Bidirectional Helmholtz Machines

L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé.Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient approximate inference. Moreover, we introduce a deep generative model for semi-supervised learning problems based on BiHM models

Retrieval of Leaf Area Index (LAI) and Soil Water Content (WC) Using Hyperspectral Remote Sensing under Controlled Glass House Conditions for Spring Barley and Sugar Beet

Leaf area index (LAI) and water content (WC) in the root zone are two major hydro-meteorological parameters that exhibit a dominant control on water, energy and carbon fluxes, and are therefore important for any regional eco-hydrological or climatological study. To investigate the potential for retrieving these parameter from hyperspectral remote sensing, we have investigated plant spectral reflectance (400-2,500 nm, ASD FieldSpec3) for two major agricultural crops (sugar beet and spring barley) in the mid-latitudes, treated under different water and nitrogen (N) conditions in a greenhouse experiment over the growing period of 2008. Along with the spectral response, we have measured soil water content and LAI for 15 intensive measurement campaigns spread over the growing season and could demonstrate a significant response of plant reflectance characteristics to variations in water content and nutrient conditions. Linear and non-linear dimensionality analysis suggests that the full band reflectance information is well represented by the set of 28 vegetation spectral indices (SI) and most of the variance is explained by three to a maximum of eight variables. Investigation of linear dependencies between LAI and soil WC and pre-selected SI's indicate that: (1) linear regression using single SI is not sufficient to describe plant/soil variables over the range of experimental conditions, however, some improvement can be seen knowing crop species beforehand; (2) the improvement is superior when applying multiple linear regression using three explanatory SI's approach. In addition to linear investigations, we applied the non-linear CART (Classification and Regression Trees) technique, which finally did not show the potential for any improvement in the retrieval process

Learning neural trans-dimensional random field language models with noise-contrastive estimation

Trans-dimensional random field language models (TRF LMs) where sentences are modeled as a collection of random fields, have shown close performance with LSTM LMs in speech recognition and are computationally more efficient in inference. However, the training efficiency of neural TRF LMs is not satisfactory, which limits the scalability of TRF LMs on large training corpus. In this paper, several techniques on both model formulation and parameter estimation are proposed to improve the training efficiency and the performance of neural TRF LMs. First, TRFs are reformulated in the form of exponential tilting of a reference distribution. Second, noise-contrastive estimation (NCE) is introduced to jointly estimate the model parameters and normalization constants. Third, we extend the neural TRF LMs by marrying the deep convolutional neural network (CNN) and the bidirectional LSTM into the potential function to extract the deep hierarchical features and bidirectionally sequential features. Utilizing all the above techniques enables the successful and efficient training of neural TRF LMs on a 40x larger training set with only 1/3 training time and further reduces the WER with relative reduction of 4.7% on top of a strong LSTM LM baseline.Comment: 5 pages and 2 figure

Natural Wake-Sleep Algorithm

The benefits of using the natural gradient are well known in a wide range of optimization problems. However, for the training of common neural networks the resulting increase in computational complexity sets a limitation to its practical application. Helmholtz Machines are a particular type of generative model composed of two Sigmoid Belief Networks (SBNs), acting as an encoder and a decoder, commonly trained using the Wake-Sleep (WS) algorithm and its reweighted version RWS. For SBNs, it has been shown how the locality of the connections in the graphical structure induces sparsity in the Fisher information matrix. The resulting block diagonal structure can be efficiently exploited to reduce the computational complexity of the Fisher matrix inversion and thus compute the natural gradient exactly, without the need of approximations. We present a geometric adaptation of well-known methods from the literature, introducing the Natural Wake-Sleep (NWS) and the Natural Reweighted Wake-Sleep (NRWS) algorithms. We present an experimental analysis of the novel geometrical algorithms based on the convergence speed and the value of the log-likelihood, both with respect to the number of iterations and the time complexity and demonstrating improvements on these aspects over their respective non-geometric baselines.Comment: 19 pages, 9 figure