With the huge success of deep learning, other machine learning paradigms have had to take back seat. Yet other models, particularly rule-based, are more readable and explainable and can even be competitive when labelled data is not abundant. However, most of the existing rule-based classifiers suffer from the production of a large number of classification rules, affecting the model readability. This hampers the classification accuracy as noisy rules might not add any useful informationfor classification and also lead to longer classification time. In this study, we propose SigD2 which uses a novel, two-stage pruning strategy which prunes most of the noisy, redundant and uninteresting rules and makes the classification model more accurate and readable. To make SigDirect more competitive with the most prevalent but uninterpretable machine learning-based classifiers like neural networks and support vector machines, we propose bagging and boosting on the ensemble of the SigDirect classifier. The results of the proposed algorithms are quite promising and we are able to obtain a minimal set of statistically significant rules for classification without jeopardizing the classification accuracy. We use 15 UCI datasets and compare our approach with eight existing systems.The SigD2 and boosted SigDirect (ACboost) ensemble model outperform various state-of-the-art classifiers not only in terms of classification accuracy but also in terms of the number of rules.

The problem of linking functional connectomics to behavior is extremely challenging due to the complex interactions between the two distinct, but related, data domains. We propose a coupled manifold optimization framework which projects fMRI data onto a low dimensional matrix manifold common to the cohort. The patient specific loadings simultaneously map onto a behavioral measure of interest via a second, non-linear, manifold. By leveraging the kernel trick, we can optimize over a potentially infinite dimensional space without explicitly computing the embeddings. As opposed to conventional manifold learning, which assumes a fixed input representation, our framework directly optimizes for embedding directions that predict behavior. Our optimization algorithm combines proximal gradient descent with the trust region method, which has good convergence guarantees. We validate our framework on resting state fMRI from fifty-eight patients with Autism Spectrum Disorder using three distinct measures of clinical severity. Our method outperforms traditional representation learning techniques in a cross validated setting, thus demonstrating the predictive power of our coupled objective.

Wireless connectivity is instrumental in enabling scalable federated learning (FL), yet wireless channels bring challenges for model training, in which channel randomness perturbs each worker's model update while multiple workers' updates incur significant interference under limited bandwidth. To address these challenges, in this work we formulate a novel constrained optimization problem, and propose an FL framework harnessing wireless channel perturbations and interference for improving privacy, bandwidth-efficiency, and scalability. The resultant algorithm is coined analog federated ADMM (A-FADMM) based on analog transmissions and the alternating direct method of multipliers (ADMM). In A-FADMM, all workers upload their model updates to the parameter server (PS) using a single channel via analog transmissions, during which all models are perturbed and aggregated over-the-air. This not only saves communication bandwidth, but also hides each worker's exact model update trajectory from any eavesdropper including the honest-but-curious PS, thereby preserving data privacy against model inversion attacks. We formally prove the convergence and privacy guarantees of A-FADMM for convex functions under time-varying channels, and numerically show the effectiveness of A-FADMM under noisy channels and stochastic non-convex functions, in terms of convergence speed and scalability, as well as communication bandwidth and energy efficiency.

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various applications. However, in GPR, how the features of an input contribute to its prediction cannot be interpreted. Herein, we propose GPR with local explanation, which reveals the feature contributions to the prediction of each sample, while maintaining the predictive performance of GPR. In the proposed model, both the prediction and explanation for each sample are performed using an easy-to-interpret locally linear model. The weight vector of the locally linear model is assumed to be generated from multivariate Gaussian process priors. The hyperparameters of the proposed models are estimated by maximizing the marginal likelihood. For a new test sample, the proposed model can predict the values of its target variable and weight vector, as well as their uncertainties, in a closed form. Experimental results on various benchmark datasets verify that the proposed model can achieve predictive performance comparable to those of GPR and superior to that of existing interpretable models, and can achieve higher interpretability than them, both quantitatively and qualitatively.

Attributed graph embedding, which learns vector representations from graph topology and node features, is a challenging task for graph analysis. Recently, methods based on graph convolutional networks (GCNs) have made great progress on this task. However,existing GCN-based methods have three major drawbacks. Firstly,our experiments indicate that the entanglement of graph convolutional filters and weight matrices will harm both the performance and robustness. Secondly, we show that graph convolutional filters in these methods reveal to be special cases of generalized Laplacian smoothing filters, but they do not preserve optimal low-pass characteristics. Finally, the training objectives of existing algorithms are usually recovering the adjacency matrix or feature matrix, which are not always consistent with real-world applications. To address these issues, we propose Adaptive Graph Encoder (AGE), a novel attributed graph embedding framework. AGE consists of two modules: (1) To better alleviate the high-frequency noises in the node features, AGE first applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an adaptive encoder that iteratively strengthens the filtered features for better node embeddings. We conduct experiments using four public benchmark datasets to validate AGE on node clustering and link prediction tasks. Experimental results show that AGE consistently outperforms state-of-the-art graph embedding methods considerably on these tasks.

