We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average $K$-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at $\alpha$-false alarm level if the predicted score is in the $\alpha$-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate $\alpha$, its decision region converges to the $\alpha$-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing $K$-NN based anomaly detection algorithms, with significant computational savings.

Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the scale of data features. This paper aims to address the problem from a new perspective and considers model-oriented dimensionality reduction in parameter spaces of binary multivariate distributions. Specifically, we propose a general parameter reduction criterion, called Confident-Information-First (CIF) principle, to maximally preserve confident parameters and rule out less confident parameters. Formally, the confidence of each parameter can be assessed by its contribution to the expected Fisher information distance within the geometric manifold over the neighbourhood of the underlying real distribution. We then revisit Boltzmann machines (BM) from a model selection perspective and theoretically show that both the fully visible BM (VBM) and the BM with hidden units can be derived from the general binary multivariate distribution using the CIF principle. This can help us uncover and formalize the essential parts of the target density that BM aims to capture and the non-essential parts that BM should discard. Guided by the theoretical analysis, we develop a sample-specific CIF for model selection of BM that is adaptive to the observed samples. The method is studied in a series of density estimation experiments and has been shown effective in terms of the estimate accuracy.

This paper describes the resource- and system-building efforts of an eight-week Johns Hopkins University Human Language Technology Center of Excellence Summer Camp for Applied Language Exploration (SCALE-2009) on Semantically-Informed Machine Translation (SIMT). We describe a new modality/negation (MN) annotation scheme, the creation of a (publicly available) MN lexicon, and two automated MN taggers that we built using the annotation scheme and lexicon. Our annotation scheme isolates three components of modality and negation: a trigger (a word that conveys modality or negation), a target (an action associated with modality or negation) and a holder (an experiencer of modality). We describe how our MN lexicon was semi-automatically produced and we demonstrate that a structure-based MN tagger results in precision around 86% (depending on genre) for tagging of a standard LDC data set. We apply our MN annotation scheme to statistical machine translation using a syntactic framework that supports the inclusion of semantic annotations. Syntactic tags enriched with semantic annotations are assigned to parse trees in the target-language training texts through a process of tree grafting. While the focus of our work is modality and negation, the tree grafting procedure is general and supports other types of semantic information. We exploit this capability by including named entities, produced by a pre-existing tagger, in addition to the MN elements produced by the taggers described in this paper. The resulting system significantly outperformed a linguistically naive baseline model (Hiero), and reached the highest scores yet reported on the NIST 2009 Urdu-English test set. This finding supports the hypothesis that both syntactic and semantic information can improve translation quality.

This paper presents an original approach for jointly fitting survival times and classifying samples into subgroups. The Coxlogit model is a generalized linear model with a common set of selected features for both tasks. Survival times and class labels are here assumed to be conditioned by a common risk score which depends on those features. Learning is then naturally expressed as maximizing the joint probability of subgroup labels and the ordering of survival events, conditioned to a common weight vector. The model is estimated by minimizing a regularized log-likelihood through a coordinate descent algorithm. Validation on synthetic and breast cancer data shows that the proposed approach outperforms a standard Cox model or logistic regression when both predicting the survival times and classifying new samples into subgroups. It is also better at selecting informative features for both tasks.

The Frank-Wolfe algorithm (hereafter FW) is a classical method for convex optimization that has seen a substantial revival in interest from researchers [1, 2, 3]. Recent results have shown that the family of FW algorithms enjoys powerful theoretical properties such as iteration complexity bounds that are independent of the problem size, provable primal-dual convergence rates, and sparsity guarantees that hold during the whole execution of the algorithm [4, 2]. Furthermore, several variants of the basic procedure exist which can improve the convergence rate and practical performance of the basic FW iteration [5, 6, 7, 8]. Finally, the fact that FW methods work with projection-free iterations is an essential advantage in applications such as matrix recovery, where a projection step (as needed, e.g., by proximal methods) has a super-linear complexity [2, 9]. As a result, FW is now considered a suitable choice for large-scale optimization 1 problems arising in several contexts such as Machine Learning, statistics, bioinformatics and other fields [10, 11, 12].

A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of information or cognitive states represented in the brain, based on distributed patterns of neural activity. In the current investigation, we propose a new approach for representation of neural data for pattern analysis, namely a Mesh Learning Model. In this approach, at each time instant, a star mesh is formed around each voxel, such that the voxel corresponding to the center node is surrounded by its p-nearest neighbors. The arc weights of each mesh are estimated from the voxel intensity values by least squares method. The estimated arc weights of all the meshes, called Mesh Arc Descriptors (MADs), are then used to train a classifier, such as Neural Networks, k-Nearest Neighbor, Na\"ive Bayes and Support Vector Machines. The proposed Mesh Model was tested on neuroimaging data acquired via functional magnetic resonance imaging (fMRI) during a recognition memory experiment using categorized word lists, employing a previously established experimental paradigm (\"Oztekin & Badre, 2011). Results suggest that the proposed Mesh Learning approach can provide an effective algorithm for pattern analysis of brain activity during cognitive processing.

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We present a model theory/semantics for first order logic based on vectors of reals. We describe the model theory, discuss some interesting properties of such a system and present a simple approach to query answering.

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We demonstrate our method in simulations and for the application of modeling senate voting records.

In clinical practice, physicians make a series of treatment decisions over the course of a patient's disease based on his/her baseline and evolving characteristics. A dynamic treatment regime is a set of sequential decision rules that operationalizes this process. Each rule corresponds to a decision point and dictates the next treatment action based on the accrued information. Using existing data, a key goal is estimating the optimal regime, that, if followed by the patient population, would yield the most favorable outcome on average. Q- and A-learning are two main approaches for this purpose. We provide a detailed account of these methods, study their performance, and illustrate them using data from a depression study.

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Propagation. Experimental results on random and real-world CSPs show that Perturbed BP is often more successful and at the same time tens to hundreds of times more efficient than standard BP guided decimation. Perturbed BP also compares favorably with state-of-the-art SP-guided decimation, which has a computational complexity that generally scales exponentially worse than our method (wrt the cardinality of variable domains and constraints). Furthermore, our experiments with random satisfiability and coloring problems demonstrate that Perturbed SP can outperform SP-guided decimation, making it the best incomplete random CSP-solver in difficult regimes.