Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin

Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables gives always the same output value). This paper proposes a global sensitivity analysis methodology for stochastic computer code (having a variability induced by some uncontrollable variables). The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, non parametric joint models (based on Generalized Additive Models and Gaussian processes) are discussed. The relevance of these new models is analyzed in terms of the obtained variance-based sensitivity indices with two case studies. Results show that the joint modeling approach leads accurate sensitivity index estimations even when clear heteroscedasticity is present

A Digital Predistortion Scheme Exploiting Degrees-of-Freedom for Massive MIMO Systems

The primary source of nonlinear distortion in wireless transmitters is the power amplifier (PA). Conventional digital predistortion (DPD) schemes use high-order polynomials to accurately approximate and compensate for the nonlinearity of the PA. This is not practical for scaling to tens or hundreds of PAs in massive multiple-input multiple-output (MIMO) systems. There is more than one candidate precoding matrix in a massive MIMO system because of the excess degrees-of-freedom (DoFs), and each precoding matrix requires a different DPD polynomial order to compensate for the PA nonlinearity. This paper proposes a low-order DPD method achieved by exploiting massive DoFs of next-generation front ends. We propose a novel indirect learning structure which adapts the channel and PA distortion iteratively by cascading adaptive zero forcing precoding and DPD. Our solution uses a 3rd order polynomial to achieve the same performance as the conventional DPD using an 11th order polynomial for a 100x10 massive MIMO configuration. Experimental results show a 70% reduction in computational complexity, enabling ultra-low latency communications.Comment: IEEE International Conference on Communications 201