Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. In this paper we study a variant of this problem where the original $n$ input variables are compressed by a random linear transformation to $m \ll n$ examples in $p$ dimensions, and establish conditions under which a sparse linear model can be successfully recovered from the compressed data. A primary motivation for this compression procedure is to anonymize the data and preserve privacy by revealing little information about the original data. We characterize the number of random projections that are required for $\ell_1$-regularized compressed regression to identify the nonzero coefficients in the true model with probability approaching one, a property called ``sparsistence.'' In addition, we show that $\ell_1$-regularized compressed regression asymptotically predicts as well as an oracle linear model, a property called ``persistence.'' Finally, we characterize the privacy properties of the compression procedure in information-theoretic terms, establishing upper bounds on the rate of information communicated between the compressed and uncompressed data that decay to zero.

We construct a biologically motivated stochastic differential model of the neural and hemodynamic activity underlying the observed Blood Oxygen Level Dependent (BOLD) signal in Functional Magnetic Resonance Imaging (fMRI). The model poses a difficult parameter estimation problem, both theoretically due to the nonlinearity and divergence of the differential system, and computationally due to its time and space complexity. We adapt a particle filter and smoother to the task, and discuss some of the practical approaches used to tackle the difficulties, including use of sparse matrices and parallelisation. Results demonstrate the tractability of the approach in its application to an effective connectivity study.

Brain-Computer Interfaces can suffer from a large variance of the subject conditions withinand across sessions. For example vigilance fluctuations in the individual, variabletask involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to define features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. We enforce invariance properties by adding terms to the denominator of a Rayleigh coefficient representation of CSP such as disturbance covariance matrices from fluctuations in visual processing. In this manner physiological prior knowledge can be used to shape the classification engine for BCI. As a proof of concept we present a BCI classifier that is robust to changes in the level of parietal α-activity. In other words, the EEG decoding still works when there are lapses in vigilance.

An important problem in many fields is the analysis of counts data to extract meaningful latent components. Methods like Probabilistic Latent Semantic Analysis (PLSA) and Latent Dirichlet Allocation (LDA) have been proposed for this purpose. However, they are limited in the number of components they can extract and also do not have a provision to control the expressiveness" of the extracted components. In this paper, we present a learning formulation to address these limitations by employing the notion of sparsity. We start with the PLSA framework and use an entropic prior in a maximum a posteriori formulation to enforce sparsity. We show that this allows the extraction of overcomplete sets of latent components which better characterize the data. We present experimental evidence of the utility of such representations."

Hierarchical penalizan'on is a generic framework for incorporating prior informa--

The notion of algorithmic stability has been used effectively in the past to derive tight generalization bounds. A key advantage of these bounds is that they are de- signed for specific learning algorithms, exploiting their particular properties. But, as in much of learning theory, existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed (i.i.d.). In many machine learning applications, however, this assumption does not hold. The observations received by the learning algorithm often have some inherent temporal dependence, which is clear in system diagnosis or time series prediction problems. This paper studies the scenario where the observations are drawn from a station- ary beta-mixing sequence, which implies a dependence between observations that weaken over time. It proves novel stability-based generalization bounds that hold even with this more general setting. These bounds strictly generalize the bounds given in the i.i.d. case. We also illustrate their application in the case of several general classes of learning algorithms, including Support Vector Regression and Kernel Ridge Regression.

Estimation of three-dimensional articulated human pose and motion from images is a central problem in computer vision. Much of the previous work has been limited by the use of crude generative models of humans represented as articulated collectionsof simple parts such as cylinders. Automatic initialization of such models has proved difficult and most approaches assume that the size and shape of the body parts are known a priori. In this paper we propose a method for automatically recovering a detailed parametric model of nonrigid body shape and pose from monocular imagery. Specifically, we represent the body using a parameterized triangulatedmesh model that is learned from a database of human range scans. We demonstrate a discriminative method to directly recover the model parameters frommonocular images using a conditional mixture of kernel regressors. This predicted pose and shape are used to initialize a generative model for more detailed pose and shape estimation. The resulting approach allows fully automatic pose and shape recovery from monocular and multi-camera imagery. Experimental resultsshow that our method is capable of robustly recovering articulated pose, shape and biometric measurements (e.g.

We present a new class of models for high-dimensional nonparametric regression and classification called sparse additive models (SpAM). Our methods combine ideas from sparse linear modeling and additive nonparametric regression. We derive amethod for fitting the models that is effective even when the number of covariates is larger than the sample size. A statistical analysis of the properties of SpAM is given together with empirical results on synthetic and real data, showing thatSpAM can be effective in fitting sparse nonparametric models in high dimensional data.

Random field approaches are a popular way of modelling spatial regularities in images.

To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user specified shiftinvariant kernel.We explore two sets of random features, provide convergence bounds on their ability to approximate various radial basis kernels, and show that in large-scale classification and regression tasks linear machine learning algorithms appliedto these features outperform state-of-the-art large-scale kernel machines.