arXiv subjects

Jörg Lücke

Publications and source records attributed to Jörg Lücke.

21 records · Page 2Linked to original sources

arXiv2014

A Truncated EM Approach for Spike-and-Slab Sparse Coding

We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the application of a more flexible `spike-and-slab' distribution which models the absence or presence of a source's contribution independently of its strength if it contributes. We investigate two approaches to optimize the parameters of spike-and-slab sparse coding: a novel truncated EM approach and, for comparison, an approach based on standard factored variational distributions. The truncated approach can be regarded as a variational approach with truncated posteriors as variational distributions. In applications to source separation we find that both approaches improve the state-of-the-art in a number of standard benchmarks, which argues for the use of `spike-and-slab' priors for the corresponding data domains. Furthermore, we find that the truncated EM approach improves on the standard factored approach in source separation tasks$-$which hints to biases introduced by assuming posterior independence in the factored variational approach. Likewise, on a standard benchmark for image denoising, we find that the truncated EM approach improves on the factored variational approach. While the performance of the factored approach saturates with increasing numbers of hidden dimensions, the performance of the truncated approach improves the state-of-the-art for higher noise levels.

stat.ML↗

arXiv2012

Autonomous Cleaning of Corrupted Scanned Documents - A Generative Modeling Approach

We study the task of cleaning scanned text documents that are strongly corrupted by dirt such as manual line strokes, spilled ink etc. We aim at autonomously removing dirt from a single letter-size page based only on the information the page contains. Our approach, therefore, has to learn character representations without supervision and requires a mechanism to distinguish learned representations from irregular patterns. To learn character representations, we use a probabilistic generative model parameterizing pattern features, feature variances, the features' planar arrangements, and pattern frequencies. The latent variables of the model describe pattern class, pattern position, and the presence or absence of individual pattern features. The model parameters are optimized using a novel variational EM approximation. After learning, the parameters represent, independently of their absolute position, planar feature arrangements and their variances. A quality measure defined based on the learned representation then allows for an autonomous discrimination between regular character patterns and the irregular patterns making up the dirt. The irregular patterns can thus be removed to clean the document. For a full Latin alphabet we found that a single page does not contain sufficiently many character examples. However, even if heavily corrupted by dirt, we show that a page containing a lower number of character types can efficiently and autonomously be cleaned solely based on the structural regularity of the characters it contains. In different examples using characters from different alphabets, we demonstrate generality of the approach and discuss its implications for future developments.

cs.CV↗

arXiv2012

Closed-form EM for Sparse Coding and its Application to Source Separation

We define and discuss the first sparse coding algorithm based on closed-form EM updates and continuous latent variables. The underlying generative model consists of a standard `spike-and-slab' prior and a Gaussian noise model. Closed-form solutions for E- and M-step equations are derived by generalizing probabilistic PCA. The resulting EM algorithm can take all modes of a potentially multi-modal posterior into account. The computational cost of the algorithm scales exponentially with the number of hidden dimensions. However, with current computational resources, it is still possible to efficiently learn model parameters for medium-scale problems. Thus the model can be applied to the typical range of source separation tasks. In numerical experiments on artificial data we verify likelihood maximization and show that the derived algorithm recovers the sparse directions of standard sparse coding distributions. On source separation benchmarks comprised of realistic data we show that the algorithm is competitive with other recent methods.

stat.ML↗