Differential Granger causality, that is understanding how Granger causal relations differ between two related time series, is of interest in many scientific applications. Modeling each time series by a vector autoregressive (VAR) model, we propose a
new method to directly learn the difference between the corresponding transition matrices in high dimensions. Key to the new method is an estimating equation constructed based on the Yule-Walker equation that links the difference in transition matrices to the difference in the corresponding precision matrices. In contrast to separately estimating each transition matrix and then calculating the difference, the proposed direct estimation method only requires sparsity of the difference of the two VAR models, and hence allows hub nodes in each high-dimensional time series. The direct estimator is shown to be consistent in estimation and support recovery under mild assumptions. These results also lead to novel consistency results with potentially faster convergence rates for estimating differences between precision matrices of i.i.d observations under weaker assumptions than existing results. We evaluate the finite sample performance of the proposed method using simulation studies and an application to electroencephalogram (EEG) data.
In this short, we study sums of the shape $sum_{nleqslant x}{f([x/n])}/{[x/n]},$ where $f$ is Euler totient function $varphi$, Dedekind function $Psi$, sum-of-divisors function $sigma$ or the alternating sum-of-divisors function $beta.$ We improve pr
evious results when $f=varphi$ and derive new estimates when $f=Psi, f=sigma$ and $f=beta.$
In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola $mathscr{H}^{1}(1)$, of center at origin and radius $1$, in the $2$ dimensional Lorentz-Minkowski plane $mathbb{R}^{2}_{1}$ along an anisotropic in
verse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic curves converge smoothly to a piece of hyperbola of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $mathscr{H}^{1}(1)$, as time tends to infinity.
Tensor factorization has been proved as an efficient unsupervised learning approach for health data analysis, especially for computational phenotyping, where the high-dimensional Electronic Health Records (EHRs) with patients history of medical proce
dures, medications, diagnosis, lab tests, etc., are converted to meaningful and interpretable medical concepts. Federated tensor factorization distributes the tensor computation to multiple workers under the coordination of a central server, which enables jointly learning the phenotypes across multiple hospitals while preserving the privacy of the patient information. However, existing federated tensor factorization algorithms encounter the single-point-failure issue with the involvement of the central server, which is not only easily exposed to external attacks, but also limits the number of clients sharing information with the server under restricted uplink bandwidth. In this paper, we propose CiderTF, a communication-efficient decentralized generalized tensor factorization, which reduces the uplink communication cost by leveraging a four-level communication reduction strategy designed for a generalized tensor factorization, which has the flexibility of modeling different tensor distribution with multiple kinds of loss functions. Experiments on two real-world EHR datasets demonstrate that CiderTF achieves comparable convergence with the communication reduction up to 99.99%.
Representation learning on static graph-structured data has shown a significant impact on many real-world applications. However, less attention has been paid to the evolving nature of temporal networks, in which the edges are often changing over time
. The embeddings of such temporal networks should encode both graph-structured information and the temporally evolving pattern. Existing approaches in learning temporally evolving network representations fail to capture the temporal interdependence. In this paper, we propose Toffee, a novel approach for temporal network representation learning based on tensor decomposition. Our method exploits the tensor-tensor product operator to encode the cross-time information, so that the periodic changes in the evolving networks can be captured. Experimental results demonstrate that Toffee outperforms existing methods on multiple real-world temporal networks in generating effective embeddings for the link prediction tasks.
In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $mathbb{R}^{n+1}_{
1}$ along the inverse Gauss curvature flow (i.e., the evolving speed equals the $(-1/n)$-th power of the Gaussian curvature) with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of the spacelike graph of a positive constant function defined over the piece of $mathscr{H}^{n}(1)$ as time tends to infinity.
