This paper introduces a new framework of algebraic equivalence relations between time series and new distance metrics between them, then applies these to investigate the Australian ``Black Summer'' bushfire season of 2019-2020. First, we introduce a general framework for defining equivalence between time series, heuristically intended to be equivalent if they differ only up to noise. Our first specific implementation is based on using change point algorithms and comparing statistical quantities such as mean or variance in stationary segments. We thus derive the existence of such equivalence relations on the space of time series, such that the quotient spaces can be equipped with a metrizable topology. Next, we illustrate specifically how to define and compute such distances among a collection of time series and perform clustering and additional analysis thereon. Then, we apply these insights to analyze air quality data across New South Wales, Australia, during the 2019-2020 bushfires. There, we investigate structural similarity with respect to this data and identify locations that were impacted anonymously by the fires relative to their location. This may have implications regarding the appropriate management of resources to avoid gaps in the defense against future fires.
相關內容
The recent promotion of sustainable urban planning combined with a growing need for public interventions to improve well-being and health have led to an increased collective interest for green spaces in and around cities. In particular, parks have proven a wide range of benefits in urban areas. This also means inequities in park accessibility may contribute to health inequities. In this work, we showcase the application of classic tools from Operations Research to assist decision-makers to improve parks' accessibility, distribution and design. Given the context of public decision-making, we are particularly concerned with equity and environmental justice, and are focused on an advanced assessment of users' behavior through a spatial interaction model. We present a two-stage fair facility location and design model, which serves as a template model to assist public decision-makers at the city-level for the planning of urban green spaces. The first-stage of the optimization model is about the optimal city-budget allocation to neighborhoods based on a data exposing inequality attributes. The second-stage seeks the optimal location and design of parks for each neighborhood, and the objective consists of maximizing the total expected probability of individuals visiting parks. We show how to reformulate the latter as a mixed-integer linear program. We further introduce a clustering method to reduce the size of the problem and determine a close to optimal solution within reasonable time. The model is tested using the case study of the city of Montreal and comparative results are discussed in detail to justify the performance of the model.
Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit, analyze and generalize this result. The chosen framework allows for a synthetic approach to computability theory, exploiting that, externally, all functions definable in constructive type theory can be shown computable. We then build on this viewpoint and furthermore internalize it by assuming a version of Church's thesis, which expresses that any function on natural numbers is representable by a formula in PA. This assumption provides for a conveniently abstract setup to carry out rigorous computability arguments, even in the theorem's mechanization. Concretely, we constructivize several classical proofs and present one inherently constructive rendering of Tennenbaum's theorem, all following arguments from the literature. Concerning the classical proofs in particular, the constructive setting allows us to highlight differences in their assumptions and conclusions which are not visible classically. All versions are accompanied by a unified mechanization in the Coq proof assistant.
Multi-Object Tracking (MOT) has gained extensive attention in recent years due to its potential applications in traffic and pedestrian detection. We note that tracking by detection may suffer from errors generated by noise detectors, such as an imprecise bounding box before the occlusions, and observed that in most tracking scenarios, objects tend to move and lost within specific locations. To counter this, we present a novel tracker to deal with the bad detector and occlusions. Firstly, we proposed a location-wise sub-region recognition method which equally divided the frame, which we called mesh. Then we proposed corresponding location-wise loss management strategies and different matching strategies. The resulting Mesh-SORT, ablation studies demonstrate its effectiveness and made 3% fragmentation 7.2% ID switches drop and 0.4% MOTA improvement compared to the baseline on MOT17 datasets. Finally, we analyze its limitation on the specific scene and discussed what future works can be extended.
The geometric median of a tuple of vectors is the vector that minimizes the sum of Euclidean distances to the vectors of the tuple. Classically called the Fermat-Weber problem and applied to facility location, it has become a major component of the robust learning toolbox. It is typically used to aggregate the (processed) inputs of different data providers, whose motivations may diverge, especially in applications like content moderation. Interestingly, as a voting system, the geometric median has well-known desirable properties: it is a provably good average approximation, it is robust to a minority of malicious voters, and it satisfies the "one voter, one unit force" fairness principle. However, what was not known is the extent to which the geometric median is strategyproof. Namely, can a strategic voter significantly gain by misreporting their preferred vector? We prove in this paper that, perhaps surprisingly, the geometric median is not even $\alpha$-strategyproof, where $\alpha$ bounds what a voter can gain by deviating from truthfulness. But we also prove that, in the limit of a large number of voters with i.i.d. preferred vectors, the geometric median is asymptotically $\alpha$-strategyproof. We show how to compute this bound $\alpha$. We then generalize our results to voters who care more about some dimensions. Roughly, we show that, if some dimensions are more polarized and regarded as more important, then the geometric median becomes less strategyproof. Interestingly, we also show how the skewed geometric medians can improve strategyproofness. Nevertheless, if voters care differently about different dimensions, we prove that no skewed geometric median can achieve strategyproofness for all. Overall, our results constitute a coherent set of insights into the extent to which the geometric median is suitable to aggregate high-dimensional disagreements.
