In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the leading eigenvectors. The last step is sometimes referred to as rounding, where one needs to decide how many leading eigenvectors to use, to determine the number of clusters, and to partition the data points. In this paper, we propose a novel method for rounding. The method differs from previous methods in three ways. First, we relax the assumption that the number of clusters equals the number of eigenvectors used. Second, when deciding the number of leading eigenvectors to use, we not only rely on information contained in the leading eigenvectors themselves, but also use subsequent eigenvectors. Third, our method is model-based and solves all the three subproblems of rounding using a class of graphical models called latent tree models. We evaluate our method on both synthetic and real-world data. The results show that our method works correctly in the ideal case where between-clusters similarity is 0, and degrades gracefully as one moves away from the ideal case.

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.

In standard passive imitation learning, the goal is to learn a target policy by passively observing full execution trajectories of it. Unfortunately, generating such trajectories can require substantial expert effort and be impractical in some cases. In this paper, we consider active imitation learning with the goal of reducing this effort by querying the expert about the desired action at individual states, which are selected based on answers to past queries and the learner's interactions with an environment simulator. We introduce a new approach based on reducing active imitation learning to i.i.d. active learning, which can leverage progress in the i.i.d. setting. Our first contribution, is to analyze reductions for both non-stationary and stationary policies, showing that the label complexity (number of queries) of active imitation learning can be substantially less than passive learning. Our second contribution, is to introduce a practical algorithm inspired by the reductions, which is shown to be highly effective in four test domains compared to a number of alternatives.

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.

Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible weighted transitions between them. A new set of metrics can be derived from this model that capture the distribution and connectivity of the local optima in the underlying configuration space. This paper departs from the descriptive analysis of local optima networks, and actively studies the correlation between network features and the performance of a local search heuristic. The NK family of landscapes and the Iterated Local Search metaheuristic are considered. With a statistically-sound approach based on multiple linear regression, it is shown that some LONs' features strongly influence and can even partly predict the performance of a heuristic search algorithm. This study validates the expressive power of LONs as a model of combinatorial fitness landscapes.

Financial statements contain quantitative information and manager's subjective evaluation of firm's financial status. Using information released in U.S. 10-K filings. Both qualitative and quantitative appraisals are crucial for quality financial decisions. To extract such opinioned statements from the reports, we built tagging models based on the conditional random field (CRF) techniques, considering a variety of combinations of linguistic factors including morphology, orthography, predicate-argument structure, syntax, and simple semantics. Our results show that the CRF models are reasonably effective to find opinion holders in experiments when we adopted the popular MPQA corpus for training and testing. The contribution of our paper is to identify opinion patterns in multiword expressions (MWEs) forms rather than in single word forms. We find that the managers of corporations attempt to use more optimistic words to obfuscate negative financial performance and to accentuate the positive financial performance. Our results also show that decreasing earnings were often accompanied by ambiguous and mild statements in the reporting year and that increasing earnings were stated in assertive and positive way.

Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal kernel by a mixture of integrated curved exponential distributions with logistic weights. This family of distributions, referred to as mixtures of experts, is broad enough to be used in the presence of multi-modality or strongly skewed distributions. The mixtures are fitted, via online-EM methods, to the optimal kernel through minimisation of the Kullback-Leibler divergence between the auxiliary target and instrumental distributions of the particle filter. At each iteration of the particle filter, the algorithm is required to solve only a single optimisation problem for the whole particle sample, yielding an algorithm with only linear complexity. In addition, we illustrate in a simulation study how the method can be successfully applied to optimal filtering in nonlinear state-space models.

This paper proposes a technique for the unsupervised detection and tracking of arbitrary objects in videos. It is intended to reduce the need for detection and localization methods tailored to specific object types and serve as a general framework applicable to videos with varied objects, backgrounds, and image qualities. The technique uses a dependent Dirichlet process mixture (DDPM) known as the Generalized Polya Urn (GPUDDPM) to model image pixel data that can be easily and efficiently extracted from the regions in a video that represent objects. This paper describes a specific implementation of the model using spatial and color pixel data extracted via frame differencing and gives two algorithms for performing inference in the model to accomplish detection and tracking. This technique is demonstrated on multiple synthetic and benchmark video datasets that illustrate its ability to, without modification, detect and track objects with diverse physical characteristics moving over non-uniform backgrounds and through occlusion.

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove a generalization of the Eckart-Young-Mirsky theorem under all unitarily invariant norms. Using this result, we obtain closed-form solutions for a set of rank/norm regularized problems, and derive closed-form solutions for a general class of subspace clustering problems (where data is modelled by unions of unknown subspaces). From these results we obtain new theoretical insights and promising experimental results.

Multi-view learning algorithms typically assume a complete bipartite mapping between the different views in order to exchange information during the learning process. However, many applications provide only a partial mapping between the views, creating a challenge for current methods. To address this problem, we propose a multi-view algorithm based on constrained clustering that can operate with an incomplete mapping. Given a set of pairwise constraints in each view, our approach propagates these constraints using a local similarity measure to those instances that can be mapped to the other views, allowing the propagated constraints to be transferred across views via the partial mapping. It uses co-EM to iteratively estimate the propagation within each view based on the current clustering model, transfer the constraints across views, and then update the clustering model. By alternating the learning process between views, this approach produces a unified clustering model that is consistent with all views. We show that this approach significantly improves clustering performance over several other methods for transferring constraints and allows multi-view clustering to be reliably applied when given a limited mapping between the views. Our evaluation reveals that the propagated constraints have high precision with respect to the true clusters in the data, explaining their benefit to clustering performance in both single- and multi-view learning scenarios.