We present a system which constructs a topological map of an environment given a sequence of images. This system includes a novel image similarity score which uses dynamic programming to match images using both the appearance and relative positionsof local features simultaneously. Additionally, an MRF is constructed tomodel the probability of loop-closures. A locally optimal labeling is found using Loopy-BP. Finally we outline a method to generate a topological map from loop closure data. Results, presented on four urban sequences and one indoor sequence, outperform the state of the art.

Little work has been done to directly combine the outputs of multiple supervised and unsupervised models. However, it can increase the accuracy and applicability of ensemble methods. First, we can boost the diversity of classification ensemble by incorporating multiple clustering outputs, each of which provides grouping constraints for the joint label predictions of a set of related objects. Secondly, ensemble of supervised models is limited in applications which have no access to raw data but to the meta-level model outputs. In this paper, we aim at calculating a consolidated classification solution for a set of objects by maximizing the consensus among both supervised predictions and unsupervised grouping constraints. We seek a global optimal label assignment for the target objects, which is different from the result of traditional majority voting and model combination approaches. We cast the problem into an optimization problem on a bipartite graph, where the objective function favors smoothness in the conditional probability estimates over the graph, as well as penalizes deviation from initial labeling of supervised models. We solve the problem through iterative propagation of conditional probability estimates among neighboring nodes, and interpret the method as conducting a constrained embedding in a transformed space, as well as a ranking on the graph. Experimental results on three real applications demonstrate the benefits of the proposed method over existing alternatives.

We show how to sequentially optimize magnetic resonance imaging measurement designs over stacks of neighbouring image slices, by performing convex variational inference on a large scale non-Gaussian linear dynamical system, tracking dominating directions of posterior covariance without imposing any factorization constraints. Our approach can be scaled up to high-resolution images by reductions to numerical mathematics primitives and parallelization on several levels. In a first study, designs are found that improve significantly on others chosen independently for each slice or drawn at random.

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties. The first is how to select the best embedding similarity among all heavy-tailed functions and the second is how to optimize the objective function once the heave-tailed function has been selected. Our contributions then are: (1) we point out that various heavy-tailed embedding similarities can be characterized by their negative score functions. Based on this finding, we present a parameterized subset of similarity functions for choosing the best tail-heaviness for HSSNE; (2) we present a fixed-point optimization algorithm that can be applied to all heavy-tailed functions and does not require the user to set any parameters; and (3) we present two empirical studies, one for unsupervised visualization showing that our optimization algorithm runs as fast and as good as the best known t-SNE implementation and the other for semi-supervised visualization showing quantitative superiority using the homogeneity measure as well as qualitative advantage in cluster separation over t-SNE.

Recently, supervised dimensionality reduction has been gaining attention, owing to the realization that data labels are often available and strongly suggest important underlying structures in the data. In this paper, we present a novel convex supervised dimensionality reduction approach based on exponential family PCA and provide a simple but novel form to project new testing data into the embedded space. This convex approach successfully avoids the local optima of the EM learning. Moreover, by introducing a sample-based multinomial approximation to exponential family models, it avoids the limitation of the prevailing Gaussian assumptions of standard PCA, and produces a kernelized formulation for nonlinear supervised dimensionality reduction. A training algorithm is then devised based on a subgradient bundle method, whose scalability can be gained through a coordinate descent procedure. The advantage of our global optimization approach is demonstrated by empirical results over both synthetic and real data.

Several key problems in machine learning, such as feature selection and active learning, can be formulated as submodular set function maximization. We present herein a novel algorithm for maximizing a submodular set function under a cardinality constraint --- the algorithm is based on a cutting-plane method and is implemented as an iterative small-scale binary-integer linear programming procedure. It is well known that this problem is NP-hard, and the approximation factor achieved by the greedy algorithm is the theoretical limit for polynomial time. As for (non-polynomial time) exact algorithms that perform reasonably in practice, there has been very little in the literature although the problem is quite important for many applications. Our algorithm is guaranteed to find the exact solution in finite iterations, and it converges fast in practice due to the efficiency of the cutting-plane mechanism. Moreover, we also provide a method that produces successively decreasing upper-bounds of the optimal solution, while our algorithm provides successively increasing lower-bounds. Thus, the accuracy of the current solution can be estimated at any point, and the algorithm can be stopped early once a desired degree of tolerance is met. We evaluate our algorithm on sensor placement and feature selection applications showing good performance.

