Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is characterized by novel observations on some unknown connected subgraph. These problems can be formulated in terms of optimization of suitable objectives on connected subgraphs, a problem which is generally computationally difficult. We overcome the combinatorics of connectivity by embedding connected subgraphs into linear matrix inequalities (LMI). Computationally efficient tests are then realized by optimizing convex objective functions subject to these LMI constraints. We prove, by means of a novel Euclidean embedding argument, that our tests are minimax optimal for exponential family of distributions on 1-D and 2-D lattices. We show that internal conductance of the connected subgraph family plays a fundamental role in characterizing detectability.

We propose a novel diverse feature selection method based on determinantal point processes (DPPs). Our model enables one to flexibly define diversity based on the covariance of features (similar to orthogonal matching pursuit) or alternatively based on side information. We introduce our approach in the context of Bayesian sparse regression, employing a DPP as a variational approximation to the true spike and slab posterior distribution. We subsequently show how this variational DPP approximation generalizes and extends mean-field approximation, and can be learned efficiently by exploiting the fast sampling properties of DPPs. Our motivating application comes from bioinformatics, where we aim to identify a diverse set of genes whose expression profiles predict a tumor type where the diversity is defined with respect to a gene-gene interaction network. We also explore an application in spatial statistics. In both cases, we demonstrate that the proposed method yields significantly more diverse feature sets than classic sparse methods, without compromising accuracy.

According to Cobanoglu et al and Murphy, it is now widely acknowledged that the single target paradigm (one protein or target, one disease, one drug) that has been the dominant premise in drug development in the recent past is untenable. More often than not, a drug-like compound (ligand) can be promiscuous - that is, it can interact with more than one target protein. In recent years, in in silico target prediction methods the promiscuity issue has been approached computationally in different ways. In this study we confine attention to the so-called ligand-based target prediction machine learning approaches, commonly referred to as target-fishing. With a few exceptions, the target-fishing approaches that are currently ubiquitous in cheminformatics literature can be essentially viewed as single-label multi-classification schemes; these approaches inherently bank on the single target paradigm assumption that a ligand can home in on one specific target. In order to address the ligand promiscuity issue, one might be able to cast target-fishing as a multi-label multi-class classification problem. For illustrative and comparison purposes, single-label and multi-label Naive Bayes classification models (denoted here by SMM and MMM, respectively) for target-fishing were implemented. The models were constructed and tested on 65,587 compounds and 308 targets retrieved from the ChEMBL17 database. SMM and MMM performed differently: for 16,344 test compounds, the MMM model returned recall and precision values of 0.8058 and 0.6622, respectively; the corresponding recall and precision values yielded by the SMM model were 0.7805 and 0.7596, respectively. However, at a significance level of 0.05 and one degree of freedom McNemar test performed on the target prediction results returned by SMM and MMM for the 16,344 test ligands gave a chi-squared value of 15.656, in favour of the MMM approach.

This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception that give rise to the above belief. Specifically, we differentiate the hardness of estimation of test statistics from the hardness of testing whether these statistics are zero or not, and explicitly discuss a notion of "fair" alternative hypotheses for these problems as dimension increases. We then demonstrate that the power of these tests actually drops polynomially with increasing dimension against fair alternatives. We end with some theoretical insights and shed light on the \textit{median heuristic} for kernel bandwidth selection. Our work advances the current understanding of the power of modern nonparametric hypothesis tests in high dimensions.

Recently fair division theory has emerged as a promising approach for allocation of multiple computational resources among agents. While in reality agents are not all present in the system simultaneously, previous work has studied static settings where all relevant information is known upfront. Our goal is to better understand the dynamic setting. On the conceptual level, we develop a dynamic model of fair division, and propose desirable axiomatic properties for dynamic resource allocation mechanisms. On the technical level, we construct two novel mechanisms that provably satisfy some of these properties, and analyze their performance using real data. We believe that our work informs the design of superior multiagent systems, and at the same time expands the scope of fair division theory by initiating the study of dynamic and fair resource allocation mechanisms.

