Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of the data shows specific grouping patterns. To address these emerging challenges, we develop a new clustering methodology that introduces the idea of a regularization path into unsupervised learning. A regularization path for a clustering problem is created by varying the degree of sparsity constraint that is imposed on the differences between objects via the minimax concave penalty with adaptive tuning parameters. Instead of providing a single solution represented by a cluster assignment for each object, the method produces a short sequence of solutions that determines not only the cluster assignment but also a corresponding number of clusters for each solution. The optimization of the penalized loss function is carried out through an MM algorithm with block coordinate descent. The advantages of this clustering algorithm compared to other existing methods are as follows: it does not require the input of the number of clusters; it is capable of simultaneously separating irrelevant or noisy observations that show no grouping pattern, which can greatly improve data interpretation; it is a general methodology that can be applied to many clustering problems. We test this method on various simulated datasets and on gene expression data, where it shows better or competitive performance compared against several clustering methods.

Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurements taken during a robot's exploration (instead of relying on prior training data) for efficiently and scalably learning the GP observation model online through our proposed novel online sparse GP. As a result, GP-Localize is capable of achieving constant time and memory (i.e., independent of the size of the data) per filtering step, which demonstrates the practical feasibility of using GPs for persistent robot localization and autonomy. Empirical evaluation via simulated experiments with real-world datasets and a real robot experiment shows that GP-Localize outperforms existing GP localization algorithms.

The automatic segmentation of human knee cartilage from 3D MR images is a useful yet challenging task due to the thin sheet structure of the cartilage with diffuse boundaries and inhomogeneous intensities. In this paper, we present an iterative multi-class learning method to segment the femoral, tibial and patellar cartilage simultaneously, which effectively exploits the spatial contextual constraints between bone and cartilage, and also between different cartilages. First, based on the fact that the cartilage grows in only certain area of the corresponding bone surface, we extract the distance features of not only to the surface of the bone, but more informatively, to the densely registered anatomical landmarks on the bone surface. Second, we introduce a set of iterative discriminative classifiers that at each iteration, probability comparison features are constructed from the class confidence maps derived by previously learned classifiers. These features automatically embed the semantic context information between different cartilages of interest. Validated on a total of 176 volumes from the Osteoarthritis Initiative (OAI) dataset, the proposed approach demonstrates high robustness and accuracy of segmentation in comparison with existing state-of-the-art MR cartilage segmentation methods.

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decisionmaking against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory. Keywords: bounded rationality, free energy, game theory, Legendre-Fenchel transform.

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling exponentially many isomorphic forms. Bhattacharyya kernel constructed between these functionals significantly outperforms the state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph classification datasets, demonstrating the superiority of our approach. The proposed methodology is simple and runs in time linear in the number of edges, which makes our kernel more efficient and scalable compared to many widely adopted graph kernels with running time cubic in the number of vertices.

As a lossy compression framework, compressed sensing has drawn much attention in wireless telemonitoring of biosignals due to its ability to reduce energy consumption and make possible the design of low-power devices. However, the non-sparseness of biosignals presents a major challenge to compressed sensing. This study proposes and evaluates a spatio-temporal sparse Bayesian learning algorithm, which has the desired ability to recover such non-sparse biosignals. It exploits both temporal correlation in each individual biosignal and inter-channel correlation among biosignals from different channels. The proposed algorithm was used for compressed sensing of multichannel electroencephalographic (EEG) signals for estimating vehicle drivers' drowsiness. Results showed that the drowsiness estimation was almost unaffected even if raw EEG signals (containing various artifacts) were compressed by 90%.

When making decisions under uncertainty, the optimal choices are often difficult to discern, especially if not enough information has been gathered. Two key questions in this regard relate to whether one should stop the information gathering process and commit to a decision (stopping criterion), and if not, what information to gather next (selection criterion). In this paper, we show that the recently introduced notion, Same-Decision Probability (SDP), can be useful as both a stopping and a selection criterion, as it can provide additional insight and allow for robust decision making in a variety of scenarios. This query has been shown to be highly intractable, being PP^PP-complete, and is exemplary of a class of queries which correspond to the computation of certain expectations. We propose the first exact algorithm for computing the SDP, and demonstrate its effectiveness on several real and synthetic networks. Finally, we present new complexity results, such as the complexity of computing the SDP on models with a Naive Bayes structure. Additionally, we prove that computing the non-myopic value of information is complete for the same complexity class as computing the SDP.

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In this paper, we propose a symmetric positive semidefinite matrix with the $(i,j)$-{th} entry equal to the covariance between normalized vectors $A^ie$ and $A^je$ ($e$ being vector of all ones) as a representation for graph with adjacency matrix $A$. We show that the proposed matrix representation encodes the spectrum of the underlying adjacency matrix and it also contains information about the counts of small sub-structures present in the graph such as triangles and small paths. In addition, we show that this matrix is a \emph{"graph invariant"}. All these properties make the proposed matrix a suitable object for representing graphs. The representation, being a covariance matrix in a fixed dimensional metric space, gives a mathematical embedding for graphs. This naturally leads to a measure of similarity on graph objects. We define similarity between two given graphs as a Bhattacharya similarity measure between their corresponding covariance matrix representations. As shown in our experimental study on the task of social network classification, such a similarity measure outperforms other widely used state-of-the-art methodologies. Our proposed method is also computationally efficient. The computation of both the matrix representation and the similarity value can be performed in operations linear in the number of edges. This makes our method scalable in practice. We believe our theoretical and empirical results provide evidence for studying truncated power iterations, of the adjacency matrix, to characterize social networks.

Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We prove that, with high probability, the margin and minimum enclosing ball in the feature space are preserved to within \epsilon-relative error, ensuring comparable generalization as in the original space in the case of classification. For regression, we show that the margin is preserved to \epsilon-relative error with high probability. We present extensive experiments with real and synthetic data to support our theory.