Related papers: Recursive Polynomial Remainder Sequence and the Ne…

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…

Learning rate schedulers have shown great success in speeding up the convergence of learning algorithms in practice. However, their convergence to a minimum has not been proven theoretically. This difficulty mainly arises from the fact…

Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…

With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge…

Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for…

We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…

Recurrent neural networks (RNNs) provide state-of-the-art performance in processing sequential data but are memory intensive to train, limiting the flexibility of RNN models which can be trained. Reversible RNNs---RNNs for which the…

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…

This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We…

We introduce segmental recurrent neural networks (SRNNs) which define, given an input sequence, a joint probability distribution over segmentations of the input and labelings of the segments. Representations of the input segments (i.e.,…

We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.

A mathematical characterization of serially-pruned permutations (SPPs) employed in variable-length permuters and their associated fast pruning algorithms and architectures are proposed. Permuters are used in many signal processing systems…

Recursive processing is considered a hallmark of human linguistic abilities. A recent study evaluated recursive processing in recurrent neural language models (RNN-LMs) and showed that such models perform below chance level on embedded…

We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…