In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly,we propose a novel approach for the construction of sparsityinducing nonconvexpenalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionally, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of negative Kullback-Leiber (KL) distance functions.Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.

Finding contours in natural images is a fundamental problem that serves as the basis of many tasks such as image segmentation and object recognition. At the core of contour detection technologies are a set of hand-designed gradient features, used by most existing approaches including the state-of-the-art Global Pb (gPb) operator. In this work, we show that contour detection accuracy can be significantly improved by computing Sparse Code Gradients (SCG), which measure contrast using patch representations automatically learned through sparse coding. We use K-SVD and Orthogonal Matching Pursuit for efficient dictionary learning and encoding, and use multi-scale pooling and power transforms to code oriented local neighborhoods before computing gradients and applying linear SVM. By extracting rich representations from pixels and avoiding collapsing them prematurely, Sparse Code Gradients effectively learn how to measure local contrasts and find contours. We improve the F-measure metric on the BSDS500 benchmark to 0.74 (up from 0.71 of gPb contours). Moreover, our learning approach can easily adapt to novel sensor data such as Kinect-style RGB-D cameras: Sparse Code Gradients on depth images and surface normals lead to promising contour detection using depth and depth+color, as verified on the NYU Depth Dataset. Our work combines the concept of oriented gradients with sparse representation and opens up future possibilities for learning contour detection and segmentation.

Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of derivatives of the Bethe free energy, provide bounds on the derivatives and bracket the locations of stationary points, introducing a new technique called Bethe bound propagation. Several results apply to pairwise models whether associative or not. Applying these to discretized pseudo-marginals in the associative case we present a polynomial time approximation scheme for global optimization provided the maximum degree is $O(\log n)$, and discuss several extensions.

Visual features can help predict if a manipulation behavior will succeed at a given location. For example, the success of a behavior that flips light switches depends on the location of the switch. Within this paper, we present methods that enable a mobile manipulator to autonomously learn a function that takes an RGB image and a registered 3D point cloud as input and returns a 3D location at which a manipulation behavior is likely to succeed. Given a pair of manipulation behaviors that can change the state of the world between two sets (e.g., light switch up and light switch down), classifiers that detect when each behavior has been successful, and an initial hint as to where one of the behaviors will be successful, the robot autonomously trains a pair of support vector machine (SVM) classifiers by trying out the behaviors at locations in the world and observing the results. When an image feature vector associated with a 3D location is provided as input to one of the SVMs, the SVM predicts if the associated manipulation behavior will be successful at the 3D location. To evaluate our approach, we performed experiments with a PR2 robot from Willow Garage in a simulated home using behaviors that flip a light switch, push a rocker-type light switch, and operate a drawer. By using active learning, the robot efficiently learned SVMs that enabled it to consistently succeed at these tasks. After training, the robot also continued to learn in order to adapt in the event of failure.

We present a method to stop the evaluation of a prediction process when the result of the full evaluation is obvious. This trait is highly desirable in prediction tasks where a predictor evaluates all its features for every example in large datasets. We observe that some examples are easier to classify than others, a phenomenon which is characterized by the event when most of the features agree on the class of an example. By stopping the feature evaluation when encountering an easy- to-classify example, the predictor can achieve substantial gains in computation. Our method provides a natural attention mechanism for linear predictors where the predictor concentrates most of its computation on hard-to-classify examples and quickly discards easy-to-classify ones. By modifying a linear prediction algorithm such as an SVM or AdaBoost to include our attentive method we prove that the average number of features computed is O(sqrt(n log 1/sqrt(delta))) where n is the original number of features, and delta is the error rate incurred due to early stopping. We demonstrate the effectiveness of Attentive Prediction on MNIST, Real-sim, Gisette, and synthetic datasets.

