Barnabás Póczos

Online group-structured dictionary learning

We develop a dictionary learning method which is (i) online, (ii) enables overlapping group structures with (iii) non-convex sparsity-inducing regularization and (iv) handles the partially observable case. Structured sparsity and the related group norms have recently gained widespread attention in group-sparsity regularized problems in the case when the dictionary is assumed to be known and fixed. However, when the dictionary also needs to be learned, the problem is much more difficult. Only a few methods have been proposed to solve this problem, and they can handle two of these four desirable properties at most. To the best of our knowledge, our proposed method is the first one that possesses all of these properties. We investigate several interesting special cases of our framework, such as the online, structured, sparse non-negative matrix factorization, and demonstrate the efficiency of our algorithm with several numerical experiments.

Independent subspace analysis using geodesic spanning trees

A novel algorithm for performing Independent Subspace Analysis, the estimation of hidden independent subspaces is introduced. This task is a generalization of Independent Component Analysis. The algorithm works by estimating the multi-dimensional differential entropy. The estimation utilizes minimal geodesic spanning trees matched to the sample points. Numerical studies include (i) illustrative examples, (ii) a generalization of the cocktail-party problem to songs played by bands, and (iii) an example on mixed independent subspaces, where subspaces have dependent sources, which are pairwise independent.

Cross-Entropy optimization for independent process analysis

We treat the problem of searching for hidden multi-dimensional independent auto-regressive processes. First, we transform the problem to Independent Subspace Analysis (ISA). Our main contribution concerns ISA. We show that under certain conditions, ISA is equivalent to a combinatorial optimization problem. For the solution of this optimization we apply the cross-entropy method. Numerical simulations indicate that the cross-entropy method can provide considerable improvements over other state-of-the-art methods.

Nonparametric kernel estimators for image classification

We introduce a new discriminative learning method for image classification. We assume that the images are represented by unordered, multi-dimensional, finite sets of feature vectors, and that these sets might have different cardinality. This allows us to use consistent nonparametric divergence estimators to define new kernels over these sets, and then apply them in kernel classifiers. Our numerical results demonstrate that in many cases this approach can outperform state-of-the-art competitors on both simulated and challenging real-world datasets.

Separation theorem for independent subspace analysis and its consequences

Independent component analysis (ICA) - the theory of mixed, independent, non-Gaussian sources - has a central role in signal processing, computer vision and pattern recognition. One of the most fundamental conjectures of this research field is that independent subspace analysis (ISA) - the extension of the ICA problem, where groups of sources are independent - can be solved by traditional ICA followed by grouping the ICA components. The conjecture, called ISA separation principle, (i) has been rigorously proven for some distribution types recently, (ii) forms the basis of the state-of-the-art ISA solvers, (iii) enables one to estimate the unknown number and the dimensions of the sources efficiently, and (iv) can be extended to generalizations of the ISA task, such as different linear-, controlled-, post nonlinear-, complex valued-, partially observed problems, as well as to problems dealing with nonparametric source dynamics. Here, we shall review the advances on this field.

Independent subspace analysis using k-nearest neighborhood distances

A novel algorithin called independent subspace analysis (ISA) is introduced to estimate independent subspaccs. The algorithm solves tile ISA problein by estimating umlti-diinensional differential entropics. Two variants are examined, both of them utilize distances be tween the k-nearest neighbors of the sample points. Numerical simulations demonstrate the usefulness of the algorithms.

Quantifying Differences and Similarities in Whole-Brain White Matter Architecture Using Local Connectome Fingerprints.

Quantifying differences or similarities in connectomes has been a challenge due to the immense complexity of global brain networks. Here we introduce a noninvasive method that uses diffusion MRI to characterize whole-brain white matter architecture as a single local connectome fingerprint that allows for a direct comparison between structural connectomes. In four independently acquired data sets with repeated scans (total N = 213), we show that the local connectome fingerprint is highly specific to an individual, allowing for an accurate self-versus-others classification that achieved 100% accuracy across 17,398 identification tests. The estimated classification error was approximately one thousand times smaller than fingerprints derived from diffusivity-based measures or region-to-region connectivity patterns for repeat scans acquired within 3 months. The local connectome fingerprint also revealed neuroplasticity within an individual reflected as a decreasing trend in self-similarity across time, whereas this change was not observed in the diffusivity measures. Moreover, the local connectome fingerprint can be used as a phenotypic marker, revealing 12.51% similarity between monozygotic twins, 5.14% between dizygotic twins, and 4.51% between none-twin siblings, relative to differences between unrelated subjects. This novel approach opens a new door for probing the influence of pathological, genetic, social, or environmental factors on the unique configuration of the human connectome.

ICA and ISA using Schweizer-Wolff measure of dependence

We propose a new algorithm for independent component and independent subspace analysis problems. This algorithm uses a contrast based on the Schweizer-Wolff measure of pairwise dependence (Schweizer & Wolff, 1981), a non-parametric measure computed on pairwise ranks of the variables. Our algorithm frequently outperforms state of the art ICA methods in the normal setting, is significantly more robust to outliers in the mixed signals, and performs well even in the presence of noise. Our method can also be used to solve independent subspace analysis (ISA) problems by grouping signals recovered by ICA methods. We provide an extensive empirical evaluation using simulated, sound, and image data.

Independent subspace analysis on innovations

Independent subspace analysis (ISA) that deals with multi-dimensional independent sources, is a generalization of independent component analysis (ICA). However, all known ISA algorithms may become ineffective when the sources possess temporal structure. The innovation process instead of the original mixtures has been proposed to solve ICA problems with temporal dependencies. Here we show that this strategy can be applied to ISA as well. We demonstrate the idea on a mixture of 3D processes and also on a mixture of facial pictures used as two-dimensional deterministic sources. ISA on innovations was able to find the original subspaces, while plain ISA was not.

A Machine Learning Approach for Dynamical Mass Measurements of Galaxy Clusters

We present a modern machine learning approach for cluster dynamical mass measurements that is a factor of two improvement over using a conventional scaling relation. Different methods are tested against a mock cluster catalog constructed using halos with mass >= 10^14 Msolar/h from Multidarks publicly-available N-body MDPL halo catalog. In the conventional method, we use a standard M(sigma_v) power law scaling relation to infer cluster mass, M, from line-of-sight (LOS) galaxy velocity dispersion, sigma_v. The resulting fractional mass error distribution is broad, with width=0.87 (68% scatter), and has extended high-error tails. The standard scaling relation can be simply enhanced by including higher-order moments of the LOS velocity distribution. Applying the kurtosis as a correction term to log(sigma_v) reduces the width of the error distribution to 0.74 (16% improvement). Machine learning can be used to take full advantage of all the information in the velocity distribution. We employ the Support Distribution Machines (SDMs) algorithm that learns from distributions of data to predict single values. SDMs trained and tested on the distribution of LOS velocities yield width=0.46 (47% improvement). Furthermore, the problematic tails of the mass error distribution are effectively eliminated. Decreasing cluster mass errors will improve measurements of the growth of structure and lead to tighter constraints on cosmological parameters.