In oncology dose-finding trials, due to staggered enrollment, it might be desirable to make dose-assignment decisions in real-time in the presence of pending toxicity outcomes, for example, when the dose-limiting toxicity is late-onset. Patients' time-to-event information may be utilized to facilitate such decisions. We review statistical frameworks for time-to-event modeling in dose-finding trials and summarize existing designs into two classes: TITE designs and POD designs. TITE designs are based on inference on toxicity probabilities, while POD designs are based on inference on dose-finding decisions. These two classes of designs contain existing individual designs as special cases and also give rise to new designs. We discuss and study the theoretical properties of these designs, including large-sample convergence properties, coherence principles, and the underlying decision rules. To facilitate the use of these designs in practice, we introduce efficient computational algorithms and review common practical considerations, such as safety rules and suspension rules. Finally, the operating characteristics of several designs are evaluated and compared through computer simulations.
Background: Outcome measures that are count variables with excessive zeros are common in health behaviors research. There is a lack of empirical data about the relative performance of prevailing statistical models when outcomes are zero-inflated, particularly compared with recently developed approaches. Methods: The current simulation study examined five commonly used analytical approaches for count outcomes, including two linear models (with outcomes on raw and log-transformed scales, respectively) and three count distribution-based models (i.e., Poisson, negative binomial, and zero-inflated Poisson (ZIP) models). We also considered the marginalized zero-inflated Poisson (MZIP) model, a novel alternative that estimates the effects on overall mean while adjusting for zero-inflation. Extensive simulations were conducted to evaluate their the statistical power and Type I error rate across various data conditions. Results: Under zero-inflation, the Poisson model failed to control the Type I error rate, resulting in higher than expected false positive results. When the intervention effects on the zero (vs. non-zero) and count parts were in the same direction, the MZIP model had the highest statistical power, followed by the linear model with outcomes on raw scale, negative binomial model, and ZIP model. The performance of a linear model with a log-transformed outcome variable was unsatisfactory. When only one of the effects on the zero (vs. non-zero) part and the count part existed, the ZIP model had the highest statistical power. Conclusions: The MZIP model demonstrated better statistical properties in detecting true intervention effects and controlling false positive results for zero-inflated count outcomes. This MZIP model may serve as an appealing analytical approach to evaluating overall intervention effects in studies with count outcomes marked by excessive zeros.
We consider the problem of finding the matching map between two sets of $d$-dimensional noisy feature-vectors. The distinctive feature of our setting is that we do not assume that all the vectors of the first set have their corresponding vector in the second set. If $n$ and $m$ are the sizes of these two sets, we assume that the matching map that should be recovered is defined on a subset of unknown cardinality $k^*\le \min(n,m)$. We show that, in the high-dimensional setting, if the signal-to-noise ratio is larger than $5(d\log(4nm/\alpha))^{1/4}$, then the true matching map can be recovered with probability $1-\alpha$. Interestingly, this threshold does not depend on $k^*$ and is the same as the one obtained in prior work in the case of $k = \min(n,m)$. The procedure for which the aforementioned property is proved is obtained by a data-driven selection among candidate mappings $\{\hat\pi_k:k\in[\min(n,m)]\}$. Each $\hat\pi_k$ minimizes the sum of squares of distances between two sets of size $k$. The resulting optimization problem can be formulated as a minimum-cost flow problem, and thus solved efficiently. Finally, we report the results of numerical experiments on both synthetic and real-world data that illustrate our theoretical results and provide further insight into the properties of the algorithms studied in this work.
Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.
In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.
Multi-object tracking (MOT) is a crucial component of situational awareness in military defense applications. With the growing use of unmanned aerial systems (UASs), MOT methods for aerial surveillance is in high demand. Application of MOT in UAS presents specific challenges such as moving sensor, changing zoom levels, dynamic background, illumination changes, obscurations and small objects. In this work, we present a robust object tracking architecture aimed to accommodate for the noise in real-time situations. We propose a kinematic prediction model, called Deep Extended Kalman Filter (DeepEKF), in which a sequence-to-sequence architecture is used to predict entity trajectories in latent space. DeepEKF utilizes a learned image embedding along with an attention mechanism trained to weight the importance of areas in an image to predict future states. For the visual scoring, we experiment with different similarity measures to calculate distance based on entity appearances, including a convolutional neural network (CNN) encoder, pre-trained using Siamese networks. In initial evaluation experiments, we show that our method, combining scoring structure of the kinematic and visual models within a MHT framework, has improved performance especially in edge cases where entity motion is unpredictable, or the data presents frames with significant gaps.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191