We extend the graph convolutional network method for deep learning on graph data to higher order in terms of neighboring nodes. In order to construct representations for a node in a graph, in addition to the features of the node and its immediate neighboring nodes, we also include more distant nodes in the calculations. In experimenting with a number of publicly available citation graph datasets, we show that this higher order neighbor visiting pays off by outperforming the original model especially when we have a limited number of available labeled data points for the training of the model.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

It has been observed in practice that applying pruning-at-initialization methods to neural networks and training the sparsified networks can not only retain the testing performance of the original dense models, but also sometimes even slightly boost the generalization performance. Theoretical understanding for such experimental observations are yet to be developed. This work makes the first attempt to study how different pruning fractions affect the model's gradient descent dynamics and generalization. Specifically, this work considers a classification task for overparameterized two-layer neural networks, where the network is randomly pruned according to different rates at the initialization. It is shown that as long as the pruning fraction is below a certain threshold, gradient descent can drive the training loss toward zero and the network exhibits good generalization performance. More surprisingly, the generalization bound gets better as the pruning fraction gets larger. To complement this positive result, this work further shows a negative result: there exists a large pruning fraction such that while gradient descent is still able to drive the training loss toward zero (by memorizing noise), the generalization performance is no better than random guessing. This further suggests that pruning can change the feature learning process, which leads to the performance drop of the pruned neural network.

This paper presents CS-Insights, an interactive web application to analyze computer science publications from DBLP through multiple perspectives. The dedicated interfaces allow its users to identify trends in research activity, productivity, accessibility, author's productivity, venues' statistics, topics of interest, and the impact of computer science research on other fields. CS-Insightsis publicly available, and its modular architecture can be easily adapted to domains other than computer science.

Objectives: To quantify the magnitude of spinal deformity in adolescent idiopathic scoliosis (AIS), the Cobb angle is measured on X-ray images of the spine. Continuous exposure to X-ray radiation to follow-up the progression of scoliosis may lead to negative side effects on patients. Furthermore, manual measurement of the Cobb angle could lead to up to 10{\deg} or more of a difference due to intra/inter observer variation. Therefore, the objective of this study is to identify the Cobb angle by developing an automated radiation-free model, using Machine learning algorithms. Methods: Thirty participants with lumbar/thoracolumbar AIS (15{\deg} < Cobb angle < 66{\deg}) performed gait cycles. The lumbosacral (L5-S1) joint efforts during six gait cycles of participants were used as features to feed training algorithms. Various regression algorithms were implemented and run. Results: The decision tree regression algorithm achieved the best result with the mean absolute error equal to 4.6{\deg} of averaged 10-fold cross-validation. Conclusions: This study shows that the lumbosacral joint efforts during gait as radiation-free data are capable to identify the Cobb angle by using Machine learning algorithms. The proposed model can be considered as an alternative, radiation-free method to X-ray radiography to assist clinicians in following-up the progression of AIS.

This work studies training one-hidden-layer overparameterized ReLU networks via gradient descent in the neural tangent kernel (NTK) regime, where the networks' biases are initialized to some constant rather than zero. The tantalizing benefit of such initialization is that the neural network will provably have sparse activation through the entire training process, which enables fast training procedures. The first set of results characterizes the convergence of gradient descent training. Surprisingly, it is shown that the network after sparsification can achieve as fast convergence as the dense network, in comparison to the previous work indicating that the sparse networks converge slower. Further, the required width is improved to ensure gradient descent can drive the training error towards zero at a linear rate. Secondly, the networks' generalization is studied: a width-sparsity dependence is provided which yields a sparsity-dependent Rademacher complexity and generalization bound. To our knowledge, this is the first sparsity-dependent generalization result via Rademacher complexity. Lastly, this work further studies the least eigenvalue of the limiting NTK. Surprisingly, while it is not shown that trainable biases are necessary, trainable bias, which is enabled by our improved analysis scheme, helps to identify a nice data-dependent region where a much finer analysis of the NTK's smallest eigenvalue can be conducted. This leads to a much sharper lower bound on the NTK's smallest eigenvalue than the one previously known and, consequently, an improved generalization bound.

Off-policy evaluation (OPE) aims to accurately evaluate the performance of counterfactual policies using only offline logged data. Although many estimators have been developed, there is no single estimator that dominates the others, because the estimators' accuracy can vary greatly depending on a given OPE task such as the evaluation policy, number of actions, and noise level. Thus, the data-driven estimator selection problem is becoming increasingly important and can have a significant impact on the accuracy of OPE. However, identifying the most accurate estimator using only the logged data is quite challenging because the ground-truth estimation accuracy of estimators is generally unavailable. This paper studies this challenging problem of estimator selection for OPE for the first time. In particular, we enable an estimator selection that is adaptive to a given OPE task, by appropriately subsampling available logged data and constructing pseudo policies useful for the underlying estimator selection task. Comprehensive experiments on both synthetic and real-world company data demonstrate that the proposed procedure substantially improves the estimator selection compared to a non-adaptive heuristic.

We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures. In contrast to popular approaches that recover the $K$ models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, Mix-IRLS succeeds in a broad range of settings where other methods fail. These include imbalanced mixtures, small sample sizes, presence of outliers, and an unknown number of models $K$. In addition, Mix-IRLS outperforms competing methods on several real-world datasets, in some cases by a large margin. We complement our empirical results by deriving a recovery guarantee for Mix-IRLS, which highlights its advantage on imbalanced mixtures.

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. With this model, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the constant parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.

Transformers have achieved great success in several domains, including Natural Language Processing and Computer Vision. However, its application to real-world graphs is less explored, mainly due to its high computation cost and its poor generalizability caused by the lack of enough training data in the graph domain. To fill in this gap, we propose a scalable Transformer-like dynamic graph learning method named Dynamic Graph Transformer (DyFormer) with spatial-temporal encoding to effectively learn graph topology and capture implicit links. To achieve efficient and scalable training, we propose temporal-union graph structure and its associated subgraph-based node sampling strategy. To improve the generalization ability, we introduce two complementary self-supervised pre-training tasks and show that jointly optimizing the two pre-training tasks results in a smaller Bayesian error rate via an information-theoretic analysis. Extensive experiments on the real-world datasets illustrate that DyFormer achieves a consistent 1%-3% AUC gain (averaged over all time steps) compared with baselines on all benchmarks.