Complex networks are used to model many real-world systems. However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like POD can be used in such cases. However, these models are susceptible to perturbations in the input data. We propose an algorithmic framework that combines techniques from pattern recognition (PR) and stochastic filtering theory to enhance the output of such models. The results of our study show that our method can improve the accuracy of the surrogate model under perturbed inputs. Deep Neural Networks (DNNs) are susceptible to adversarial attacks. However, recent research has revealed that neural Ordinary Differential Equations (ODEs) exhibit robustness in specific applications. We benchmark our algorithmic framework with a Neural ODE-based approach as a reference.
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模式識別是一個成熟的、令人興奮的、快速發展的領域，它支撐著計算機視覺、圖像處理、文本和文檔分析以及神經網絡等相關領域的發展。它與機器學習非常相似，在生物識別、生物信息學、多媒體數據分析和最新的數據科學等新興領域也有應用。模式識別（Pattern Recognition）雜志成立于大約50年前，當時該領域剛剛出現計算機科學的早期。在這期間，它已大大擴大。只要這些論文的背景得到了清晰的解釋并以模式識別文獻為基礎，該雜志接受那些對模式識別理論、方法和在任何領域的應用做出原創貢獻的論文。
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Next Point-of-Interest (POI) recommendation is a critical task in location-based services that aim to provide personalized suggestions for the user's next destination. Previous works on POI recommendation have laid focused on modeling the user's spatial preference. However, existing works that leverage spatial information are only based on the aggregation of users' previous visited positions, which discourages the model from recommending POIs in novel areas. This trait of position-based methods will harm the model's performance in many situations. Additionally, incorporating sequential information into the user's spatial preference remains a challenge. In this paper, we propose Diff-POI: a Diffusion-based model that samples the user's spatial preference for the next POI recommendation. Inspired by the wide application of diffusion algorithm in sampling from distributions, Diff-POI encodes the user's visiting sequence and spatial character with two tailor-designed graph encoding modules, followed by a diffusion-based sampling strategy to explore the user's spatial visiting trends. We leverage the diffusion process and its reversed form to sample from the posterior distribution and optimized the corresponding score function. We design a joint training and inference framework to optimize and evaluate the proposed Diff-POI. Extensive experiments on four real-world POI recommendation datasets demonstrate the superiority of our Diff-POI over state-of-the-art baseline methods. Further ablation and parameter studies on Diff-POI reveal the functionality and effectiveness of the proposed diffusion-based sampling strategy for addressing the limitations of existing methods.
Permutation tests are widely recognized as robust alternatives to tests based on the normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this standing challenge, we develop a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2\alpha$ given any targeted level $\alpha$, for arbitrary fixed-designs and error distributions. We confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT), which also offers theoretical guarantees, PALMRT does not significantly compromise power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate their differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test, while CPT suffered from a drastic loss of power. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity.
Missing data frequently occurs in datasets across various domains, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the imputation method is scalable and the logic behind the imputation is explainable, which is especially difficult for complex methods that are, for example, based on deep learning. Based on these considerations, we propose a new algorithm named "conditional Distribution-based Imputation of Missing Values with Regularization" (DIMV). DIMV operates by determining the conditional distribution of a feature that has missing entries, using the information from the fully observed features as a basis. As will be illustrated via experiments in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods; (ii) fast and scalable; (iii) is explainable as coefficients in a regression model, allowing reliable and trustable analysis, makes it a suitable choice for critical domains where understanding is important such as in medical fields, finance, etc; (iv) can provide an approximated confidence region for the missing values in a given sample; (v) suitable for both small and large scale data; (vi) in many scenarios, does not require a huge number of parameters as deep learning approaches; (vii) handle multicollinearity in imputation effectively; and (viii) is robust to the normally distributed assumption that its theoretical grounds rely on.
This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable that controls the variance of the outgoing weights of that node. We make minimal assumptions on these per-node random variables: they are iid and their sum, in each layer, converges to some finite random variable in the infinite-width limit. Under this model, we show that each layer of the infinite-width neural network can be characterised by two simple quantities: a non-negative scalar parameter and a L\'evy measure on the positive reals. If the scalar parameters are strictly positive and the L\'evy measures are trivial at all hidden layers, then one recovers the classical Gaussian process (GP) limit, obtained with iid Gaussian weights. More interestingly, if the L\'evy measure of at least one layer is non-trivial, we obtain a mixture of Gaussian processes (MoGP) in the large-width limit. The behaviour of the neural network in this regime is very different from the GP regime. One obtains correlated outputs, with non-Gaussian distributions, possibly with heavy tails. Additionally, we show that, in this regime, the weights are compressible, and some nodes have asymptotically non-negligible contributions, therefore representing important hidden features. Many sparsity-promoting neural network models can be recast as special cases of our approach, and we discuss their infinite-width limits; we also present an asymptotic analysis of the pruning error. We illustrate some of the benefits of the MoGP regime over the GP regime in terms of representation learning and compressibility on simulated, MNIST and Fashion MNIST datasets.
