arXiv subjects

Ole Winther

Publications and source records attributed to Ole Winther.

At least 73 records · Page 4Linked to original sources

arXiv2016

Self-Averaging Expectation Propagation

We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to overcome the numerical bottleneck of EP caused by the inversion of large matrices. Assuming that the measurement matrices are realizations of specific types of ensembles we use the concept of freeness from random matrix theory to show that the EP cavity variances exhibit an asymptotic self-averaging property. They can be pre-computed using specific generating functions, i.e. the R- and/or S-transforms in free probability, which do not require matrix inversions. Our approach extends the framework of (generalized) approximate message passing -- assumes zero-mean iid entries of the measurement matrix -- to a general class of random matrix ensembles. The generalization is via a simple formulation of the R- and/or S-transforms of the limiting eigenvalue distribution of the Gramian of the measurement matrix. We demonstrate the performance of our approach on a signal recovery problem of nonlinear compressed sensing and compare it with that of EP.

cs.IT↗

arXiv2016

An Adaptive Resample-Move Algorithm for Estimating Normalizing Constants

The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard choice of using a fixed number of particles at each iteration is suboptimal because some steps will contribute disproportionately to the variance of the estimate. We introduce an adaptive version of the Resample-Move algorithm, in which the particle set is adaptively expanded whenever a better approximation of an intermediate distribution is needed. The algorithm builds on the expression for the optimal number of particles and the corresponding minimum variance found under ideal conditions. Benchmark results on challenging Gaussian Process Classification and Restricted Boltzmann Machine applications show that Adaptive Resample-Move (ARM) estimates the normalizing constant with a smaller variance, using less computational resources, than either Resample-Move with a fixed number of particles or Annealed Importance Sampling. A further advantage over Annealed Importance Sampling is that ARM is easier to tune.

stat.ML↗

arXiv2016

Auxiliary Deep Generative Models

Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the variational approximation. The auxiliary variables leave the generative model unchanged but make the variational distribution more expressive. Inspired by the structure of the auxiliary variable we also propose a model with two stochastic layers and skip connections. Our findings suggest that more expressive and properly specified deep generative models converge faster with better results. We show state-of-the-art performance within semi-supervised learning on MNIST, SVHN and NORB datasets.

stat.ML↗

arXiv2016

Ladder Variational Autoencoders

Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

stat.ML↗

arXiv2016

Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the Laplace method or expectation propagation (EP). We study the properties of several Bayesian leave-one-out (LOO) cross-validation approximations that in most cases can be computed with a small additional cost after forming the posterior approximation given the full data. Our main objective is to assess the accuracy of the approximative LOO cross-validation estimators. That is, for each method (Laplace and EP) we compare the approximate fast computation with the exact brute force LOO computation. Secondarily, we evaluate the accuracy of the Laplace and EP approximations themselves against a ground truth established through extensive Markov chain Monte Carlo simulation. Our empirical results show that the approach based upon a Gaussian approximation to the LOO marginal distribution (the so-called cavity distribution) gives the most accurate and reliable results among the fast methods.

stat.CO↗

arXiv2016

A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices

We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if an AT stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.

cond-mat.dis-nn↗

arXiv2016

Autoencoding beyond pixels using a learned similarity metric

We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.

cs.LG↗

arXiv2015

Recurrent Spatial Transformer Networks

We integrate the recently proposed spatial transformer network (SPN) [Jaderberg et. al 2015] into a recurrent neural network (RNN) to form an RNN-SPN model. We use the RNN-SPN to classify digits in cluttered MNIST sequences. The proposed model achieves a single digit error of 1.5% compared to 2.9% for a convolutional networks and 2.0% for convolutional networks with SPN layers. The SPN outputs a zoomed, rotated and skewed version of the input image. We investigate different down-sampling factors (ratio of pixel in input and output) for the SPN and show that the RNN-SPN model is able to down-sample the input images without deteriorating performance. The down-sampling in RNN-SPN can be thought of as adaptive down-sampling that minimizes the information loss in the regions of interest. We attribute the superior performance of the RNN-SPN to the fact that it can attend to a sequence of regions of interest.

cs.CV↗

arXiv2015

Spatio-temporal Spike and Slab Priors for Multiple Measurement Vector Problems

We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizing the structured spike and slab prior and the associated Expectation Propagation inference scheme. Based on numerical experiments, we demonstrate the viability of the model and the approximate inference scheme.

stat.ML↗

arXiv2015

Convolutional LSTM Networks for Subcellular Localization of Proteins

Machine learning is widely used to analyze biological sequence data. Non-sequential models such as SVMs or feed-forward neural networks are often used although they have no natural way of handling sequences of varying length. Recurrent neural networks such as the long short term memory (LSTM) model on the other hand are designed to handle sequences. In this study we demonstrate that LSTM networks predict the subcellular location of proteins given only the protein sequence with high accuracy (0.902) outperforming current state of the art algorithms. We further improve the performance by introducing convolutional filters and experiment with an attention mechanism which lets the LSTM focus on specific parts of the protein. Lastly we introduce new visualizations of both the convolutional filters and the attention mechanisms and show how they can be used to extract biological relevant knowledge from the LSTM networks.

