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Jörg Lücke

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14 papers

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JMLR Journal 2023 Journal Article

Generic Unsupervised Optimization for a Latent Variable Model With Exponential Family Observables

Hamid Mousavi
Jakob Drefs
Florian Hirschberger
Jörg Lücke

Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic sparse coding which both assume a weighted linear summation of the latents to determine the mean of a Gaussian distribution for the observables. In many cases, however, observables do not follow a Gaussian distribution. For unsupervised learning, LVMs which assume specific non-Gaussian observables (e.g., Bernoulli or Poisson) have therefore been considered. Already for specific choices of distributions, parameter optimization is challenging and only a few previous contributions considered LVMs with more generally defined observable distributions. In this contribution, we do consider LVMs that are defined for a range of different distributions, i.e., observables can follow any (regular) distribution of the exponential family. Furthermore, the novel class of LVMs presented here is defined for binary latents, and it uses maximization in place of summation to link the latents to observables. In order to derive an optimization procedure, we follow an expectation maximization approach for maximum likelihood parameter estimation. We then show, as our main result, that a set of very concise parameter update equations can be derived which feature the same functional form for all exponential family distributions. The derived generic optimization can consequently be applied (without further derivations) to different types of metric data (Gaussian and non-Gaussian) as well as to different types of discrete data. Moreover, the derived optimization equations can be combined with a recently suggested variational acceleration which is likewise generically applicable to the LVMs considered here. Thus, the combination maintains generic and direct applicability of the derived optimization procedure, but, crucially, enables efficient scalability. We numerically verify our analytical results using different observable distributions, and, furthermore, discuss some potential applications such as learning of variance structure, noise type estimation and denoising. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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JMLR Journal 2022 Journal Article

Evolutionary Variational Optimization of Generative Models

Jakob Drefs
Enrico Guiraud
Jörg Lücke

We combine two popular optimization approaches to derive learning algorithms for generative models: variational optimization and evolutionary algorithms. The combination is realized for generative models with discrete latents by using truncated posteriors as the family of variational distributions. The variational parameters of truncated posteriors are sets of latent states. By interpreting these states as genomes of individuals and by using the variational lower bound to define a fitness, we can apply evolutionary algorithms to realize the variational loop. The used variational distributions are very flexible and we show that evolutionary algorithms can effectively and efficiently optimize the variational bound. Furthermore, the variational loop is generally applicable (“black box”) with no analytical derivations required. To show general applicability, we apply the approach to three generative models (we use Noisy-OR Bayes Nets, Binary Sparse Coding, and Spike-and-Slab Sparse Coding). To demonstrate effectiveness and efficiency of the novel variational approach, we use the standard competitive benchmarks of image denoising and inpainting. The benchmarks allow quantitative comparisons to a wide range of methods including probabilistic approaches, deep deterministic and generative networks, and non-local image processing methods. In the category of “zero-shot” learning (when only the corrupted image is used for training), we observed the evolutionary variational algorithm to significantly improve the state-of-the-art in many benchmark settings. For one well-known inpainting benchmark, we also observed state-of-the-art performance across all categories of algorithms although we only train on the corrupted image. In general, our investigations highlight the importance of research on optimization methods for generative models to achieve performance improvements. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

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YNIMG Journal 2021 Journal Article

Generalizable dimensions of human cortical auditory processing of speech in natural soundscapes: A data-driven ultra high field fMRI approach

Moritz Boos
Jörg Lücke
Jochem W. Rieger

Speech comprehension in natural soundscapes rests on the ability of the auditory system to extract speech information from a complex acoustic signal with overlapping contributions from many sound sources. Here we reveal the canonical processing of speech in natural soundscapes on multiple scales by using data-driven modeling approaches to characterize sounds to analyze ultra high field fMRI recorded while participants listened to the audio soundtrack of a movie. We show that at the functional level the neuronal processing of speech in natural soundscapes can be surprisingly low dimensional in the human cortex, highlighting the functional efficiency of the auditory system for a seemingly complex task. Particularly, we find that a model comprising three functional dimensions of auditory processing in the temporal lobes is shared across participants' fMRI activity. We further demonstrate that the three functional dimensions are implemented in anatomically overlapping networks that process different aspects of speech in natural soundscapes. One is most sensitive to complex auditory features present in speech, another to complex auditory features and fast temporal modulations, that are not specific to speech, and one codes mainly sound level. These results were derived with few a-priori assumptions and provide a detailed and computationally reproducible account of the cortical activity in the temporal lobe elicited by the processing of speech in natural soundscapes.

