In this paper, we consider the problem of debugging large pipelines by human labeling. We represent the execution of a pipeline using a directed acyclic graph of AND and OR nodes, where each node represents a data item produced by some operator in the pipeline. We assume that each operator assigns a confidence to each of its output data. We want to reduce the uncertainty in the output by issuing queries to a human expert, where a query consists of checking if a given data item is correct. In this paper, we consider the problem of asking the optimal set of queries to minimize the resulting output uncertainty. We perform a detailed evaluation of the complexity of the problem for various classes of graphs. We give efficient algorithms for the problem for trees, and show that, for a general dag, the problem is intractable.

Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing lowlevel imagecomponents. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a linear combination.The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piecewise Gibbssampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN^{2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN^{D+1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently. We present some experiments to demonstrate that our proposed method works more efficiently to estimate HHMM parameters than do some existing methods such as the flattening method and Gibbs sampling method.

Non-linear dynamical systems (DS) have been used extensively for building generative models of human behavior. Its applications range from modeling brain dynamics to encoding motor commands. Many schemes have been proposed for encoding robot motions using dynamical systems with a single attractor placed at a predefined target in state space. Although these enable the robots to react against sudden perturbations without any re-planning, the motions are always directed towards a single target. In this work, we focus on combining several such DS with distinct attractors, resulting in a multi-stable DS. We show its applicability in reach-to-grasp tasks where the attractors represent several grasping points on the target object. While exploiting multiple attractors provides more flexibility in recovering from unseen perturbations, it also increases the complexity of the underlying learning problem. Here we present the Augmented-SVM (A-SVM) model which inherits region partitioning ability of the well known SVM classifier and is augmented with novel constraints derived from the individual DS. The new constraints modify the original SVM dual whose optimal solution then results in a new class of support vectors (SV). These new SV ensure that the resulting multi-stable DS incurs minimum deviation from the original dynamics and is stable at each of the attractors within a finite region of attraction. We show, via implementations on a simulated 10 degrees of freedom mobile robotic platform, that the model is capable of real-time motion generation and is able to adapt on-the-fly to perturbations.

We consider the problem of cardinality penalized optimization of a convex function over the probability simplex with additional convex constraints. It's well-known that the classical L1 regularizer fails to promote sparsity on the probability simplex since L1 norm on the probability simplex is trivially constant. We propose a direct relaxation of the minimum cardinality problem and show that it can be efficiently solved using convex programming. As a first application we consider recovering a sparse probability measure given moment constraints, in which our formulation becomes linear programming, hence can be solved very efficiently. A sufficient condition for exact recovery of the minimum cardinality solution is derived for arbitrary affine constraints. We then develop a penalized version for the noisy setting which can be solved using second order cone programs. The proposed method outperforms known heuristics based on L1 norm. As a second application we consider convex clustering using a sparse Gaussian mixture and compare our results with the well known soft k-means algorithm.

This paper addresses the problem of category-level 3D object detection. Given a monocular image, our aim is to localize the objects in 3D by enclosing them with tight oriented 3D bounding boxes. We propose a novel approach that extends the well-acclaimed deformable part-based model[Felz.] to reason in 3D. Our model represents an object class as a deformable 3D cuboid composed of faces and parts, which are both allowed to deform with respect to their anchors on the 3D box. We model the appearance of each face in fronto-parallel coordinates, thus effectively factoring out the appearance variation induced by viewpoint. Our model reasons about face visibility patters called aspects. We train the cuboid model jointly and discriminatively and share weights across all aspects to attain efficiency. Inference then entails sliding and rotating the box in 3D and scoring object hypotheses. While for inference we discretize the search space, the variables are continuous in our model. We demonstrate the effectiveness of our approach in indoor and outdoor scenarios, and show that our approach outperforms the state-of-the-art in both 2D[Felz09] and 3D object detection[Hedau12].

This paper studies a novel discriminative part-based model to represent and recognize object shapes with an “And-Or graph”. We define this model consisting of three layers: the leaf-nodes with collaborative edges for localizing local parts, the or-nodes specifying the switch of leaf-nodes, and the root-node encoding the global verification. A discriminative learning algorithm, extended from the CCCP [23], is proposed to train the model in a dynamical manner: the model structure (e.g., the configuration of the leaf-nodes associated with the or-nodes) is automatically determined with optimizing the multi-layer parameters during the iteration. The advantages of our method are two-fold. (i) The And-Or graph model enables us to handle well large intra-class variance and background clutters for object shape detection from images. (ii) The proposed learning algorithm is able to obtain the And-Or graph representation without requiring elaborate supervision and initialization. We validate the proposed method on several challenging databases (e.g., INRIA-Horse, ETHZ-Shape, and UIUC-People), and it outperforms the state-of-the-arts approaches.

We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model’s continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model’s main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective.

Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation that minimizes the maximum of the tasks' empirical risks. Via a certain relaxation of minimax MTL, we obtain a continuum of MTL formulations spanning minimax MTL and classical MTL. The full paradigm itself is loss-compositional, operating on the vector of empirical risks. It incorporates minimax MTL, its relaxations, and many new MTL formulations as special cases. We show theoretically that minimax MTL tends to avoid worst case outcomes on newly drawn test tasks in the learning to learn (LTL) test setting. The results of several MTL formulations on synthetic and real problems in the MTL and LTL test settings are encouraging.

Probabilistic graphical models are powerful tools for analyzing constrained, continuous domains. However, finding most-probable explanations (MPEs) in these models can be computationally expensive. In this paper, we improve the scalability of MPE inference in a class of graphical models with piecewise-linear and piecewise-quadratic dependencies and linear constraints over continuous domains. We derive algorithms based on a consensus-optimization framework and demonstrate their superior performance over state of the art. We show empirically that in a large-scale voter-preference modeling problem our algorithms scale linearly in the number of dependencies and constraints.