Alternating Direction Method of Multipliers (ADMM) has become a widely used optimization method for convex problems, particularly in the context of data mining in which large optimization problems are often encountered. ADMM has several desirable properties, including the ability to decompose large problems into smaller tractable sub-problems and ease of parallelization, that are essential in these scenarios. The most common form of ADMM is the two-block, in which two sets of primal variables are updated alternatingly. Recent years have seen advances in multi-block ADMM, which update more than two blocks of primal variables sequentially. In this paper, we study the empirical question: {\em Is two-block ADMM always comparable with sequential multi-block ADMM solving an equivalent problem?} In the context of optimization problems arising in multi-task learning, through a comprehensive set of experiments we surprisingly show that multi-block ADMM consistently outperformed two-block ADMM on optimization performance, and as a consequence on prediction performance, across all datasets and for the entire range of dual step sizes. Our results have an important practical implication: rather than simply using the popular two-block ADMM, one may considerably benefit from experimenting with multi-block ADMM applied to an equivalent problem.

The time series cluster kernel (TCK) provides a powerful tool for analysing multivariate time series subject to missing data. TCK is designed using an ensemble learning approach in which Bayesian mixture models form the base models. Because of the Bayesian approach, TCK can naturally deal with missing values without resorting to imputation and the ensemble strategy ensures robustness to hyperparameters, making it particularly well suited for unsupervised learning. However, TCK assumes missing at random and that the underlying missingness mechanism is ignorable, i.e. uninformative, an assumption that does not hold in many real-world applications, such as e.g. medicine. To overcome this limitation, we present a kernel capable of exploiting the potentially rich information in the missing values and patterns, as well as the information from the observed data. In our approach, we create a representation of the missing pattern, which is incorporated into mixed mode mixture models in such a way that the information provided by the missing patterns is effectively exploited. Moreover, we also propose a semi-supervised kernel, capable of taking advantage of incomplete label information to learn more accurate similarities. Experiments on benchmark data, as well as a real-world case study of patients described by longitudinal electronic health record data who potentially suffer from hospital-acquired infections, demonstrate the effectiveness of the proposed methods.

Graph classification is practically important in many domains. To solve this problem, one usually calculates a low-dimensional representation for each node in the graph with supervised or unsupervised approaches. Most existing approaches consider all the edges between nodes while overlooking whether the edge will brings positive or negative influence to the node representation learning. In many real-world applications, however, some connections among the nodes can be noisy for graph convolution, and not all the edges deserve your attention. In this work, we distinguish the positive and negative impacts of the neighbors to the node in graph node classification, and propose to enhance the graph convolutional network by considering the labels between the neighbor edges. We present a novel GCN framework, called Label-aware Graph Convolutional Network (LAGCN), which incorporates the supervised and unsupervised learning by introducing the edge label predictor. As a general model, LAGCN can be easily adapted in various previous GCN and enhance their performance with some theoretical guarantees. Experimental results on multiple real-world datasets show that LAGCN is competitive against various state-of-the-art methods in graph classification.

We consider probabilistic programming for birth-death models of evolution and introduce a new widely-applicable inference method that combines an extension of the alive particle filter (APF) with automatic Rao-Blackwellization via delayed sampling. Birth-death models of evolution are an important family of phylogenetic models of the diversification processes that lead to evolutionary trees. Probabilistic programming languages (PPLs) give phylogeneticists a new and exciting tool: their models can be implemented as probabilistic programs with just a basic knowledge of programming. The general inference methods in PPLs reduce the need for external experts, allow quick prototyping and testing, and accelerate the development and deployment of new models. We show how these birth-death models can be implemented as simple programs in existing PPLs, and demonstrate the usefulness of the proposed inference method for such models. For the popular BiSSE model the method yields an increase of the effective sample size and the conditional acceptance rate by a factor of 30 in comparison with a standard bootstrap particle filter. Although concentrating on phylogenetics, the extended APF is a general inference method that shows its strength in situations where particles are often assigned zero weight. In the case when the weights are always positive, the extra cost of using the APF rather than the bootstrap particle filter is negligible, making our method a suitable drop-in replacement for the bootstrap particle filter in probabilistic programming inference.