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NeurIPS Conference 2016 Conference Paper

Neurons Equipped with Intrinsic Plasticity Learn Stimulus Intensity Statistics

Travis Monk
Cristina Savin
Jörg Lücke

Experience constantly shapes neural circuits through a variety of plasticity mechanisms. While the functional roles of some plasticity mechanisms are well-understood, it remains unclear how changes in neural excitability contribute to learning. Here, we develop a normative interpretation of intrinsic plasticity (IP) as a key component of unsupervised learning. We introduce a novel generative mixture model that accounts for the class-specific statistics of stimulus intensities, and we derive a neural circuit that learns the input classes and their intensities. We will analytically show that inference and learning for our generative model can be achieved by a neural circuit with intensity-sensitive neurons equipped with a specific form of IP. Numerical experiments verify our analytical derivations and show robust behavior for artificial and natural stimuli. Our results link IP to non-trivial input statistics, in particular the statistics of stimulus intensities for classes to which a neuron is sensitive. More generally, our work paves the way toward new classification algorithms that are robust to intensity variations.

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NeurIPS Conference 2016 Conference Paper

Select-and-Sample for Spike-and-Slab Sparse Coding

Abdul-Saboor Sheikh
Jörg Lücke

Probabilistic inference serves as a popular model for neural processing. It is still unclear, however, how approximate probabilistic inference can be accurate and scalable to very high-dimensional continuous latent spaces. Especially as typical posteriors for sensory data can be expected to exhibit complex latent dependencies including multiple modes. Here, we study an approach that can efficiently be scaled while maintaining a richly structured posterior approximation under these conditions. As example model we use spike-and-slab sparse coding for V1 processing, and combine latent subspace selection with Gibbs sampling (select-and-sample). Unlike factored variational approaches, the method can maintain large numbers of posterior modes and complex latent dependencies. Unlike pure sampling, the method is scalable to very high-dimensional latent spaces. Among all sparse coding approaches with non-trivial posterior approximations (MAP or ICA-like models), we report the largest-scale results. In applications we firstly verify the approach by showing competitiveness in standard denoising benchmarks. Secondly, we use its scalability to, for the first time, study highly-overcomplete settings for V1 encoding using sophisticated posterior representations. More generally, our study shows that very accurate probabilistic inference for multi-modal posteriors with complex dependencies is tractable, functionally desirable and consistent with models for neural inference.

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JMLR Journal 2014 Journal Article

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

Abdul-Saboor Sheikh
Jacquelyn A. Shelton
Jörg Lücke

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. [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

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JMLR Journal 2014 Journal Article

Efficient Occlusive Components Analysis

Marc Henniges
Richard E. Turner
Maneesh Sahani
Julian Eggert
Jörg Lücke

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learned from an unlabeled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. Tractable approximations can be derived, however, by applying a truncated variational approach to Expectation Maximization (EM). In numerical experiments it is shown that these approximations recover the underlying set of object parameters including data noise and sparsity. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating components. The studied approach demonstrates that the multiple-causes generative approach can be generalized to extract occluding components, which links research on occlusion to the field of sparse coding approaches. [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

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NeurIPS Conference 2013 Conference Paper

What Are the Invariant Occlusive Components of Image Patches? A Probabilistic Generative Approach

