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.

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.

Predicting residue-wise contact orders in proteins by support vector regression

Background The residue-wise contact order (RWCO) describes the sequence separations between the residues of interest and its contacting residues in a protein sequence. It is a new kind of one-dimensional protein structure that represents the extent of long-range contacts and is considered as a generalization of contact order. Together with secondary structure, accessible surface area, the B factor, and contact number, RWCO provides comprehensive and indispensable important information to reconstructing the protein three-dimensional structure from a set of one-dimensional structural properties. Accurately predicting RWCO values could have many important applications in protein three-dimensional structure prediction and protein folding rate prediction, and give deep insights into protein sequence-structure relationships. Results We developed a novel approach to predict residue-wise contact order values in proteins based on support vector regression (SVR), starting from primary amino acid sequences. We explored seven different sequence encoding schemes to examine their effects on the prediction performance, including local sequence in the form of PSI-BLAST profiles, local sequence plus amino acid composition, local sequence plus molecular weight, local sequence plus secondary structure predicted by PSIPRED, local sequence plus molecular weight and amino acid composition, local sequence plus molecular weight and predicted secondary structure, and local sequence plus molecular weight, amino acid composition and predicted secondary structure. When using local sequences with multiple sequence alignments in the form of PSI-BLAST profiles, we could predict the RWCO distribution with a Pearson correlation coefficient (CC) between the predicted and observed RWCO values of 0.55, and root mean square error (RMSE) of 0.82, based on a well-defined dataset with 680 protein sequences. Moreover, by incorporating global features such as molecular weight and amino acid composition we could further improve the prediction performance with the CC to 0.57 and an RMSE of 0.79. In addition, combining the predicted secondary structure by PSIPRED was found to significantly improve the prediction performance and could yield the best prediction accuracy with a CC of 0.60 and RMSE of 0.78, which provided at least comparable performance compared with the other existing methods. Conclusion The SVR method shows a prediction performance competitive with or at least comparable to the previously developed linear regression-based methods for predicting RWCO values. In contrast to support vector classification (SVC), SVR is very good at estimating the raw value profiles of the samples. The successful application of the SVR approach in this study reinforces the fact that support vector regression is a powerful tool in extracting the protein sequence-structure relationship and in estimating the protein structural profiles from amino acid sequences.

Speech recognition in adverse environments using lip information

The performance of automatic speech recognition systems deteriorates in the presence of noise. One known solution is to incorporate video information with an existing acoustic speech recognition system. We investigate the performance of the individual acoustic and visual sub-systems and then examine different ways in which the integration of the two systems may be performed. The system is to be implemented in real time on a Texas Instruments' TMS320C80 DSP.

Super-resolved faces for improved face recognition from surveillance video advances in biometrics

Characteristics of surveillance video generally include low resolution and poor quality due to environmental, storage and processing limitations. It is extremely difficult for computers and human operators to identify individuals from these videos. To overcome this problem, super-resolution can be used in conjunction with an automated face recognition system to enhance the spatial resolution of video frames containing the subject and narrow down the number of manual verifications performed by the human operator by presenting a list of most likely candidates from the database. As the super-resolution reconstruction process is ill-posed, visual artifacts are often generated as a result. These artifacts can be visually distracting to humans and/or affect machine recognition algorithms. While it is intuitive that higher resolution should lead to improved recognition accuracy, the effects of super-resolution and such artifacts on face recognition performance have not been systematically studied. This paper aims to address this gap while illustrating that super-resolution allows more accurate identification of individuals from low-resolution surveillance footage. The proposed optical flow-based super-resolution method is benchmarked against Baker et al.’s hallucination and Schultz et al.’s super-resolution techniques on images from the Terrascope and XM2VTS databases. Ground truth and interpolated images were also tested to provide a baseline for comparison. Results show that a suitable super-resolution system can improve the discriminability of surveillance video and enhance face recognition accuracy. The experiments also show that Schultz et al.’s method fails when dealing surveillance footage due to its assumption of rigid objects in the scene. The hallucination and optical flow-based methods performed comparably, with the optical flow-based method producing less visually distracting artifacts that interfered with human recognition.

The rademacher complexity of coregularized kernel classes

In the multi-view approach to semisupervised learning, we choose one predictor from each of multiple hypothesis classes, and we co-regularize our choices by penalizing disagreement among the predictors on the unlabeled data. We examine the co-regularization method used in the co-regularized least squares (CoRLS) algorithm, in which the views are reproducing kernel Hilbert spaces (RKHS's), and the disagreement penalty is the average squared difference in predictions. The final predictor is the pointwise average of the predictors from each view. We call the set of predictors that can result from this procedure the co-regularized hypothesis class. Our main result is a tight bound on the Rademacher complexity of the co-regularized hypothesis class in terms of the kernel matrices of each RKHS. We find that the co-regularization reduces the Rademacher complexity by an amount that depends on the distance between the two views, as measured by a data dependent metric. We then use standard techniques to bound the gap between training error and test error for the CoRLS algorithm. Experimentally, we find that the amount of reduction in complexity introduced by co regularization correlates with the amount of improvement that co-regularization gives in the CoRLS algorithm.

REGAL : a regularization based algorithm for reinforcement learning in weakly communicating MDPs

We provide an algorithm that achieves the optimal regret rate in an unknown weakly communicating Markov Decision Process (MDP). The algorithm proceeds in episodes where, in each episode, it picks a policy using regularization based on the span of the optimal bias vector. For an MDP with S states and A actions whose optimal bias vector has span bounded by H, we show a regret bound of ~ O(HS p AT ). We also relate the span to various diameter-like quantities associated with the MDP, demonstrating how our results improve on previous regret bounds.