Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an efficient Bayesian method to cluster curve data using an elastic shape metric that is based on joint registration and comparison of shapes of curves. The elastic-inner product matrix obtained from the data is modeled using a Wishart distribution whose parameters are assigned carefully chosen prior distributions to allow for automatic inference on the number of clusters. Posterior is sampled through an efficient Markov chain Monte Carlo procedure based on the Chinese restaurant process to infer (1) the posterior distribution on the number of clusters, and (2) clustering configuration of shapes. This method is demonstrated on a variety of synthetic data and real data examples on protein structure analysis, cell shape analysis in microscopy images, and clustering of shaped from MPEG7 database.

We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical inference approaches to understanding their complexity. The result is an alternative view of the relationship between predictability, complexity, and learning that highlights the distinct ways in which informational and correlational divergences arise in complex ergodic and nonergodic processes. We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical.

A discourse typically involves numerous entities, but few are mentioned more than once. Distinguishing those that die out after just one mention (singleton) from those that lead longer lives (coreferent) would dramatically simplify the hypothesis space for coreference resolution models, leading to increased performance. To realize these gains, we build a classifier for predicting the singleton/coreferent distinction. The models feature representations synthesize linguistic insights about the factors affecting discourse entity lifespans (especially negation, modality, and attitude predication) with existing results about the benefits of surface (part-of-speech and n-gram-based) features for coreference resolution. The model is effective in its own right, and the feature representations help to identify the anchor phrases in bridging anaphora as well. Furthermore, incorporating the model into two very different state-of-the-art coreference resolution systems, one rule-based and the other learning-based, yields significant performance improvements.

In unsupervised learning, an unbiased uniform sampling strategy is typically used, in order that the learned features faithfully encode the statistical structure of the training data. In this work, we explore whether active example selection strategies - algorithms that select which examples to use, based on the current estimate of the features - can accelerate learning. Specifically, we investigate effects of heuristic and saliency-inspired selection algorithms on the dictionary learning task with sparse activations. We show that some selection algorithms do improve the speed of learning, and we speculate on why they might work.

This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of parallelization. Without exchanging elements from the distributed training sets and keeping inter-node communications at affordable levels, the local (per-node) learners consent to the desired quantity inferred globally, meaning the one obtained if the entire training data set were centrally available. Impact of the decentralized learning framework to contemporary wireless communications and networking tasks is illustrated through case studies including target tracking using wireless sensor networks, unveiling Internet traffic anomalies, power system state estimation, as well as spectrum cartography for wireless cognitive radio networks.

Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications like belief propagation and reinforcement learning can exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively to Gaussian processes on benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.

Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to deal with precisely this setting. Our algorithms are as efficient as OMP, and improve on the best-known results for missing and noisy data in regression, both in the high-dimensional setting where we seek to recover a sparse vector from only a few measurements, and in the classical low-dimensional setting where we recover an unstructured regressor. In the high-dimensional setting, our support-recovery algorithm requires no knowledge of even the statistics of the noise. Along the way, we also obtain improved performance guarantees for OMP for the standard sparse regression problem with Gaussian noise.

Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains are projected to a common space by linear transformations in order to search closely related vectors across domains. We would like to find projection matrices to minimize distances between closely related data vectors. This formulation of cross-domain matching is regarded as an extension of the spectral graph embedding to multi-domain setting, and it includes several multivariate analysis methods of statistics such as multiset canonical correlation analysis, correspondence analysis, and principal component analysis. Similar approaches are very popular recently in pattern recognition and vision. In this paper, instead of proposing a novel method, we will introduce an embarrassingly simple idea of coding the data vectors for explaining all the above mentioned approaches. A data vector is concatenated with zero vectors from all other domains to make an augmented vector. The cross-domain matching is solved by applying the single-domain version of spectral graph embedding to these augmented vectors of all the domains. An interesting connection to the classical associative memory model of neural networks is also discussed by noticing a coding for association. A cross-validation method for choosing the dimension of the common space and a regularization parameter will be discussed in an illustrative numerical example.

Active authentication is the problem of continuously verifying the identity of a person based on behavioral aspects of their interaction with a computing device. In this study, we collect and analyze behavioral biometrics data from 200subjects, each using their personal Android mobile device for a period of at least 30 days. This dataset is novel in the context of active authentication due to its size, duration, number of modalities, and absence of restrictions on tracked activity. The geographical colocation of the subjects in the study is representative of a large closed-world environment such as an organization where the unauthorized user of a device is likely to be an insider threat: coming from within the organization. We consider four biometric modalities: (1) text entered via soft keyboard, (2) applications used, (3) websites visited, and (4) physical location of the device as determined from GPS (when outdoors) or WiFi (when indoors). We implement and test a classifier for each modality and organize the classifiers as a parallel binary decision fusion architecture. We are able to characterize the performance of the system with respect to intruder detection time and to quantify the contribution of each modality to the overall performance.

We consider the problem of learning convex aggregation of models, that is as good as the best convex aggregation, for the binary classification problem. Working in the stream based active learning setting, where the active learner has to make a decision on-the-fly, if it wants to query for the label of the point currently seen in the stream, we propose a stochastic-mirror descent algorithm, called SMD-AMA, with entropy regularization. We establish an excess risk bounds for the loss of the convex aggregate returned by SMD-AMA to be of the order of $O\left(\sqrt{\frac{\log(M)}{{T^{1-\mu}}}}\right)$, where $\mu\in [0,1)$ is an algorithm dependent parameter, that trades-off the number of labels queried, and excess risk.