The COVID-19 pandemic significantly disrupted the educational sector. Faced with this life-threatening pandemic, educators had to swiftly pivot to an alternate form of course delivery without severely impacting the quality of the educational experien
ce. Following the transition to online learning, educators had to grapple with a host of challenges. With interrupted face-to-face delivery, limited access to state-of-the-art labs, barriers with educational technologies, challenges of academic integrity, and obstacles with remote teamwork and student participation, creative solutions were urgently needed. In this chapter, we provide a rationale for a variety of course delivery models at different stages of the pandemic and highlight the approaches we took to overcome some of the pressing challenges of remote education. We also discuss how we ensured that hands-on learning remains an integral part of engineering curricula, and we argue that some of the applied changes during the pandemic will likely serve as a catalyst for modernizing education.
Stroke is the top leading causes of death in China (Zhou et al. The Lancet 2019). A dataset from Shanxi Province is used to identify the risk of each patients at four states low/medium/high/attack and provide the state transition tendency through a S
HAP DeepExplainer. To improve the accuracy on an imbalance sample set, the Quadratic Interactive Deep Neural Network (QIDNN) model is first proposed by flexible selecting and appending of quadratic interactive features. The experimental results showed that the QIDNN model with 7 interactive features achieve the state-of-art accuracy $83.25%$. Blood pressure, physical inactivity, smoking, weight and total cholesterol are the top five important features. Then, for the sake of high recall on the most urgent state, attack state, the stroke occurrence prediction is taken as an auxiliary objective to benefit from multi-objective optimization. The prediction accuracy was promoted, meanwhile the recall of the attack state was improved by $24.9%$ (to $84.83%$) compared to QIDNN (from $67.93%$) with same features. The prediction model and analysis tool in this paper not only gave the theoretical optimized prediction method, but also provided the attribution explanation of risk states and transition direction of each patient, which provided a favorable tool for doctors to analyze and diagnose the disease.
Federated learning has emerged as an important paradigm for training machine learning models in different domains. For graph-level tasks such as graph classification, graphs can also be regarded as a special type of data samples, which can be collect
ed and stored in separate local systems. Similar to other domains, multiple local systems, each holding a small set of graphs, may benefit from collaboratively training a powerful graph mining model, such as the popular graph neural networks (GNNs). To provide more motivation towards such endeavors, we analyze real-world graphs from different domains to confirm that they indeed share certain graph properties that are statistically significant compared with random graphs. However, we also find that different sets of graphs, even from the same domain or same dataset, are non-IID regarding both graph structures and node features. To handle this, we propose a graph clustered federated learning (GCFL) framework that dynamically finds clusters of local systems based on the gradients of GNNs, and theoretically justify that such clusters can reduce the structure and feature heterogeneity among graphs owned by the local systems. Moreover, we observe the gradients of GNNs to be rather fluctuating in GCFL which impedes high-quality clustering, and design a gradient sequence-based clustering mechanism based on dynamic time warping (GCFL+). Extensive experimental results and in-depth analysis demonstrate the effectiveness of our proposed frameworks.
It is commonly seen that buses are blocked by the ones in front serving passengers and have to queue outside a curbside bus stop although there are vacant berths at the stop. The resultant bus delays degrade the service level of urban public transpor
tation. A potential solution is to reschedule the arrivals of the buses at the stop for full utilization of the berths with the aid of connected vehicle technologies. This study proposes a mixed-integer linear programming model to optimize the scheduling of bus arrivals and the bus-berth matching at a curbside stop under connected vehicle environment. The objective is the minimization of the bus delays weighted by the number of passengers on the buses. Bus arrival times at the stop and the assignment of berths are optimized together with bus departure times from the stop. Bus punctuality is also taken into consideration. The proposed model could be applied dynamically to cater to time-varying traffic conditions. Numerical studies validate the advantages of the proposed model over the first-come-first-service strategy and the relaxed model without bus punctuality in terms of weighted bus delays and bus punctuality. Sensitivity analyses show that: 1) the proposed model is robust to the fluctuation of bus service time; and 2) a smaller number of berths may be preferred on condition that the bus demand does not exceed the stop capacity.