Zhenwen Dai
Georgios Exarchakis
Jörg Lücke

We study optimal image encoding based on a generative approach with non-linear feature combinations and explicit position encoding. By far most approaches to unsupervised learning learning of visual features, such as sparse coding or ICA, account for translations by representing the same features at different positions. Some earlier models used a separate encoding of features and their positions to facilitate invariant data encoding and recognition. All probabilistic generative models with explicit position encoding have so far assumed a linear superposition of components to encode image patches. Here, we for the first time apply a model with non-linear feature superposition and explicit position encoding. By avoiding linear superpositions, the studied model represents a closer match to component occlusions which are ubiquitous in natural images. In order to account for occlusions, the non-linear model encodes patches qualitatively very different from linear models by using component representations separated into mask and feature parameters. We first investigated encodings learned by the model using artificial data with mutually occluding components. We find that the model extracts the components, and that it can correctly identify the occlusive components with the hidden variables of the model. On natural image patches, the model learns component masks and features for typical image components. By using reverse correlation, we estimate the receptive fields associated with the model's hidden units. We find many Gabor-like or globular receptive fields as well as fields sensitive to more complex structures. Our results show that probabilistic models that capture occlusions and invariances can be trained efficiently on image patches, and that the resulting encoding represents an alternative model for the neural encoding of images in the primary visual cortex.

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NeurIPS Conference 2012 Conference Paper

Why MCA? Nonlinear sparse coding with spike-and-slab prior for neurally plausible image encoding

Philip Sterne
Joerg Bornschein
Abdul-Saboor Sheikh
Jörg Lücke
Jacquelyn Shelton

Modelling natural images with sparse coding (SC) has faced two main challenges: ﬂexibly representing varying pixel intensities and realistically representing low- level image components. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a lin- ear combination. The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the ﬁrst time that a model combining both improvements can be trained efﬁciently while retaining the rich structure of the posteriors. We design an exact piece- wise Gibbs sampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions. Applying the model to image patches we study the optimal encoding of images by simple cells in V1 and compare the model’s predictions with in vivo neural recordings. In contrast to standard SC, we ﬁnd that the optimal prior favors asymmetric and bimodal ac- tivity of simple cells. Testing our model for consistency we ﬁnd that the average posterior is approximately equal to the prior. Furthermore, we ﬁnd that the model predicts a high percentage of globular receptive ﬁelds alongside Gabor-like ﬁelds. Similarly high percentages are observed in vivo. Our results thus argue in favor of improvements of the standard sparse coding model for simple cells by using ﬂexible priors and nonlinear combinations.

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NeurIPS Conference 2011 Conference Paper

Select and Sample - A Model of Efficient Neural Inference and Learning

Jacquelyn Shelton
Abdul Sheikh
Pietro Berkes
Joerg Bornschein
Jörg Lücke

An increasing number of experimental studies indicate that perception encodes a posterior probability distribution over possible causes of sensory stimuli, which is used to act close to optimally in the environment. One outstanding difficulty with this hypothesis is that the exact posterior will in general be too complex to be represented directly, and thus neurons will have to represent an approximation of this distribution. Two influential proposals of efficient posterior representation by neural populations are: 1) neural activity represents samples of the underlying distribution, or 2) they represent a parametric representation of a variational approximation of the posterior. We show that these approaches can be combined for an inference scheme that retains the advantages of both: it is able to represent multiple modes and arbitrary correlations, a feature of sampling methods, and it reduces the represented space to regions of high probability mass, a strength of variational approximations. Neurally, the combined method can be interpreted as a feed-forward preselection of the relevant state space, followed by a neural dynamics implementation of Markov Chain Monte Carlo (MCMC) to approximate the posterior over the relevant states. We demonstrate the effectiveness and efficiency of this approach on a sparse coding model. In numerical experiments on artificial data and image patches, we compare the performance of the algorithms to that of exact EM, variational state space selection alone, MCMC alone, and the combined select and sample approach. The select and sample approach integrates the advantages of the sampling and variational approximations, and forms a robust, neurally plausible, and very efficient model of processing and learning in cortical networks. For sparse coding we show applications easily exceeding a thousand observed and a thousand hidden dimensions.

