Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information is available along with the graph data. For example, for neurological disorder identification, in addition to the brain networks derived from neuroimaging data, hundreds of clinical, immunologic, serologic and cognitive measures may also be documented for each subject. These measures compose multiple side views encoding a tremendous amount of supplemental information for diagnostic purposes, yet are often ignored. In this paper, we study the problem of discriminative subgraph selection using multiple side views and propose a novel solution to find an optimal set of subgraph features for graph classification by exploring a plurality of side views. We derive a feature evaluation criterion, named gSide, to estimate the usefulness of subgraph patterns based upon side views. Then we develop a branch-and-bound algorithm, called gMSV, to efficiently search for optimal subgraph features by integrating the subgraph mining process and the procedure of discriminative feature selection. Empirical studies on graph classification tasks for neurological disorders using brain networks demonstrate that subgraph patterns selected by the multi-side-view guided subgraph selection approach can effectively boost graph classification performances and are relevant to disease diagnosis.

Compared to conventional cars, electric vehicles (EVs) still suffer from considerably shorter cruising ranges. Combined with the sparsity of battery loading stations, the complete transition to E-mobility still seems a long way to go. In this paper, we consider the problem of placing as few loading stations as possible so that on any shortest path there are sufficiently many not to run out of energy. We show how to model this problem and introduce heuristics which provide close-to-optimal solutions even in large road networks.

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can be computed one by one, repeatedly solving the single-component problem and deflating the input data matrix, but as we show this greedy procedure is suboptimal. We present a novel algorithm for sparse PCA that jointly optimizes multiple disjoint components. The extracted features capture variance that lies within a multiplicative factor arbitrarily close to 1 from the optimal. Our algorithm is combinatorial and computes the desired components by solving multiple instances of the bipartite maximum weight matching problem. Its complexity grows as a low order polynomial in the ambient dimension of the input data matrix, but exponentially in its rank. However, it can be effectively applied on a low-dimensional sketch of the data; this allows us to obtain polynomial-time approximation guarantees via spectral bounds. We evaluate our algorithm on real data-sets and empirically demonstrate that in many cases it outperforms existing, deflation-based approaches.

We introduce a new notion of systematicity for satisfiability algorithms with restarts, saying that an algorithm is strongly systematic if it is systematic independent of restart policy but weakly systematic if it is systematic for some restart policies but not others. We show that existing satisfiability engines are generally only weakly systematic, and describe flex, a strongly systematic algorithm that uses an amount of memory polynomial in the size of the problem. On large number factoring problems, flex appears to outperform weakly systematic approaches.

We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still bounded). Given a realization of such graph, we aim at identifying the hidden subset of vertices. This can be regarded as a model for the problem of finding a tightly knitted community in a social network, or a cluster in a relational dataset. In this paper we present two sets of contributions: $(i)$ We use the cavity method from spin glass theory to derive an exact phase diagram for the reconstruction problem. In particular, as the difference in edge probability increases, the problem undergoes two phase transitions, a static phase transition and a dynamic one. $(ii)$ We establish rigorous bounds on the dynamic phase transition and prove that, above a certain threshold, a local algorithm (belief propagation) correctly identify most of the hidden set. Below the same threshold \emph{no local algorithm} can achieve this goal. However, in this regime the subset can be identified by exhaustive search. For small hidden sets and large average degree, the phase transition for local algorithms takes an intriguingly simple form. Local algorithms succeed with high probability for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} > \sqrt{{\rm deg}_{\rm out}/e}$ and fail for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} < \sqrt{{\rm deg}_{\rm out}/e}$ (with ${\rm deg}_{\rm in}$, ${\rm deg}_{\rm out}$ the average degrees inside and outside the community). We argue that spectral algorithms are also ineffective in the latter regime. It is an open problem whether any polynomial time algorithms might succeed for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} < \sqrt{{\rm deg}_{\rm out}/e}$.

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived by following an established information-theoretic approach to minimax estimation. The main conceptual contribution of this paper is the adaption of the information-theoretic approach to minimax estimation for the DL problem in order to derive lower bounds on the worst case MSE of any DL scheme. We derive three different lower bounds applying to different generative models for the observed signals. The first bound applies to a wide range of models, it only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions, and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL schemes in terms of a signal to noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. While, compared with the previous two bounds, the applicability of this final bound is the most limited it is the tightest of the three bounds in the low SNR regime.

Conflict-Based Search (CBS) and its enhancements, Meta-Agent CBS and bypassing conflicts are amongst the strongest newly introduced algorithms for Multi-Agent Path Finding. This paper introduces two new improvements to CBS and incorporates them into a coherent, improved version of CBS, namely ICBS. Experimental results show that each of these improvements further reduces the runtime over the existing CBS-based approaches. When all improvements are combined, an even larger improvement is achieved, producing state-of-the art results for a number of domains.

Probabilistic Classifiers Chains (PCC) offers interesting properties to solve multi-label classification tasks due to its ability to estimate the joint probability of the labels. However, PCC presents the major drawback of having a high computational cost in the inference process required to predict new samples. Lately, several approaches have been proposed to overcome this issue, including beam search and an epsilon-Approximate algorithm based on uniform-cost search. Surprisingly, the obvious possibility of using heuristic search has not been considered yet. This paper studies this alternative and proposes an admisible heuristic that, applied in combination with A* algorithm, guarantees, not only optimal predictions in terms of subset 0/1 loss, but also that it always explores less nodes than epsilon-Approximate algorithm. In the experiments reported, the number of nodes explored by our method is less than two times the number of labels for all datasets analyzed. But, the difference in explored nodes must be large enough to compensate the overhead of the heuristic in order to improve prediction time. Thus, our proposal may be a good choice for complex multi-label problems.

Symmetries are common in many constraint problems. They can be broken statically or dynamically. The focus of this paper is the symmetry breaking during search (SBDS) method that adds conditional symmetry breaking constraints upon each backtracking during search. To trade completeness for efficiency, partial SBDS (ParSBDS) is proposed by posting only a subset of symmetries. We propose an adaptation method recursive SBDS (ReSBDS) of ParSBDS which extends ParSBDS to break more symmetry compositions. We observe that the symmetry breaking constraints added for each symmetry at a search node are nogoods and increasing. A global constraint (incNGs), which is logically equivalent to a set of increasing nogoods, is derived. To further trade pruning power for efficiency, we propose weak-nogood consistency (WNC) for nogoods and a lazy propagator for SBDS (and its variants) using watched literal technology. We further define generalized weak-incNGs consistency (GWIC) for a conjunction of increasing nogoods, and give a lazy propagator for incNGs.

My thesis is largely focused on the parallelisation of UCT (and other Best-First Search techniques) and the ramifications of doing so. I have identified issues with chunking in UCT, created by some forms of parallelisation, and developed a solution to this involving buffering of simulations that appear “out of order” and reevaluation of propagation data. I have developed a technique for scalable distribution of both tree data and computation across a large scale compute cluster. The context of most of my work is General Game Playing, but the techniques themselves are largely agnostic to domain.