This work proposes an adjacent-category autoregressive model for time series of ordinal variables. We apply this model to dendrochronological records to study the effect of climate on the intensity of spruce budworm defoliation during outbreaks in two sites in eastern Canada. The model's parameters are estimated using the maximum likelihood approach. We show that this estimator is consistent and asymptotically Gaussian distributed. We also propose a Portemanteau test for goodness-of-fit. Our study shows that the seasonal ranges of maximum daily temperatures in the spring and summer have a significant quadratic effect on defoliation. The study reveals that for both regions, a greater range of summer daily maximum temperatures is associated with lower levels of defoliation up to a threshold estimated at 22.7C (CI of 0-39.7C at 95%) in T\'emiscamingue and 21.8C (CI of 0-54.2C at 95%) for Matawinie. For Matawinie, a greater range in spring daily maximum temperatures increased defoliation, up to a threshold of 32.5C (CI of 0-80.0C). We also present a statistical test to compare the autoregressive parameter values between different fits of the model, which allows us to detect changes in the defoliation dynamics between the study sites in terms of their respective autoregression structures.
The inherent nature of patient data poses several challenges. Prevalent cases amass substantial longitudinal data owing to their patient volume and consistent follow-ups, however, longitudinal laboratory data are renowned for their irregularity, temporality, absenteeism, and sparsity; In contrast, recruitment for rare or specific cases is often constrained due to their limited patient size and episodic observations. This study employed self-supervised learning (SSL) to pretrain a generalized laboratory progress (GLP) model that captures the overall progression of six common laboratory markers in prevalent cardiovascular cases, with the intention of transferring this knowledge to aid in the detection of specific cardiovascular event. GLP implemented a two-stage training approach, leveraging the information embedded within interpolated data and amplify the performance of SSL. After GLP pretraining, it is transferred for TVR detection. The proposed two-stage training improved the performance of pure SSL, and the transferability of GLP exhibited distinctiveness. After GLP processing, the classification exhibited a notable enhancement, with averaged accuracy rising from 0.63 to 0.90. All evaluated metrics demonstrated substantial superiority (p < 0.01) compared to prior GLP processing. Our study effectively engages in translational engineering by transferring patient progression of cardiovascular laboratory parameters from one patient group to another, transcending the limitations of data availability. The transferability of disease progression optimized the strategies of examinations and treatments, and improves patient prognosis while using commonly available laboratory parameters. The potential for expanding this approach to encompass other diseases holds great promise.
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our method is substantially enhanced to improve irregularities in the model which are both inherent and induced. Furthermore, the system of coupled PDEs is strongly nonlinear and involves several time-dependent coefficients that include the first-order derivative of the early exercise boundary. These coefficients are approximated from a fourth-order analytical approximation which is derived using a regularized square-root function. The semi-discrete equation for the option value and delta sensitivity is obtained from a non-uniform fourth-order compact finite difference scheme. Fifth-order 5(4) Dormand-Prince time integration method is used to solve the coupled system of discrete equations. Enhancing the performance of our proposed method with local mesh refinement and adaptive strategies enables us to obtain highly accurate solution with very coarse space grids, hence reducing computational runtime substantially. We further verify the performance of our methodology as compared with some of the well-known and better-performing existing methods.
In this paper we establish limit theorems for power variations of stochastic processes controlled by fractional Brownian motions with Hurst parameter $H\leq 1/2$. We show that the power variations of such processes can be decomposed into the mix of several weighted random sums plus some remainder terms, and the convergences of power variations are dominated by different combinations of those weighted sums depending on whether $H<1/4$, $H=1/4$, or $H>1/4$. We show that when $H\geq 1/4$ the centered power variation converges stably at the rate $n^{-1/2}$, and when $H<1/4$ it converges in probability at the rate $n^{-2H}$. We determine the limit of the mixed weighted sum based on a rough path approach developed in \cite{LT20}.
Multiagent systems aim to accomplish highly complex learning tasks through decentralised consensus seeking dynamics and their use has garnered a great deal of attention in the signal processing and computational intelligence societies. This article examines the behaviour of multiagent networked systems with nonlinear filtering/learning dynamics. To this end, a general formulation for the actions of an agent in multiagent networked systems is presented and conditions for achieving a cohesive learning behaviour is given. Importantly, application of the so derived framework in distributed and federated learning scenarios are presented.
StreamBed is a capacity planning system for stream processing.It predicts, ahead of any production deployment, the resources that a query will require to process an incoming data rate sustainably, and the appropriate configuration of these resources. StreamBed builds a capacity planning model by piloting a series of runs of the target query in a small-scale, controlled testbed. We implement StreamBed for the popular Flink DSP engine. Our evaluation with large-scale queries of the Nexmark benchmark demonstrates that StreamBed can effectively and accurately predict capacity requirements for jobs spanning more than 1,000 cores using a testbed of only 48 cores.
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