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JMLR Journal 2010 Journal Article

Expectation Truncation and the Benefits of Preselection In Training Generative Models

Jörg Lücke
Julian Eggert

We show how a preselection of hidden variables can be used to efficiently train generative models with binary hidden variables. The approach is based on Expectation Maximization (EM) and uses an efficiently computable approximation to the sufficient statistics of a given model. The computational cost to compute the sufficient statistics is strongly reduced by selecting, for each data point, the relevant hidden causes. The approximation is applicable to a wide range of generative models and provides an interpretation of the benefits of preselection in terms of a variational EM approximation. To empirically show that the method maximizes the data likelihood, it is applied to different types of generative models including: a version of non-negative matrix factorization (NMF), a model for non-linear component extraction (MCA), and a linear generative model similar to sparse coding. The derived algorithms are applied to both artificial and realistic data, and are compared to other models in the literature. We find that the training scheme can reduce computational costs by orders of magnitude and allows for a reliable extraction of hidden causes. [abs] [ pdf ][ bib ] &copy JMLR 2010. ( edit, beta )

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NeurIPS Conference 2010 Conference Paper

The Maximal Causes of Natural Scenes are Edge Filters

Jose Puertas
Joerg Bornschein
Jörg Lücke

We study the application of a strongly non-linear generative model to image patches. As in standard approaches such as Sparse Coding or Independent Component Analysis, the model assumes a sparse prior with independent hidden variables. However, in the place where standard approaches use the sum to combine basis functions we use the maximum. To derive tractable approximations for parameter estimation we apply a novel approach based on variational Expectation Maximization. The derived learning algorithm can be applied to large-scale problems with hundreds of observed and hidden variables. Furthermore, we can infer all model parameters including observation noise and the degree of sparseness. In applications to image patches we find that Gabor-like basis functions are obtained. Gabor-like functions are thus not a feature exclusive to approaches assuming linear superposition. Quantitatively, the inferred basis functions show a large diversity of shapes with many strongly elongated and many circular symmetric functions. The distribution of basis function shapes reflects properties of simple cell receptive fields that are not reproduced by standard linear approaches. In the study of natural image statistics, the implications of using different superposition assumptions have so far not been investigated systematically because models with strong non-linearities have been found analytically and computationally challenging. The presented algorithm represents the first large-scale application of such an approach.

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NeurIPS Conference 2009 Conference Paper

Occlusive Components Analysis

Jörg Lücke
Richard Turner
Maneesh Sahani
Marc Henniges

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learnt from an unlabelled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. However, we show that tractable approximations to Expectation Maximization (EM) can be found if the training images each contain only a small number of objects on average. In numerical experiments it is shown that these approximations recover the correct set of object parameters. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating causes. Experiments based on the standard bars benchmark test for object learning show that the algorithm performs well in comparison to other recent component extraction approaches. The model and the learning algorithm thus connect research on occlusion with the research field of multiple-cause component extraction methods.

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JMLR Journal 2008 Journal Article

Maximal Causes for Non-linear Component Extraction

Jörg Lücke
Maneesh Sahani

We study a generative model in which hidden causes combine competitively to produce observations. Multiple active causes combine to determine the value of an observed variable through a max function, in the place where algorithms such as sparse coding, independent component analysis, or non-negative matrix factorization would use a sum. This max rule can represent a more realistic model of non-linear interaction between basic components in many settings, including acoustic and image data. While exact maximum-likelihood learning of the parameters of this model proves to be intractable, we show that efficient approximations to expectation-maximization (EM) can be found in the case of sparsely active hidden causes. One of these approximations can be formulated as a neural network model with a generalized softmax activation function and Hebbian learning. Thus, we show that learning in recent softmax-like neural networks may be interpreted as approximate maximization of a data likelihood. We use the bars benchmark test to numerically verify our analytical results and to demonstrate the competitiveness of the resulting algorithms. Finally, we show results of learning model parameters to fit acoustic and visual data sets in which max-like component combinations arise naturally. [abs] [ pdf ][ bib ] &copy JMLR 2008. ( edit, beta )

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