A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types

Identification of metabotypes in complex biological data using tensor decomposition

Differences in the physiological response to treatment, such as dietary intervention, has led to the development of precision approaches in nutrition and medicine to tailor treatment for improved benefits to the individual. One such approach is to identify metabotypes, i.e., groups of individuals with similar metabolic profiles and/or regulation. Metabotyping has previously been performed using e.g., principal component analysis (PCA) on matrix data. However, metabotyping methods suitable for more complex experimental designs such as repeated measures or cross-over studies are needed. We have developed a metabotyping method for tensor data, based on CANDECOMP/PARAFAC (CP) tensor decomposition. Metabotypes are inferred from CP scores using k-means clustering, and robustness is evaluated using bootstrapping of metabolites. As a proof-of-concept, we identified metabotypes from metabolomics data where 79 metabolites were analyzed in 8 time points postprandially in 17 overweight men that underwent a three-arm dietary crossover intervention. Two metabotypes were found, characterized by differences in amino acid metabolite concentration, that were differentially associated with baseline plasma creatinine (p = 0.007) and with the baseline metabolome (p = 0.004). These results suggest that CP decomposition provides a viable approach for metabotype identification directly from complex, high-dimensional data with improved biological interpretation compared to the more simplistic PCA approach. A simulation study together with results from measured data concluded that several preprocessing methods should be taken into consideration for CP-based metabotyping on complex tensor data

A biologically inspired meta-control navigation system for the Psikharpax rat robot

A biologically inspired navigation system for the mobile rat-like robot named Psikharpax is presented, allowing for self-localization and autonomous navigation in an initially unknown environment. The ability of parts of the model (e. g. the strategy selection mechanism) to reproduce rat behavioral data in various maze tasks has been validated before in simulations. But the capacity of the model to work on a real robot platform had not been tested. This paper presents our work on the implementation on the Psikharpax robot of two independent navigation strategies (a place-based planning strategy and a cue-guided taxon strategy) and a strategy selection meta-controller. We show how our robot can memorize which was the optimal strategy in each situation, by means of a reinforcement learning algorithm. Moreover, a context detector enables the controller to quickly adapt to changes in the environment-recognized as new contexts-and to restore previously acquired strategy preferences when a previously experienced context is recognized. This produces adaptivity closer to rat behavioral performance and constitutes a computational proposition of the role of the rat prefrontal cortex in strategy shifting. Moreover, such a brain-inspired meta-controller may provide an advancement for learning architectures in robotics

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page