Alignment of time series is an important problem to solve in many scientific disciplines. In particular, temporal alignment of two or more subjects performing similar activities is a challenging problem due to the large temporal scale difference between human actions as well as the inter/intra subject variability. In this paper we present canonical time warping (CTW), an extension of canonical correlation analysis (CCA) for spatio-temporal alignment of the behavior between two subjects. CTW extends previous work on CCA in two ways: (i) it combines CCA with dynamic time warping for temporal alignment; and (ii) it extends CCA to allow local spatial deformations. We show CTWs effectiveness in three experiments: alignment of synthetic data, alignment of motion capture data of two subjects performing similar actions, and alignment of two people with similar facial expressions. Our results demonstrate that CTW provides both visually and qualitatively better alignment than state-of-the-art techniques based on dynamic time warping.

We consider multi-label prediction problems with large output spaces under the assumption of output sparsity - that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems needonly be logarithmic in the total number of possible labels, making this approach radically more efficient than others. We also state and prove robustness guarantees for this method in the form of regret transform bounds (in general), and also provide a more detailed analysis for the linear prediction setting.

Many popular optimization algorithms, like the Levenberg-Marquardt algorithm (LMA), use heuristic-based controllers'' that modulate the behavior of the optimizer during the optimization process. For example, in the LMA a damping parameter is dynamically modified based on a set rules that were developed using various heuristic arguments. Reinforcement learning (RL) is a machine learning approach to learn optimal controllers by examples and thus is an obvious candidate to improve the heuristic-based controllers implicit in the most popular and heavily used optimization algorithms. Improving the performance of off-the-shelf optimizers is particularly important for time-constrained optimization problems. For example the LMA algorithm has become popular for many real-time computer vision problems, including object tracking from video, where only a small amount of time can be allocated to the optimizer on each incoming video frame. Here we show that a popular modern reinforcement learning technique using a very simply state space can dramatically improve the performance of general purpose optimizers, like the LMA. Most surprisingly the controllers learned for a particular domain appear to work very well also on very different optimization domains. For example we used RL methods to train a new controller for the damping parameter of the LMA. This controller was trained on a collection of classic, relatively small, non-linear regression problems. The modified LMA performed better than the standard LMA on these problems. Most surprisingly, it also dramatically outperformed the standard LMA on a difficult large scale computer vision problem for which it had not been trained before. Thus the controller appeared to have extracted control rules that were not just domain specific but generalized across a wide range of optimization domains."

Language comprehension in humans is significantly constrained by memory, yet rapid, highly incremental, and capable of utilizing a wide range of contextual information to resolve ambiguity and form expectations about future input. In contrast, most of the leading psycholinguistic models and fielded algorithms for natural language parsing are non-incremental, have run time superlinear in input length, and/or enforce structural locality constraints on probabilistic dependencies between events. We present a new limited-memory model of sentence comprehension which involves an adaptation of the particle filter, a sequential Monte Carlo method, to the problem of incremental parsing. We show that this model can reproduce classic results in online sentence comprehension, and that it naturally provides the first rational account of an outstanding problem in psycholinguistics, in which the preferred alternative in a syntactic ambiguity seems to grow more attractive over time even in the absence of strong disambiguating information.

Locality information is crucial in datasets where each variable corresponds to a measurement in a manifold (silhouettes, motion trajectories, 2D and 3D images). Although these datasets are typically under-sampled and high-dimensional, they often need to be represented with low-complexity statistical models, which are comprised of only the important probabilistic dependencies in the datasets. Most methods attempt to reduce model complexity by enforcing structure sparseness. However, sparseness cannot describe inherent regularities in the structure. Hence, in this paper we first propose a new class of Gaussian graphical models which, together with sparseness, imposes local constancy through ${\ell}_1$-norm penalization. Second, we propose an efficient algorithm which decomposes the strictly convex maximum likelihood estimation into a sequence of problems with closed form solutions. Through synthetic experiments, we evaluate the closeness of the recovered models to the ground truth. We also test the generalization performance of our method in a wide range of complex real-world datasets and demonstrate that it can capture useful structures such as the rotation and shrinking of a beating heart, motion correlations between body parts during walking and functional interactions of brain regions. Our method outperforms the state-of-the-art structure learning techniques for Gaussian graphical models both for small and large datasets.

We present a multi-label multiple kernel learning (MKL) formulation, in which the data are embedded into a low-dimensional space directed by the instance-label correlations encoded into a hypergraph. We formulate the problem in the kernel-induced feature space and propose to learn the kernel matrix as a linear combination of a given collection of kernel matrices in the MKL framework. The proposed learning formulation leads to a non-smooth min-max problem, and it can be cast into a semi-infinite linear program (SILP). We further propose an approximate formulation with a guaranteed error bound which involves an unconstrained and convex optimization problem. In addition, we show that the objective function of the approximate formulation is continuously differentiable with Lipschitz gradient, and hence existing methods can be employed to compute the optimal solution efficiently. We apply the proposed formulation to the automated annotation of Drosophila gene expression pattern images, and promising results have been reported in comparison with representative algorithms.

We study convergence properties of empirical minimization of a stochastic strongly convex objective, where the stochastic component is linear. We show that the value attained by the empirical minimizer converges to the optimal value with rate 1/n. The result applies, in particular, to the SVM objective. Thus, we obtain a rate of 1/n on the convergence of the SVM objective (with fixed regularization parameter)to its infinite data limit. We demonstrate how this is essential for obtaining certain type of oracle inequalities for SVMs.

Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise ($l_2$, $l_1$) distances, in static, large-scale, and sparse data sets such as text and Web data. It was previously presented using a heuristic argument. This study extends CRS to handle dynamic or streaming data, which much better reflect the real-world situation than assuming static data. Compared with other known sketching algorithms for dimension reductions such as stable random projections, CRS exhibits a significant advantage in that it is ``one-sketch-for-all.'' In particular, we demonstrate that CRS can be applied to efficiently compute the $l_p$ distance and the Hilbertian metrics, both are popular in machine learning. Although a fully rigorous analysis of CRS is difficult, we prove that, with a simple modification, CRS is rigorous at least for an important application of computing Hamming norms. A generic estimator and an approximate variance formula are provided and tested on various applications, for computing Hamming norms, Hamming distances, and $\chi^2$ distances.

We address the problem of learning classifiers for several related tasks that may differ in their joint distribution of input and output variables. For each task, small - possibly even empty - labeled samples and large unlabeled samples are available. While the unlabeled samples reflect the target distribution, the labeled samples may be biased. We derive a solution that produces resampling weights which match the pool of all examples to the target distribution of any given task. Our work is motivated by the problem of predicting sociodemographic features for users of web portals, based on the content which they have accessed. Here, questionnaires offered to a small portion of each portal's users produce biased samples. Transfer learning enables us to make predictions even for new portals with few or no training data and improves the overall prediction accuracy.

Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments. For sufficiently rich (characteristic) RKHSs, each probability distribution has a unique embedding, allowing all statistical properties of the distribution to be taken into consideration. Necessary and sufficient conditions for an RKHS to be characteristic exist for $\R^n$. In the present work, conditions are established for an RKHS to be characteristic on groups and semigroups. Illustrative examples are provided, including characteristic kernels on periodic domains, rotation matrices, and $\R^n_+$.