Spatial point processes can be found in a range of applications from astronomy and biology to ecology and criminology. These processes can be characterized by a nonnegative intensity function λpxq which predicts the number of events that occur across space parameterized byxPX [8, 4]. A standard approach to estimate the intensity function of a process is to use nonparametric kernel density-based methods [6, 7]. These smoothing techniques require, however, careful tuning of kernel bandwidth parameters and are, more importantly, subject to selection biases. That is, in regions where no events have been observed, the intensity is inferred to be zero and no measure is readily available for a user to assess the uncertainty of such predictions. More advanced methods infer the intensity by assuming a parameterized model of the data-generating process, such as inhomogeneous Poisson point process models.

Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge - many recently proposed scalable GNN approaches rely on an expensive message-passing procedure to propagate information through the graph. We present the PPRGo model which utilizes an efficient approximation of information diffusion in GNNs resulting in significant speed gains while maintaining state-of-the-art prediction performance. In addition to being faster, PPRGo is inherently scalable, and can be trivially parallelized for large datasets like those found in industry settings. We demonstrate that PPRGo outperforms baselines in both distributed and single-machine training environments on a number of commonly used academic graphs. To better analyze the scalability of large-scale graph learning methods, we introduce a novel benchmark graph with 12.4 million nodes, 173 million edges, and 2.8 million node features. We show that training PPRGo from scratch and predicting labels for all nodes in this graph takes under 2 minutes on a single machine, far outpacing other baselines on the same graph. We discuss the practical application of PPRGo to solve large-scale node classification problems at Google.

Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold. In this paper, we further improve on existing variance reduction methods for non-convex Riemannian optimization, including R-SVRG and R-SRG/R-SPIDER with batch size adaptation. We show that this strategy can achieve lower total complexities for optimizing both general non-convex and gradient dominated functions under both finite-sum and online settings. As a result, we also provide simpler convergence analysis for R-SVRG and improve complexity bounds for R-SRG under finite-sum setting. Specifically, we prove that R-SRG achieves the same near-optimal complexity as R-SPIDER without requiring a small step size. Empirical experiments on a variety of tasks demonstrate effectiveness of proposed adaptive batch size scheme.

In this paper, we analyze the convergence rate of the gradient temporal difference learning (GTD) family of algorithms. Previous analyses of this class of algorithms use ODE techniques to prove asymptotic convergence, and to the best of our knowledge, no finite-sample analysis has been done. Moreover, there has been not much work on finite-sample analysis for convergent off-policy reinforcement learning algorithms. In this paper, we formulate GTD methods as stochastic gradient algorithms w.r.t.~a primal-dual saddle-point objective function, and then conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Two revised algorithms are also proposed, namely projected GTD2 and GTD2-MP, which offer improved convergence guarantees and acceleration, respectively. The results of our theoretical analysis show that the GTD family of algorithms are indeed comparable to the existing LSTD methods in off-policy learning scenarios.

We develop and analyze a projected particle Langevin optimization method to learn the distribution in the Sch\"{o}nberg integral representation of the radial basis functions from training samples. More specifically, we characterize a distributionally robust optimization method with respect to the Wasserstein distance to optimize the distribution in the Sch\"{o}nberg integral representation. To provide theoretical performance guarantees, we analyze the scaling limits of a projected particle online (stochastic) optimization method in the mean-field regime. In particular, we prove that in the scaling limits, the empirical measure of the Langevin particles converges to the law of a reflected It\^{o} diffusion-drift process. Moreover, the drift is also a function of the law of the underlying process. Using It\^{o} lemma for semi-martingales and Grisanov's change of measure for the Wiener processes, we then derive a Mckean-Vlasov type partial differential equation (PDE) with Robin boundary conditions that describes the evolution of the empirical measure of the projected Langevin particles in the mean-field regime. In addition, we establish the existence and uniqueness of the steady-state solutions of the derived PDE in the weak sense. We apply our learning approach to train radial kernels in the kernel locally sensitive hash (LSH) functions, where the training data-set is generated via a $k$-mean clustering method on a small subset of data-base. We subsequently apply our kernel LSH with a trained kernel for image retrieval task on MNIST data-set, and demonstrate the efficacy of our kernel learning approach. We also apply our kernel learning approach in conjunction with the kernel support vector machines (SVMs) for classification of benchmark data-sets.