q-bio.QM↗

arXiv2015

S-AMP for Non-linear Observation Models

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP) algorithm as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation propagation (EP) like algorithms from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

cs.IT↗

arXiv2015

Deep Belief Nets for Topic Modeling

Applying traditional collaborative filtering to digital publishing is challenging because user data is very sparse due to the high volume of documents relative to the number of users. Content based approaches, on the other hand, is attractive because textual content is often very informative. In this paper we describe large-scale content based collaborative filtering for digital publishing. To solve the digital publishing recommender problem we compare two approaches: latent Dirichlet allocation (LDA) and deep belief nets (DBN) that both find low-dimensional latent representations for documents. Efficient retrieval can be carried out in the latent representation. We work both on public benchmarks and digital media content provided by Issuu, an online publishing platform. This article also comes with a newly developed deep belief nets toolbox for topic modeling tailored towards performance evaluation of the DBN model and comparisons to the LDA model.

cs.CL↗

arXiv2015

Protein Secondary Structure Prediction with Long Short Term Memory Networks

Prediction of protein secondary structure from the amino acid sequence is a classical bioinformatics problem. Common methods use feed forward neural networks or SVMs combined with a sliding window, as these models does not naturally handle sequential data. Recurrent neural networks are an generalization of the feed forward neural network that naturally handle sequential data. We use a bidirectional recurrent neural network with long short term memory cells for prediction of secondary structure and evaluate using the CB513 dataset. On the secondary structure 8-class problem we report better performance (0.674) than state of the art (0.664). Our model includes feed forward networks between the long short term memory cells, a path that can be further explored.

q-bio.QM↗

arXiv2014

Scalable Bayesian Modelling of Paired Symbols

We present a novel, scalable and Bayesian approach to modelling the occurrence of pairs of symbols (i,j) drawn from a large vocabulary. Observed pairs are assumed to be generated by a simple popularity based selection process followed by censoring using a preference function. By basing inference on the well-founded principle of variational bounding, and using new site-independent bounds, we show how a scalable inference procedure can be obtained for large data sets. State of the art results are presented on real-world movie viewing data.

stat.ML↗

arXiv2014

S-AMP: Approximate Message Passing for General Matrix Ensembles

In this work we propose a novel iterative estimation algorithm for linear observation systems called S-AMP whose fixed points are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

cs.IT↗

arXiv2013

Perturbative Corrections for Approximate Inference in Gaussian Latent Variable Models

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correction, and can be applied to the model's partition function and other moments of interest. The correction is expressed over the higher-order cumulants which are neglected by EP's local matching of moments. Through the expansion, we see that EP is correct to first order. By considering higher orders, corrections of increasing polynomial complexity can be applied to the approximation. The second order provides a correction in quadratic time, which we apply to an array of Gaussian process and Ising models. The corrections generalize to arbitrarily complex approximating families, which we illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution.

stat.ML↗

arXiv2013

FindZebra: A search engine for rare diseases

Background: The web has become a primary information resource about illnesses and treatments for both medical and non-medical users. Standard web search is by far the most common interface for such information. It is therefore of interest to find out how well web search engines work for diagnostic queries and what factors contribute to successes and failures. Among diseases, rare (or orphan) diseases represent an especially challenging and thus interesting class to diagnose as each is rare, diverse in symptoms and usually has scattered resources associated with it. Methods: We use an evaluation approach for web search engines for rare disease diagnosis which includes 56 real life diagnostic cases, state-of-the-art evaluation measures, and curated information resources. In addition, we introduce FindZebra, a specialized (vertical) rare disease search engine. FindZebra is powered by open source search technology and uses curated freely available online medical information. Results: FindZebra outperforms Google Search in both default setup and customised to the resources used by FindZebra. We extend FindZebra with specialized functionalities exploiting medical ontological information and UMLS medical concepts to demonstrate different ways of displaying the retrieved results to medical experts. Conclusions: Our results indicate that a specialized search engine can improve the diagnostic quality without compromising the ease of use of the currently widely popular web search engines. The proposed evaluation approach can be valuable for future development and benchmarking. The FindZebra search engine is available at http://www.findzebra.com/.

cs.IR↗

arXiv2011

Sparse Linear Identifiable Multivariate Modeling

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for sparse models using slab and spike priors (two-component delta-function and continuous mixtures), non-Gaussian latent factors and a stochastic search over the ordering of the variables. The framework, which we call SLIM (Sparse Linear Identifiable Multivariate modeling), is validated and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable computational complexity. We attribute this mainly to the stochastic search strategy used, and to parsimony (sparsity and identifiability), which is an explicit part of the model. We propose two extensions to the basic i.i.d. linear framework: non-linear dependence on observed variables, called SNIM (Sparse Non-linear Identifiable Multivariate modeling) and allowing for correlations between latent variables, called CSLIM (Correlated SLIM), for the temporal and/or spatial data. The source code and scripts are available from http://cogsys.imm.dtu.dk/slim/.

stat.ML↗