Learning minimum volume sets of an underlying nominal distribution is a very effective approach to anomaly detection. Several approaches to learning minimum volume sets have been proposed in the literature, including the K-point nearest neighbor graph (K-kNNG) algorithm based on the geometric entropy minimization (GEM) principle [4]. The K-kNNG detector, while possessing several desirable characteristics, suffers from high computation complexity, and in [4] a simpler heuristic approximation, the leave-one-out kNNG (L1O-kNNG) was proposed. In this paper, we propose a novel bipartite k-nearest neighbor graph (BP-kNNG) anomaly detection scheme for estimating minimum volume sets. Our bipartite estimator retains all the desirable theoretical properties of the K-kNNG, while being computationally simpler than the K-kNNG and the surrogate L1O-kNNG detectors. We show that BP-kNNG is asymptotically consistent in recovering the p-value of each test point. Experimental results are given that illustrate the superior performance of BP-kNNG as compared to the L1O-kNNG and other state of the art anomaly detection schemes.

We are motivated by an application to extract a representative subset of machine learning training data and by the poor empirical performance we observe of the popular minimum norm algorithm. In fact, for our application, minimum norm can have a running time of about O(n^7 ) (O(n^5 ) oracle calls). We therefore propose a fast approximate method to minimize arbitrary submodular functions. For a large sub-class of submodular functions, the algorithm is exact. Other submodular functions are iteratively approximated by tight submodular upper bounds, and then repeatedly optimized. We show theoretical properties, and empirical results suggest significant speedups over minimum norm while retaining higher accuracies.

This paper studies the problem of semi-supervised learning from the vector field perspective. Many of the existing work use the graph Laplacian to ensure the smoothness of the prediction function on the data manifold. However, beyond smoothness, it is suggested by recent theoretical work that we should ensure second order smoothness for achieving faster rates of convergence for semi-supervised regression problems. To achieve this goal, we show that the second order smoothness measures the linearity of the function, and the gradient field of a linear function has to be a parallel vector field. Consequently, we propose to find a function which minimizes the empirical error, and simultaneously requires its gradient field to be as parallel as possible. We give a continuous objective function on the manifold and discuss how to discretize it by using random points. The discretized optimization problem turns out to be a sparse linear system which can be solved very efficiently. The experimental results have demonstrated the effectiveness of our proposed approach.

This paper presents an approach that predicts the effectiveness of HIV combination therapies by simultaneously addressing several problems affecting the available HIV clinical data sets: the different treatment backgrounds of the samples, the uneven representation of the levels of therapy experience, the missing treatment history information, the uneven therapy representation and the unbalanced therapy outcome representation. The computational validation on clinical data shows that, compared to the most commonly used approach that does not account for the issues mentioned above, our model has significantly higher predictive power. This is especially true for samples stemming from patients with longer treatment history and samples associated with rare therapies. Furthermore, our approach is at least as powerful for the remaining samples.

We study the family of p-resistances on graphs for p ≥ 1. This family generalizes the standard resistance distance. We prove that for any fixed graph, for p=1, the p-resistance coincides with the shortest path distance, for p=2 it coincides with the standard resistance distance, and for p → ∞ it converges to the inverse of the minimal s-t-cut in the graph. Secondly, we consider the special case of random geometric graphs (such as k-nearest neighbor graphs) when the number n of vertices in the graph tends to infinity. We prove that an interesting phase-transition takes place. There exist two critical thresholds p^* and p^** such that if p < p^*, then the p-resistance depends on meaningful global properties of the graph, whereas if p > p^**, it only depends on trivial local quantities and does not convey any useful information. We can explicitly compute the critical values: p^* = 1 + 1/(d-1) and p^** = 1 + 1/(d-2) where d is the dimension of the underlying space (we believe that the fact that there is a small gap between p^* and p^** is an artifact of our proofs. We also relate our findings to Laplacian regularization and suggest to use q-Laplacians as regularizers, where q satisfies 1/p^* + 1/q = 1.

This paper studies privacy preserving M-estimators using perturbed histograms. The proposed approach allows the release of a wide class of M-estimators with both differential privacy and statistical utility without knowing a priori the particular inference procedure. The performance of the proposed method is demonstrated through a careful study of the convergence rates. A practical algorithm is given and applied on a real world data set containing both continuous and categorical variables.

The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. We have performed empirical evaluations using both synthetic and the breast cancer gene expression data set, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results show that the proposed algorithm is more efficient than existing state-of-the-art algorithms.

Given one feature of a novel animal, humans readily make inferences about other features of the animal. For example, winged creatures often fly, and creatures that eat fish often live in the water. We explore the knowledge that supports these inferences and compare two approaches. The first approach proposes that humans rely on abstract representations of dependency relationships between features, and is formalized here as a graphical model. The second approach proposes that humans rely on specific knowledge of previously encountered animals, and is formalized here as a family of exemplar models. We evaluate these models using a task where participants reason about chimeras, or animals with pairs of features that have not previously been observed to co-occur. The results support the hypothesis that humans rely on explicit representations of relationships between features.

Inferring key unobservable features of individuals is an important task in the applied sciences. In particular, an important source of data in fields such as marketing, social sciences and medicine is questionnaires: answers in such questionnaires are noisy measures of target unobserved features. While comprehensive surveys help to better estimate the latent variables of interest, aiming at a high number of questions comes at a price: refusal to participate in surveys can go up, as well as the rate of missing data; quality of answers can decline; costs associated with applying such questionnaires can also increase. In this paper, we cast the problem of refining existing models for questionnaire data as follows: solve a constrained optimization problem of preserving the maximum amount of information found in a latent variable model using only a subset of existing questions. The goal is to find an optimal subset of a given size. For that, we first define an information theoretical measure for quantifying the quality of a reduced questionnaire. Three different approximate inference methods are introduced to solve this problem. Comparisons against a simple but powerful heuristic are presented.

Speech conveys different yet mixed information ranging from linguistic to speaker-specific components, and each of them should be exclusively used in a specific task. However, it is extremely difficult to extract a specific information component given the fact that nearly all existing acoustic representations carry all types of speech information. Thus, the use of the same representation in both speech and speaker recognition hinders a system from producing better performance due to interference of irrelevant information. In this paper, we present a deep neural architecture to extract speaker-specific information from MFCCs. As a result, a multi-objective loss function is proposed for learning speaker-specific characteristics and regularization via normalizing interference of non-speaker related information and avoiding information loss. With LDC benchmark corpora and a Chinese speech corpus, we demonstrate that a resultant speaker-specific representation is insensitive to text/languages spoken and environmental mismatches and hence outperforms MFCCs and other state-of-the-art techniques in speaker recognition. We discuss relevant issues and relate our approach to previous work.