provide stable inference results, especially for high/low quantiles.

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density separation assumption is implemented via quadratic margin maximization. The algorithm has an explicit solution with rich theoretical properties, and we show that particular cases of our algorithm are the least-square support vector machine in the supervised case, the spectral clustering in the fully unsupervised regime, and a class of semi-supervised graph-based approaches. As such, QLDS establishes a smooth bridge between these supervised and unsupervised learning methods. Using recent advances in the random matrix theory, we formally derive a theoretical evaluation of the classification error in the asymptotic regime. As an application, we derive a hyperparameter selection policy that finds the best balance between the supervised and the unsupervised terms of our learning criterion. Finally, we provide extensive illustrations of our framework, as well as an experimental study on several benchmarks to demonstrate that QLDS, while being computationally more efficient, improves over cross-validation for hyperparameter selection, indicating a high promise of the usage of random matrix theory for semi-supervised model selection.

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which eliminates the shortcomings of conventional online techniques while computing the entire probability density function of model parameters. The limitations to Gaussian noise, the application to only linear in the parameters (LIP) systems, and the persistent excitation (PE) needs are some of these drawbacks. In ARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution is proposed. The forgetting factor can be presented adaptively using the TFF in many dynamical systems as an alternative to a constant hyperparameter. By offering a trade-off between exploitation and exploration, the specific jump distribution has been optimised towards hybrid/multi-modal systems that permit inferences among modes. These trade-off are adjusted based on parameter evolution rate. We demonstrate that ARMCMC requires fewer samples than conventional MCMC methods to achieve the same precision and reliability. We demonstrate our approach using parameter estimation in a soft bending actuator and the Hunt-Crossley dynamic model, two challenging hybrid/multi-modal benchmarks. Additionally, we compare our method with recursive least squares and the particle filter, and show that our technique has significantly more accurate point estimates as well as a decrease in tracking error of the value of interest.