Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures

Probabilistic graphical models are a central tool in AI; however, they are generally not as expressive as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic models such as sum-product networks (SPNs) capture joint distributions in a tractable fashion, but still lack the expressive power of intractable models based on deep neural networks. Therefore, we introduce conditional SPNs (CSPNs), conditional density estimators for multivariate and potentially hybrid domains which allow harnessing the expressive power of neural networks while still maintaining tractability guarantees. One way to implement CSPNs is to use an existing SPN structure and condition its parameters on the input, e.g., via a deep neural network. This approach, however, might misrepresent the conditional independence structure present in data. Consequently, we also develop a structure-learning approach that derives both the structure and parameters of CSPNs from data. Our experimental evidence demonstrates that CSPNs are competitive with other probabilistic models and yield superior performance on multilabel image classification compared to mean field and mixture density networks. Furthermore, they can successfully be employed as building blocks for structured probabilistic models, such as autoregressive image models.Comment: 13 pages, 6 figure

Model-based kernel sum rule: kernel Bayesian inference with probabilistic model

Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of kernel Bayesian inference have been developed by combining kernelized basic probabilistic operations such as the kernel sum rule and kernel Bayes’ rule. However, the current framework is fully nonparametric, and it does not allow a user to flexibly combine nonparametric and model-based inferences. This is inefficient when there are good probabilistic models (or simulation models) available for some parts of a graphical model; this is in particular true in scientific fields where “models” are the central topic of study. Our contribution in this paper is to introduce a novel approach, termed the model-based kernel sum rule (Mb-KSR), to combine a probabilistic model and kernel Bayesian inference. By combining the Mb-KSR with the existing kernelized probabilistic rules, one can develop various algorithms for hybrid (i.e., nonparametric and model-based) inferences. As an illustrative example, we consider Bayesian filtering in a state space model, where typically there exists an accurate probabilistic model for the state transition process. We propose a novel filtering method that combines model-based inference for the state transition process and data-driven, nonparametric inference for the observation generating process. We empirically validate our approach with synthetic and real-data experiments, the latter being the problem of vision-based mobile robot localization in robotics, which illustrates the effectiveness of the proposed hybrid approach

True-false lumen segmentation of aortic dissection using multi-scale wavelet analysis and generative-discriminative model matching

Computer aided diagnosis in the medical image domain requires sophisticated probabilistic models to formulate quantitative behavior in image space. In the diagnostic process detailed knowledge of model performance with respect to accuracy, variability, and uncertainty is crucial. This challenge has lead to the fusion of two successful learning schools namely generative and discriminative learning. In this paper, we propose a generative-discriminative learning approach to predict object boundaries in medical image datasets. In our approach, we perform probabilistic model matching of both modeling domains to fuse into the prediction step appearance and structural information of the object of interest while exploiting the strength of both learning paradigms. In particular, we apply our method to the task of true-false lumen segmentation of aortic dissections an acute disease that requires automated quantification for assisted medical diagnosis. We report empirical results for true-false lumen discrimination of aortic dissection segmentation showing superior behavior of the hybrid generative-discriminative approach over their non hybrid generative counterpart

Hybrid Models for Human Motion Recognition

Probabilistic models have been previously shown to be efficient and effective for modeling and recognition of human motion. In particular we focus on methods which represent the human motion model as a triangulated graph. Previous approaches learned models based just on positions and velocities of the body parts while ignoring their appearance. Moreover, a heuristic approach was commonly used to obtain translation invariance. In this paper we suggest an improved approach for learning such models and using them for human motion recognition. The suggested approach combines multiple cues, i.e., positions, velocities and appearance into both the learning and detection phases. Furthermore, we introduce global variables in the model, which can represent global properties such as translation, scale or view-point. The model is learned in an unsupervised manner from unlabelled data. We show that the suggested hybrid probabilistic model (which combines global variables, like translation, with local variables, like relative positions and appearances of body parts), leads to: (i) faster convergence of learning phase, (ii) robustness to occlusions, and, (iii) higher recognition rate

Continuous Mixtures of Tractable Probabilistic Models

Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven expressive tools for generative and probabilistic modelling, but are at odds with tractable probabilistic inference, that is, computing marginals and conditionals of the represented probability distribution. Meanwhile, tractable probabilistic models such as probabilistic circuits (PCs) can be understood as hierarchical discrete mixture models, which allows them to perform exact inference, but often they show subpar performance in comparison to continuous latent-space models. In this paper, we investigate a hybrid approach, namely continuous mixtures of tractable models with a small latent dimension. While these models are analytically intractable, they are well amenable to numerical integration schemes based on a finite set of integration points. With a large enough number of integration points the approximation becomes de-facto exact. Moreover, using a finite set of integration points, the approximation method can be compiled into a PC performing `exact inference in an approximate model'. In experiments, we show that this simple scheme proves remarkably effective, as PCs learned this way set new state-of-the-art for tractable models on many standard density estimation benchmarks