Computer Science

We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD truncation, and works well down to the very sparse regime where the edge density has constant order. Our analysis is based on a Master Theorem describing sharp asymptotics for isolated eigenvalues/eigenvectors of sparse, non-symmetric matrices with independent entries. We also describe the limiting distribution of the entries of these eigenvectors; in the task of digraph clustering with spectral embeddings, we provide numerical evidence for the superiority of Gaussian Mixture clustering over the widely used k-means algorithm.

Human Activity Recognition (HAR) is one of the key applications of health monitoring that requires continuous use of wearable devices to track daily activities. State-of-the-art works using wearable devices have been following fog/cloud computing architecture where the data is classified at the mobile phones/remote servers. This kind of approach suffers from energy, latency, and privacy issues. Therefore, we follow edge computing architecture where the wearable device solutions provide adequate performance while being energy and memory-efficient. This paper proposes an Adaptive CNN for energy-efficient HAR (AHAR) suitable for low-power edge devices. AHAR uses a novel adaptive architecture that selects a portion of the baseline architecture to use during the inference phase. We validate our methodology in classifying locomotion activities from two datasets- Opportunity and w-HAR. Compared to the fog/cloud computing approaches for the Opportunity dataset, our baseline and adaptive architecture shows a comparable weighted F1 score of 91.79%, and 91.57%, respectively. For the w-HAR dataset, our baseline and adaptive architecture outperforms the state-of-the-art works with a weighted F1 score of 97.55%, and 97.64%, respectively. Evaluation on real hardware shows that our baseline architecture is significantly energy-efficient (422.38x less) and memory-efficient (14.29x less) compared to the works on the Opportunity dataset. For the w-HAR dataset, our baseline architecture requires 2.04x less energy and 2.18x less memory compared to the state-of-the-art work. Moreover, experimental results show that our adaptive architecture is 12.32% (Opportunity) and 11.14% (w-HAR) energy-efficient than our baseline while providing similar (Opportunity) or better (w-HAR) performance with no significant memory overhead.

Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a drawback in sensitivity to parameter re-scaling which leaves the loss unaffected, leading to weakening of the connection between sharpness and generalization gap. In this paper, we introduce the concept of adaptive sharpness which is scale-invariant and propose the corresponding generalization bound. We suggest a novel learning method, adaptive sharpness-aware minimization (ASAM), utilizing the proposed generalization bound. Experimental results in various benchmark datasets show that ASAM contributes to significant improvement of model generalization performance.

We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it to Abelian semigroup operations using the characterization of associative symmetric polynomials. Both models take advantage of the analytic invertibility of invertible neural networks. For each case, by repeating the binary operations, we can represent a function for multiset input thanks to the algebraic structure. Naturally, our multiset architecture has size-generalization ability, which has not been obtained in existing methods. Further, we present modeling the Abelian group operation itself is useful in a word analogy task. We train our models over fixed word embeddings and demonstrate improved performance over the original word2vec and another naive learning method.

Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known causal decision making and prediction problems associated with those real-world applications. Recently, recursive causal discovery algorithms have gained particular attention among the research community due to their ability to provide good results by using Conditional Independent (CI) tests in smaller sub-problems. However, each of such algorithms needs a refinement function to remove undesired causal relations of the discovered graphs. Notably, with the increase of the problem size, the computation cost (i.e., the number of CI-tests) of the refinement function makes an algorithm expensive to deploy in practice. This paper proposes a generic causal structure refinement strategy that can locate the undesired relations with a small number of CI-tests, thus speeding up the algorithm for large and complex problems. We theoretically prove the correctness of our algorithm. We then empirically evaluate its performance against the state-of-the-art algorithms in terms of solution quality and completion time in synthetic and real datasets.

Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function that maps a set of node representations into a compact form. A simple sum or average over all node representations considers all node features equally without consideration of their task relevance, and any structural dependencies among them. Recently proposed hierarchical graph pooling methods, on the other hand, may yield the same representation for two different graphs that are distinguished by the Weisfeiler-Lehman test, as they suboptimally preserve information from the node features. To tackle these limitations of existing graph pooling methods, we first formulate the graph pooling problem as a multiset encoding problem with auxiliary information about the graph structure, and propose a Graph Multiset Transformer (GMT) which is a multi-head attention based global pooling layer that captures the interaction between nodes according to their structural dependencies. We show that GMT satisfies both injectiveness and permutation invariance, such that it is at most as powerful as the Weisfeiler-Lehman graph isomorphism test. Moreover, our methods can be easily extended to the previous node clustering approaches for hierarchical graph pooling. Our experimental results show that GMT significantly outperforms state-of-the-art graph pooling methods on graph classification benchmarks with high memory and time efficiency, and obtains even larger performance gain on graph reconstruction and generation tasks.

