Multitask learning with expert advice

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the “ideal” algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

A unifying view of multiple kernel learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion’s dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

Online discovery of similarity mappings

We consider the problem of choosing, sequentially, a map which assigns elements of a set A to a few elements of a set B. On each round, the algorithm suffers some cost associated with the chosen assignment, and the goal is to minimize the cumulative loss of these choices relative to the best map on the entire sequence. Even though the offline problem of finding the best map is provably hard, we show that there is an equivalent online approximation algorithm, Randomized Map Prediction (RMP), that is efficient and performs nearly as well. While drawing upon results from the "Online Prediction with Expert Advice" setting, we show how RMP can be utilized as an online approach to several standard batch problems. We apply RMP to online clustering as well as online feature selection and, surprisingly, RMP often outperforms the standard batch algorithms on these problems.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

Sparseness vs estimating conditional probabilities : some asymptotic results

One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Implicit online learning

Online learning algorithms have recently risen to prominence due to their strong theoretical guarantees and an increasing number of practical applications for large-scale data analysis problems. In this paper, we analyze a class of online learning algorithms based on fixed potentials and nonlinearized losses, which yields algorithms with implicit update rules. We show how to efficiently compute these updates, and we prove regret bounds for the algorithms. We apply our formulation to several special cases where our approach has benefits over existing online learning methods. In particular, we provide improved algorithms and bounds for the online metric learning problem, and show improved robustness for online linear prediction problems. Results over a variety of data sets demonstrate the advantages of our framework.

Adaptive online gradient descent

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between [square root T] and [log T]. Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

Multitask learning with expert advice

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the "ideal" algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

Robotics, Vision and Control : Fundamental Algorithms in MATLAB

The practice of robotics and computer vision each involve the application of computational algorithms to data. The research community has developed a very large body of algorithms but for a newcomer to the field this can be quite daunting. For more than 10 years the author has maintained two open-source MATLAB® Toolboxes, one for robotics and one for vision. They provide implementations of many important algorithms and allow users to work with real problems, not just trivial examples. This new book makes the fundamental algorithms of robotics, vision and control accessible to all. It weaves together theory, algorithms and examples in a narrative that covers robotics and computer vision separately and together. Using the latest versions of the Toolboxes the author shows how complex problems can be decomposed and solved using just a few simple lines of code. The topics covered are guided by real problems observed by the author over many years as a practitioner of both robotics and computer vision. It is written in a light but informative style, it is easy to read and absorb, and includes over 1000 MATLAB® and Simulink® examples and figures. The book is a real walk through the fundamentals of mobile robots, navigation, localization, arm-robot kinematics, dynamics and joint level control, then camera models, image processing, feature extraction and multi-view geometry, and finally bringing it all together with an extensive discussion of visual servo systems.

Geometry vs appearance for discriminating between posed and spontaneous emotions

Spontaneous facial expressions differ from posed ones in appearance, timing and accompanying head movements. Still images cannot provide timing or head movement information directly. However, indirectly the distances between key points on a face extracted from a still image using active shape models can capture some movement and pose changes. This information is superposed on information about non-rigid facial movement that is also part of the expression. Does geometric information improve the discrimination between spontaneous and posed facial expressions arising from discrete emotions? We investigate the performance of a machine vision system for discrimination between posed and spontaneous versions of six basic emotions that uses SIFT appearance based features and FAP geometric features. Experimental results on the NVIE database demonstrate that fusion of geometric information leads only to marginal improvement over appearance features. Using fusion features, surprise is the easiest emotion (83.4% accuracy) to be distinguished, while disgust is the most difficult (76.1%). Our results find different important facial regions between discriminating posed versus spontaneous version of one emotion and classifying the same emotion versus other emotions. The distribution of the selected SIFT features shows that mouth is more important for sadness, while nose is more important for surprise, however, both the nose and mouth are important for disgust, fear, and happiness. Eyebrows, eyes, nose and mouth are important for anger.

Evaluation of texture and geometry for dimensional facial expression recognition

Facial expression recognition (FER) algorithms mainly focus on classification into a small discrete set of emotions or representation of emotions using facial action units (AUs). Dimensional representation of emotions as continuous values in an arousal-valence space is relatively less investigated. It is not fully known whether fusion of geometric and texture features will result in better dimensional representation of spontaneous emotions. Moreover, the performance of many previously proposed approaches to dimensional representation has not been evaluated thoroughly on publicly available databases. To address these limitations, this paper presents an evaluation framework for dimensional representation of spontaneous facial expressions using texture and geometric features. SIFT, Gabor and LBP features are extracted around facial fiducial points and fused with FAP distance features. The CFS algorithm is adopted for discriminative texture feature selection. Experimental results evaluated on the publicly accessible NVIE database demonstrate that fusion of texture and geometry does not lead to a much better performance than using texture alone, but does result in a significant performance improvement over geometry alone. LBP features perform the best when fused with geometric features. Distributions of arousal and valence for different emotions obtained via the feature extraction process are compared with those obtained from subjective ground truth values assigned by viewers. Predicted valence is found to have a more similar distribution to ground truth than arousal in terms of covariance or Bhattacharya distance, but it shows a greater distance between the means.

Multi-objective optimisation of bijective s-boxes

In this paper we investigate the heuristic construction of bijective s-boxes that satisfy a wide range of cryptographic criteria including algebraic complexity, high nonlinearity, low autocorrelation and have none of the known weaknesses including linear structures, fixed points or linear redundancy. We demonstrate that the power mappings can be evolved (by iterated mutation operators alone) to generate bijective s-boxes with the best known tradeoffs among the considered criteria. The s-boxes found are suitable for use directly in modern encryption algorithms.