**Genetic Programming Relevance Vector Machine (GP-RVM)**

This paper proposes a hybrid basis function construction method (GP-RVM) for Symbolic Regression problem, which combines an extended version of Genetic Programming called Kaizen Programming and Relevance Vector Machine to evolve an optimal set of basis functions. Different from traditional evolutionary algorithms where a single individual is a complete solution, our method proposes a solution based on linear combination of basis functions built from individuals during the evolving process. RVM which is a sparse Bayesian kernel method selects suitable functions to constitute the basis. RVM determines the posterior weight of a function by evaluating its quality and sparsity. The solution produced by GP-RVM is a sparse Bayesian linear model of the coefficients of many non-linear functions. Our hybrid approach is focused on nonlinear white-box models selecting the right combination of functions to build robust predictions without prior knowledge about data. Experimental results show that GP-RVM outperforms conventional methods, which suggest that it is an efficient and accurate technique for solving SR. The computational complexity of GP-RVM scales in $O( M^{3})$, where $M$ is the number of functions in the basis set and is typically much smaller than the number $N$ of training patterns. … **Deep Learning Virtual Machine (DLVM)**

Many current approaches to deep learning make use of high-level toolkits such as TensorFlow, Torch, or Caffe. Toolkits such as Caffe have a layer-based programming framework with hard-coded gradients specified for each layer type, making research using novel layer types problematic. Toolkits such as Torch and TensorFlow define a computation graph in a host language such as Python, where each node represents a linear algebra operation parallelized as a compute kernel on GPU and stores the result of evaluation; some of these toolkits subsequently perform runtime interpretation over that graph, storing the results of forward calculations and reverse-accumulated gradients at each node. This approach is more flexible, but these toolkits take a very limited and ad-hoc approach to performing optimization. Also problematic are the facts that most toolkits lack type safety, and target only a single (usually GPU) architecture, limiting users’ abilities to make use of heterogeneous and emerging hardware architectures. We introduce a novel framework for high-level programming that addresses all of the above shortcomings. … **Declarative Statistics**

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant counting and matrix constraints and associated decompositions, some of which novel, that are instrumental in the design of statistical constraints. Second, we introduce a selection of novel statistical constraints and associated decompositions, which constitute a self-contained toolbox that can be used to tackle a wide range of problems typically encountered by statisticians. Finally, we deploy these statistical constraints to a wide range of application areas drawn from classical statistics and we contrast our framework against established practices. …

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Aug 2018

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