Some data analysis applications comprise datasets, where explanatory variables are expensive or tedious to acquire, but auxiliary data are readily available and might help to construct an insightful training set. An example is neuroimaging research on mental disorders, specifically learning a diagnosis/prognosis model based on variables derived from expensive Magnetic Resonance Imaging (MRI) scans, which often requires large sample sizes. Auxiliary data, such as demographics, might help in selecting a smaller sample that comprises the individuals with the most informative MRI scans. In active learning literature, this problem has not yet been studied, despite promising results in related problem settings that concern the selection of instances or instance-feature pairs. Therefore, we formulate this complementary problem of Active Selection of Classification Features (ASCF): Given a primary task, which requires to learn a model f: x-> y to explain/predict the relationship between an expensive-to-acquire set of variables x and a class label y. Then, the ASCF-task is to use a set of readily available selection variables z to select these instances, that will improve the primary task's performance most when acquiring their expensive features z and including them to the primary training set. We propose two utility-based approaches for this problem, and evaluate their performance on three public real-world benchmark datasets. In addition, we illustrate the use of these approaches to efficiently acquire MRI scans in the context of neuroimaging research on mental disorders, based on a simulated study design with real MRI data.

Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends crucially on the search of optimal slicing directions to discriminate between two distributions. Unfortunately, previous gradient-based optimisation approaches for this task return sub-optimal results: they are computationally expensive, sensitive to initialization, and they lack theoretical guarantees for convergence. We address these issues in two steps. First, we provide theoretical results stating that the requirement of using optimal slicing directions in the kernelized version of SSD can be relaxed, validating the resulting discrepancy with finite random slicing directions. Second, given that good slicing directions are crucial for practical performance, we propose a fast algorithm for finding such slicing directions based on ideas of active sub-space construction and spectral decomposition. Experiments on goodness-of-fit tests and model learning show that our approach achieves both improved performance and faster convergence. Especially, we demonstrate a 14-80x speed-up in goodness-of-fit tests when comparing with gradient-based alternatives.

Many cases exist in which a black-box function f with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental} variables that have random variation following a certain distribution P . In such cases, an important task is to find the range of design variables $\bm x$ such that the function $f(\bm x, \bm w)$ has the desired properties by incorporating the random variation of the environmental variables $\bm w$. A natural measure of robustness is the probability that $f(\bm x, \bm w)$ exceeds a given threshold h , which is known as the \emph{probability threshold robustness} (PTR) measure in the literature on robust optimization. However, this robustness measure cannot be correctly evaluated when the distribution P is unknown. In this study, we addressed this problem by considering the \textit{distributionally robust PTR} (DRPTR) measure, which considers the worst-case PTR within given candidate distributions. Specifically, we studied the problem of efficiently identifying a reliable set H , which is defined as a region in which the DRPTR measure exceeds a certain desired probability α , which can be interpreted as a level set estimation (LSE) problem for DRPTR. We propose a theoretically grounded and computationally efficient active learning method for this problem. We show that the proposed method has theoretical guarantees on convergence and accuracy, and confirmed through numerical experiments that the proposed method outperforms existing methods.

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which represent a major class of physics-enhanced neural networks. We introduce a class of HNNs capable of adaptable prediction of nonlinear physical systems: by training the neural network based on time series from a small number of bifurcation-parameter values of the target Hamiltonian system, the HNN can predict the dynamical states at other parameter values, where the network has not been exposed to any information about the system at these parameter values. The architecture of the HNN differs from the previous ones in that we incorporate an input parameter channel, rendering the HNN parameter--cognizant. We demonstrate, using paradigmatic Hamiltonian systems, that training the HNN using time series from as few as four parameter values bestows the neural machine with the ability to predict the state of the target system in an entire parameter interval. Utilizing the ensemble maximum Lyapunov exponent and the alignment index as indicators, we show that our parameter-cognizant HNN can successfully predict the route of transition to chaos. Physics-enhanced machine learning is a forefront area of research, and our adaptable HNNs provide an approach to understanding machine learning with broad applications.