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth objective functions such as support vector machines. In this paper, we investigate the performance of SGD without such smoothness assumptions, as well as a running average scheme to convert the SGD iterates to a solution with optimal optimization accuracy. In this framework, we prove that after T rounds, the suboptimality of the last SGD iterate scales as O(log(T)/\sqrt{T}) for non-smooth convex objective functions, and O(log(T)/T) in the non-smooth strongly convex case. To the best of our knowledge, these are the first bounds of this kind, and almost match the minimax-optimal rates obtainable by appropriate averaging schemes. We also propose a new and simple averaging scheme, which not only attains optimal rates, but can also be easily computed on-the-fly (in contrast, the suffix averaging scheme proposed in Rakhlin et al. (2011) is not as simple to implement). Finally, we provide some experimental illustrations.

A plethora of words are used to describe the spectrum of human emotions, but how many emotions are there really, and how do they interact? Over the past few decades, several theories of emotion have been proposed, each based around the existence of a set of 'basic emotions', and each supported by an extensive variety of research including studies in facial expression, ethology, neurology and physiology. Here we present research based on a theory that people transmit their understanding of emotions through the language they use surrounding emotion keywords. Using a labelled corpus of over 21,000 tweets, six of the basic emotion sets proposed in existing literature were analysed using Latent Semantic Clustering (LSC), evaluating the distinctiveness of the semantic meaning attached to the emotional label. We hypothesise that the more distinct the language is used to express a certain emotion, then the more distinct the perception (including proprioception) of that emotion is, and thus more 'basic'. This allows us to select the dimensions best representing the entire spectrum of emotion. We find that Ekman's set, arguably the most frequently used for classifying emotions, is in fact the most semantically distinct overall. Next, taking all analysed (that is, previously proposed) emotion terms into account, we determine the optimal semantically irreducible basic emotion set using an iterative LSC algorithm. Our newly-derived set (Accepting, Ashamed, Contempt, Interested, Joyful, Pleased, Sleepy, Stressed) generates a 6.1% increase in distinctiveness over Ekman's set (Angry, Disgusted, Joyful, Sad, Scared). We also demonstrate how using LSC data can help visualise emotions. We introduce the concept of an Emotion Profile and briefly analyse compound emotions both visually and mathematically.

Given a current news event, we tackle the problem of generating plausible predictions of future events it might cause. We present a new methodology for modeling and predicting such future news events using machine learning and data mining techniques. Our Pundit algorithm generalizes examples of causality pairs to infer a causality predictor. To obtain precisely labeled causality examples, we mine 150 years of news articles and apply semantic natural language modeling techniques to headlines containing certain predefined causality patterns. For generalization, the model uses a vast number of world knowledge ontologies. Empirical evaluation on real news articles shows that our Pundit algorithm performs as well as non-expert humans.

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. In this paper, we propose a GP Regression model with a latent variable that serves as an additional unobserved covariate for the regression. This model (which we call GPLC) allows for heteroscedasticity since it allows the function to have a changing partial derivative with respect to this unobserved covariate. With a suitable covariance function, our GPLC model can handle (a) Gaussian residuals with input-dependent variance, or (b) non-Gaussian residuals with input-dependent variance, or (c) Gaussian residuals with constant variance. We compare our model, using synthetic datasets, with a model proposed by Goldberg, Williams and Bishop (1998), which we refer to as GPLV, which only deals with case (a), as well as a standard GP model which can handle only case (c). Markov Chain Monte Carlo methods are developed for both modelsl. Experiments show that when the data is heteroscedastic, both GPLC and GPLV give better results (smaller mean squared error and negative log-probability density) than standard GP regression. In addition, when the residual are Gaussian, our GPLC model is generally nearly as good as GPLV, while when the residuals are non-Gaussian, our GPLC model is better than GPLV.

Classifying streaming data requires the development of methods which are computationally efficient and able to cope with changes in the underlying distribution of the stream, a phenomenon known in the literature as concept drift. We propose a new method for detecting concept drift which uses an Exponentially Weighted Moving Average (EWMA) chart to monitor the misclassification rate of an streaming classifier. Our approach is modular and can hence be run in parallel with any underlying classifier to provide an additional layer of concept drift detection. Moreover our method is computationally efficient with overhead O(1) and works in a fully online manner with no need to store data points in memory. Unlike many existing approaches to concept drift detection, our method allows the rate of false positive detections to be controlled and kept constant over time.