Finding maximally sparse representations from overcomplete feature dictionaries frequently involves minimizing a cost function composed of a likelihood (or data fit) term and a prior (or penalty function) that favors sparsity. While typically the prior is factorial, here we examine non-factorial alternatives that have a number of desirable properties relevant to sparse estimation and are easily implemented using an efficient, globally-convergent reweighted $\ell_1$ minimization procedure. The first method under consideration arises from the sparse Bayesian learning (SBL) framework. Although based on a highly non-convex underlying cost function, in the context of canonical sparse estimation problems, we prove uniform superiority of this method over the Lasso in that, (i) it can never do worse, and (ii) for any dictionary and sparsity profile, there will always exist cases where it does better. These results challenge the prevailing reliance on strictly convex penalty functions for finding sparse solutions. We then derive a new non-factorial variant with similar properties that exhibits further performance improvements in empirical tests. For both of these methods, as well as traditional factorial analogs, we demonstrate the effectiveness of reweighted $\ell_1$-norm algorithms in handling more general sparse estimation problems involving classification, group feature selection, and non-negativity constraints. As a byproduct of this development, a rigorous reformulation of sparse Bayesian classification (e.g., the relevance vector machine) is derived that, unlike the original, involves no approximation steps and descends a well-defined objective function.

In analogy to the PCA setting, the sparse PCA problem is often solved by iteratively alternating between two subtasks: cardinality-constrained rank-one variance maximization and matrix deflation. While the former has received a great deal of attention in the literature, the latter is seldom analyzed and is typically borrowed without justification from the PCA context. In this work, we demonstrate that the standard PCA deflation procedure is seldom appropriate for the sparse PCA setting. To rectify the situation, we first develop several heuristic deflation alternatives with more desirable properties. We then reformulate the sparse PCA optimization problem to explicitly reflect the maximum additional variance objective on each round. The result is a generalized deflation procedure that typically outperforms more standard techniques on real-world datasets.

We propose a novel information theoretic approach for semi-supervised learning of conditional random fields. Our approach defines a training objective that combines the conditional likelihood on labeled data and the mutual information on unlabeled data. Different from previous minimum conditional entropy semi-supervised discriminative learning methods, our approach can be naturally cast into the rate distortion theory framework in information theory. We analyze the tractability of the framework for structured prediction and present a convergent variational training algorithm to defy the combinatorial explosion of terms in the sum over label configurations. Our experimental results show that the rate distortion approach outperforms standard $l_2$ regularization and minimum conditional entropy regularization on both multi-class classification and sequence labeling problems.

In this paper we make several contributions towards accelerating approximate Bayesian structural inference for non-decomposable GGMs. Our first contribution is to show how to efficiently compute a BIC or Laplace approximation to the marginal likelihood of non-decomposable graphs using convex methods for precision matrix estimation. This optimization technique can be used as a fast scoring function inside standard Stochastic Local Search (SLS) for generating posterior samples. Our second contribution is a novel framework for efficiently generating large sets of high-quality graph topologies without performing local search. This graph proposal method, which we call Neighborhood Fusion" (NF), samples candidate Markov blankets at each node using sparse regression techniques. Our final contribution is a hybrid method combining the complementary strengths of NF and SLS. Experimental results in structural recovery and prediction tasks demonstrate that NF and hybrid NF/SLS out-perform state-of-the-art local search methods, on both synthetic and real-world datasets, when realistic computational limits are imposed."