In multi-instance learning, there are two kinds of prediction failure, i.e., false negative and false positive. Current research mainly focus on avoding the former. We attempt to utilize the geometric distribution of instances inside positive bags to avoid both the former and the latter. Based on kernel principal component analysis, we define a projection constraint for each positive bag to classify its constituent instances far away from the separating hyperplane while place positive instances and negative instances at opposite sides. We apply the Constrained Concave-Convex Procedure to solve the resulted problem. Empirical results demonstrate that our approach offers improved generalization performance.

We extend Latent Dirichlet Allocation (LDA) by explicitly allowing for the encoding of side information in the distribution over words. This results in a variety of new capabilities, such as improved estimates for infrequently occurring words, as well as the ability to leverage thesauri and dictionaries in order to boost topic cohesion within and across languages. We present experiments on multi-language topic synchronisation where dictionary information is used to bias corresponding words towards similar topics. Results indicate that our model substantially improves topic cohesion when compared to the standard LDA model.

Most active learning approaches select either informative or representative unlabeled instances to query their labels. Although several active learning algorithms have been proposed to combine the two criterions for query selection, they are usually ad hoc in finding unlabeled instances that are both informative and representative. We address this challenge by a principled approach, termed QUIRE, based on the min-max view of active learning. The proposed approach provides a systematic way for measuring and combining the informativeness and representativeness of an instance. Extensive experimental results show that the proposed QUIRE approach outperforms several state-of -the-art active learning approaches.

A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The proposed algorithm does not require the number of clusters in advance, and it will be determined by the property of a given set of data points. The minimum average cost clustering problem is parameterized with a real variable, and surprisingly, we show that all information about optimal clusterings for all parameters can be computed in polynomial time in total. Additionally, we evaluate the performance of the proposed algorithm through computational experiments.

We consider the online binary classification problem, where we are given m classifiers. At each stage, the classifiers map the input to the probability that the input belongs to the positive class. An online classification meta-algorithm is an algorithm that combines the outputs of the classifiers in order to attain a certain goal, without having prior knowledge on the form and statistics of the input, and without prior knowledge on the performance of the given classifiers. In this paper, we use sensitivity and specificity as the performance metrics of the meta-algorithm. In particular, our goal is to design an algorithm which satisfies the following two properties (asymptotically): (i) its average false positive rate (fp-rate) is under some given threshold, and (ii) its average true positive rate (tp-rate) is not worse than the tp-rate of the best convex combination of the m given classifiers that satisfies fp-rate constraint, in hindsight. We show that this problem is in fact a special case of the regret minimization problem with constraints, and therefore the above goal is not attainable. Hence, we pose a relaxed goal and propose a corresponding practical online learning meta-algorithm that attains it. In the case of two classifiers, we show that this algorithm takes a very simple form. To our best knowledge, this is the first algorithm that addresses the problem of the average tp-rate maximization under average fp-rate constraints in the online setting.

When animals repeatedly choose actions from multiple alternatives, they can allocate their choices stochastically depending on past actions and outcomes. It is commonly assumed that this ability is achieved by modifications in synaptic weights related to decision making. Choice behavior has been empirically found to follow Herrnstein’s matching law. Loewenstein & Seung (2006) demonstrated that matching behavior is a steady state of learning in neural networks if the synaptic weights change proportionally to the covariance between reward and neural activities. However, their proof did not take into account the change in entire synaptic distributions. In this study, we show that matching behavior is not necessarily a steady state of the covariance-based learning rule when the synaptic strength is sufficiently strong so that the fluctuations in input from individual sensory neurons influence the net input to output neurons. This is caused by the increasing variance in the input potential due to the diffusion of synaptic weights. This effect causes an undermatching phenomenon, which has been observed in many behavioral experiments. We suggest that the synaptic diffusion effects provide a robust neural mechanism for stochastic choice behavior.

The Random Projection Tree (RPTree) structures proposed in [Dasgupta-Freund-STOC-08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTree-Max and the RPTree-Mean data structures. Our result for RPTree-Max gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor s >= 2. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds possess bounded Local Covariance Dimension. As a consequence we show that RPTree-Mean adapts to manifold dimension as well.

We present the Copula Bayesian Network model for representing multivariate continuous distributions. Our approach builds on a novel copula-based parameterization of a conditional density that, joined with a graph that encodes independencies, offers great flexibility in modeling high-dimensional densities, while maintaining control over the form of the univariate marginals. We demonstrate the advantage of our framework for generalization over standard Bayesian networks as well as tree structured copula models for varied real-life domains that are of substantially higher dimension than those typically considered in the copula literature.

Recent years have witnessed the popularity of using rank minimization as a regularizer for various signal processing and machine learning problems. As rank minimization problems are often converted to nuclear norm minimization (NNM) problems, they have to be solved iteratively and each iteration requires computing a singular value decomposition (SVD). Therefore, their solution suffers from the high computation cost of multiple SVDs. To relieve this issue, we propose using the block Lanczos method to compute the partial SVDs, where the principal singular subspaces obtained in the previous iteration are used to start the block Lanczos procedure. To avoid the expensive reorthogonalization in the Lanczos procedure, the block Lanczos procedure is performed for only a few steps. Our block Lanczos with warm start (BLWS) technique can be adopted by different algorithms that solve NNM problems. We present numerical results on applying BLWS to Robust PCA and Matrix Completion problems. Experimental results show that our BLWS technique usually accelerates its host algorithm by at least two to three times.

Intrusion detection systems (IDSs) fall into two high-level categories: network-based systems (NIDS) that monitor network behaviors, and host-based systems (HIDS) that monitor system calls. In this work, we present a general technique for both systems. We use anomaly detection, which identifies patterns not conforming to a historic norm. In both types of systems, the rates of change vary dramatically over time (due to burstiness) and over components (due to service difference). To efficiently model such systems, we use continuous time Bayesian networks (CTBNs) and avoid specifying a fixed update interval common to discrete-time models. We build generative models from the normal training data, and abnormal behaviors are flagged based on their likelihood under this norm. For NIDS, we construct a hierarchical CTBN model for the network packet traces and use Rao-Blackwellized particle filtering to learn the parameters. We illustrate the power of our method through experiments on detecting real worms and identifying hosts on two publicly available network traces, the MAWI dataset and the LBNL dataset. For HIDS, we develop a novel learning method to deal with the finite resolution of system log file time stamps, without losing the benefits of our continuous time model. We demonstrate the method by detecting intrusions in the DARPA 1998 BSM dataset.