Parking, matching, scheduling, and routing are common problems in train maintenance. In particular, train units are commonly maintained and cleaned at dedicated shunting yards. The planning problem that results from such situations is referred to as the Train Unit Shunting Problem (TUSP). This problem involves matching arriving train units to service tasks and determining the schedule for departing trains. The TUSP is an important problem as it is used to determine the capacity of shunting yards and arises as a sub-problem of more general scheduling and planning problems. In this paper, we consider the case of the Dutch Railways (NS) TUSP. As the TUSP is complex, NS currently uses a local search (LS) heuristic to determine if an instance of the TUSP has a feasible solution. Given the number of shunting yards and the size of the planning problems, improving the evaluation speed of the LS brings significant computational gain. In this work, we use a machine learning approach that complements the LS and accelerates the search process. We use a Deep Graph Convolutional Neural Network (DGCNN) model to predict the feasibility of solutions obtained during the run of the LS heuristic. We use this model to decide whether to continue or abort the search process. In this way, the computation time is used more efficiently as it is spent on instances that are more likely to be feasible. Using simulations based on real-life instances of the TUSP, we show how our approach improves upon the previous method on prediction accuracy and leads to computational gains for the decision-making process.

Real life business processes change over time, in both planned and unexpected ways. The detection of these changes is crucial for organizations to ensure that the expected and the real behavior are as similar as possible. These changes over time are called concept drift and its detection is a big challenge in process mining since the inherent complexity of the data makes difficult distinguishing between a change and an anomalous execution. In this paper, we present C2D2 (Conformance Checking-based Drift Detection), a new approach to detect sudden control-flow changes in the process models from event traces. C2D2 combines discovery techniques with conformance checking methods to perform an offline detection. Our approach has been validated with a synthetic benchmarking dataset formed by 68 logs, showing an improvement in the accuracy while maintaining a minimum delay in the drift detection.

We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps. We prove the neural network converges in distribution to a random ODE with a Gaussian distribution using mean field analysis. The limit is completely different than in the typical mean-field results for neural networks due to the $\frac{1}{\sqrt{N}}$ normalization factor in the Xavier initialization (versus the $\frac{1}{N}$ factor in the typical mean-field framework). Although the pre-limit problem of optimizing a neural network is non-convex (and therefore the neural network may converge to a local minimum), the limit equation minimizes a (quadratic) convex objective function and therefore converges to a global minimum. Furthermore, under reasonable assumptions, the matrix in the limiting quadratic objective function is positive definite and thus the neural network (in the limit) will converge to a global minimum with zero loss on the training set.

One shirt size cannot fit everybody, while we cannot make a unique shirt that fits perfectly for everyone because of resource limitation. This analogy is true for the policy making. Policy makers cannot establish a single policy to solve all problems for all regions because each region has its own unique issue. In the other extreme, policy makers also cannot create a policy for each small village due to the resource limitation. Would it be better if we can find a set of largest regions such that the population of each region within this set has common issues and we can establish a single policy for them? In this work, we propose a framework using regression analysis and minimum description length (MDL) to find a set of largest areas that have common indicators, which can be used to predict household incomes efficiently. Given a set of household features, and a multi-resolution partition that represents administrative divisions, our framework reports a set C* of largest subdivisions that have a common model for population-income prediction. We formalize a problem of finding C* and propose the algorithm as a solution. We use both simulation datasets as well as a real-world dataset of Thailand's population household information to demonstrate our framework performance and application. The results show that our framework performance is better than the baseline methods. We show the results of our method can be used to find indicators of income prediction for many areas in Thailand. By increasing these indicator values, we expect people in these areas to gain more incomes. Hence, the policy makers can plan to establish the policies by using these indicators in our results as a guideline to solve low-income issues. Our framework can be used to support policy makers to establish policies regarding any other dependent variable beyond incomes in order to combat poverty and other issues.

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally intractable, we first show that generic instances of the problem can be solved efficiently. More specifically, for a generic problem instance, certain strict complementarity (SC) condition holds for all Karush-Kuhn-Tucker (KKT) solutions (with probability one). The SC condition is then used to establish an equivalence relationship between two different notions of SOSPs, one of which is computationally easy to verify. Based on this particular notion of SOSP, we design an algorithm named the Successive Negative-curvature grAdient Projection (SNAP), which successively performs either conventional gradient projection or some negative curvature based projection steps to find SOSPs. SNAP and its first-order extension SNAP$^+$, require $\mathcal{O}(1/\epsilon^{2.5})$ iterations to compute an $(\epsilon, \sqrt{\epsilon})$-SOSP, and their per-iteration computational complexities are polynomial in the number of constraints and problem dimension. To our knowledge, this is the first time that first-order algorithms with polynomial per-iteration complexity and global sublinear rate have been designed to find SOSPs of the important class of non-convex problems with linear constraints.

In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of sparse and low-rank matrices. The resulting formulation, a nonnegative variant of robust principal component analysis, is more computationally tractable than its commonly employed convex relaxation, although not generally solvable to global optimality. In spite of this limitation, we derive intuitive and interpretable conditions on the video data under which the uniqueness and global optimality of the object segmentation are guaranteed using local search methods. We illustrate these novel optimality criteria through example segmentations using real video data.