The Workflow Satisfiability Problem (WSP) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a plan - an assignment of tasks to authorized users - such that all constraints are satisfied. It is natural to see the WSP as a subclass of the Constraint Satisfaction Problem (CSP) in which the variables are tasks and the domain is the set of users. What makes the WSP distinctive is that the number of tasks is usually very small compared to the number of users, so it is appropriate to ask for which constraint languages the WSP is fixed-parameter tractable (FPT), parameterized by the number of tasks. This novel approach to the WSP, using techniques from CSP, has enabled us to design a generic algorithm which is FPT for several families of workflow constraints considered in the literature. Furthermore, we prove that the union of FPT languages remains FPT if they satisfy a simple compatibility condition. Lastly, we identify a new FPT constraint language, user-independent constraints, that includes many of the constraints of interest in business processing systems. We demonstrate that our generic algorithm has provably optimal running time O*(2^(klog k)), for this language, where k is the number of tasks.

In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "likes" or "friendships" are observed. The problem of learning from only positive and unlabeled examples, called PU (positive-unlabeled) learning, has been studied in the context of binary classification. We consider the PU matrix completion problem, where an underlying real-valued matrix M is first quantized to generate one-bit observations and then a subset of positive entries is revealed. Under the assumption that M has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a "shifted matrix completion" method that recovers M using only a subset of indices corresponding to ones, while for the second case, we propose a "biased matrix completion" method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds --- if M is n by n, the Frobenius error is bounded as O(1/((1-rho)n), where 1-rho denotes the fraction of ones observed. This implies a sample complexity of O(n\log n) ones to achieve a small error, when M is dense and n is large. We extend our methods and guarantees to the inductive matrix completion problem, where rows and columns of M have associated features. We provide efficient and scalable optimization procedures for both the methods and demonstrate the effectiveness of the proposed methods for link prediction (on real-world networks consisting of over 2 million nodes and 90 million links) and semi-supervised clustering tasks.

Originally designed to model text, topic modeling has become a powerful tool for uncovering latent structure in domains including medicine, finance, and vision. The goals for the model vary depending on the application: in some cases, the discovered topics may be used for prediction or some other downstream task. In other cases, the content of the topic itself may be of intrinsic scientific interest. Unfortunately, even using modern sparse techniques, the discovered topics are often difficult to interpret due to the high dimensionality of the underlying space. To improve topic interpretability, we introduce Graph-Sparse LDA, a hierarchical topic model that leverages knowledge of relationships between words (e.g., as encoded by an ontology). In our model, topics are summarized by a few latent concept-words from the underlying graph that explain the observed words. Graph-Sparse LDA recovers sparse, interpretable summaries on two real-world biomedical datasets while matching state-of-the-art prediction performance.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

In this thesis, we propose several modelling strategies to tackle evolving data in different contexts. In the framework of static clustering, we start by introducing a soft kernel spectral clustering (SKSC) algorithm, which can better deal with overlapping clusters with respect to kernel spectral clustering (KSC) and provides more interpretable outcomes. Afterwards, a whole strategy based upon KSC for community detection of static networks is proposed, where the extraction of a high quality training sub-graph, the choice of the kernel function, the model selection and the applicability to large-scale data are key aspects. This paves the way for the development of a novel clustering algorithm for the analysis of evolving networks called kernel spectral clustering with memory effect (MKSC), where the temporal smoothness between clustering results in successive time steps is incorporated at the level of the primal optimization problem, by properly modifying the KSC formulation. Later on, an application of KSC to fault detection of an industrial machine is presented. Here, a smart pre-processing of the data by means of a proper windowing operation is necessary to catch the ongoing degradation process affecting the machine. In this way, in a genuinely unsupervised manner, it is possible to raise an early warning when necessary, in an online fashion. Finally, we propose a new algorithm called incremental kernel spectral clustering (IKSC) for online learning of non-stationary data. This ambitious challenge is faced by taking advantage of the out-of-sample property of kernel spectral clustering (KSC) to adapt the initial model, in order to tackle merging, splitting or drifting of clusters across time. Real-world applications considered in this thesis include image segmentation, time-series clustering, community detection of static and evolving networks.